diff --git a/Make_coq.local b/Make_coq.local index f60b072d1..e2ced9a22 100644 --- a/Make_coq.local +++ b/Make_coq.local @@ -52,16 +52,26 @@ uninstall :: TESTDIR=tests TESTS_SRC=$(TESTDIR)/Morph.v $(TESTDIR)/Test.v $(TESTDIR)/Polymorph.v \ - $(TESTDIR)/PrimitiveProjections.v\ + $(TESTDIR)/PrimitiveProjections.v $(TESTDIR)/ModuleTypeLocked.v \ + $(TESTDIR)/NestedModules.v $(TESTDIR)/PeanoNatBitwise.v \ + $(TESTDIR)/Proofs.v \ $(TESTDIR)/Morph.cmd $(TESTDIR)/Test.cmd $(TESTDIR)/search.cmd \ - $(TESTDIR)/Polymorph.cmd $(TESTDIR)/PrimitiveProjections.cmd + $(TESTDIR)/Polymorph.cmd $(TESTDIR)/PrimitiveProjections.cmd \ + $(TESTDIR)/ModuleTypeLocked.cmd $(TESTDIR)/NestedModules.cmd \ + $(TESTDIR)/PeanoNatBitwise.cmd $(TESTDIR)/Proofs.cmd TESTS_DPD=$(TESTDIR)/graph.dpd $(TESTDIR)/graph2.dpd \ $(TESTDIR)/Morph.dpd $(TESTDIR)/Morph_rw.dpd \ $(TESTDIR)/Polymorph.dpd \ $(TESTDIR)/PrimitiveProjections.dpd \ - $(TESTDIR)/PrimitiveProjections2.dpd + $(TESTDIR)/PrimitiveProjections2.dpd \ + $(TESTDIR)/ModuleTypeLocked.dpd \ + $(TESTDIR)/NestedModules.dpd \ + $(TESTDIR)/PeanoNatBitwise.dpd \ + $(TESTDIR)/Proofs.dpd TESTS_VO=$(TESTDIR)/Morph.vo $(TESTDIR)/Test.vo $(TESTDIR)/Polymorph.vo\ - $(TESTDIR)/PrimitiveProjections.vo + $(TESTDIR)/PrimitiveProjections.vo $(TESTDIR)/ModuleTypeLocked.vo \ + $(TESTDIR)/NestedModules.vo $(TESTDIR)/PeanoNatBitwise.vo \ + $(TESTDIR)/Proofs.vo TESTS_DOT=$(TESTS_DPD:%.dpd=%.dot) TESTS_ERR_DPD=$(wildcard $(TESTDIR)/*.err.dpd) @@ -78,6 +88,11 @@ clean_test : rm -f $(TESTDIR)/Morph.vo $(TESTDIR)/Morph.glob rm -f $(TESTDIR)/Polymorph.vo $(TESTDIR)/Polymorph.glob rm -f $(TESTDIR)/PrimitiveProjections.vo $(TESTDIR)/PrimitiveProjections.glob + rm -f $(TESTDIR)/ModuleTypeLocked.vo $(TESTDIR)/ModuleTypeLocked.glob + rm -f $(TESTDIR)/ModuleTypeLocked_regular.dpd $(TESTDIR)/ModuleTypeLocked_axiom.dpd + rm -f $(TESTDIR)/NestedModules.vo $(TESTDIR)/NestedModules.glob + rm -f $(TESTDIR)/PeanoNatBitwise.vo $(TESTDIR)/PeanoNatBitwise.glob + rm -f $(TESTDIR)/Proofs.vo $(TESTDIR)/Proofs.glob rm -f $(TESTDIR)/.*.vo.aux .PRECIOUS : $(TESTS) $(TESTS_LOG) $(TESTS_ORACLE) @@ -140,6 +155,19 @@ $(TESTDIR)/PrimitiveProjections.dpd $(TESTDIR)/PrimitiveProjections2.dpd: \ # cd to tests to generate .dpd file there. cd $(TESTDIR); rocq repl $(TEST_INCLUDE) < PrimitiveProjections.cmd > /dev/null 2>&1 +$(TESTDIR)/ModuleTypeLocked.dpd $(TESTDIR)/ModuleTypeLocked_regular.dpd $(TESTDIR)/ModuleTypeLocked_axiom.dpd: \ + $(TESTDIR)/ModuleTypeLocked.vo $(TESTDIR)/ModuleTypeLocked.cmd $(DPDPLUGIN) + cd $(TESTDIR); rocq repl $(TEST_INCLUDE) < ModuleTypeLocked.cmd > /dev/null 2>&1 + +$(TESTDIR)/NestedModules.dpd: $(TESTDIR)/NestedModules.vo $(TESTDIR)/NestedModules.cmd $(DPDPLUGIN) + cd $(TESTDIR); rocq repl $(TEST_INCLUDE) < NestedModules.cmd > /dev/null 2>&1 + +$(TESTDIR)/PeanoNatBitwise.dpd: $(TESTDIR)/PeanoNatBitwise.vo $(TESTDIR)/PeanoNatBitwise.cmd $(DPDPLUGIN) + cd $(TESTDIR); rocq repl $(TEST_INCLUDE) < PeanoNatBitwise.cmd > /dev/null 2>&1 + +$(TESTDIR)/Proofs.dpd: $(TESTDIR)/Proofs.vo $(TESTDIR)/Proofs.cmd $(DPDPLUGIN) + cd $(TESTDIR); rocq repl $(TEST_INCLUDE) < Proofs.cmd > /dev/null 2>&1 + %.dpd : %.vo %.cmd # cd to tests to generate .dpd file there. cd $(TESTDIR); rocq repl $(TEST_INCLUDE) < $(*F).cmd > /dev/null 2>&1 diff --git a/graphdepend.mlg b/graphdepend.mlg index 0fabbd612..ef7425a87 100644 --- a/graphdepend.mlg +++ b/graphdepend.mlg @@ -14,6 +14,10 @@ DECLARE PLUGIN "coq-dpdgraph.plugin" open Pp open Stdarg +let pr_global_safe gref = + try Printer.pr_global gref + with Not_found -> Names.GlobRef.print gref + let debug msg = if false then Feedback.msg_debug msg let feedback msg = Feedback.msg_notice (str "Info: " ++ msg) @@ -28,7 +32,7 @@ let get_dirlist_grefs dirlist = let selected_gref = ref [] in let select gref kind env sigma constr = if Search.module_filter (SearchInside dirlist) gref kind env sigma constr then - (debug (str "Select " ++ Printer.pr_global gref); + (debug (str "Select " ++ pr_global_safe gref); selected_gref := gref::!selected_gref) in Search.generic_search (Global.env()) (Evd.from_env (Global.env())) select; @@ -64,21 +68,38 @@ module G = struct Nametab.shortest_qualid_of_global Names.Id.Set.empty (gref n) in Libnames.string_of_qualid qualid + let qualid_of n = + try Some (Nametab.shortest_qualid_of_global Names.Id.Set.empty (gref n)) + with Not_found -> None + + (** Fallback name for GlobRefs not registered in the Nametab + (e.g. constants hidden by module type constraints). *) + let fallback_split_name n = + let open Names in + match gref n with + | GlobRef.ConstRef cst -> + let kn = Constant.canonical cst in + let mp, lab = KerName.repr kn in + (ModPath.to_string mp, Label.to_string lab) + | GlobRef.IndRef (mind, _) -> + let kn = MutInd.canonical mind in + let mp, lab = KerName.repr kn in + (ModPath.to_string mp, Label.to_string lab) + | GlobRef.ConstructRef ((mind, _), _) -> + let kn = MutInd.canonical mind in + let mp, lab = KerName.repr kn in + (ModPath.to_string mp, Label.to_string lab) + | GlobRef.VarRef id -> ("", Id.to_string id) + let split_name n = - let qualid = - Nametab.shortest_qualid_of_global Names.Id.Set.empty (gref n) in - let dirpath, ident = Libnames.repr_qualid qualid in - let dirpath = Names.DirPath.to_string dirpath in - let dirpath = if dirpath = "<>" then "" else dirpath in - let name = Names.Id.to_string ident in + match qualid_of n with + | Some qualid -> + let dirpath, ident = Libnames.repr_qualid qualid in + let dirpath = Names.DirPath.to_string dirpath in + let dirpath = if dirpath = "<>" then "" else dirpath in + let name = Names.Id.to_string ident in (dirpath, name) - (* - let mod_list = Names.repr_dirpath dir_path in - let rec dirname l = match l with [] -> "" - | m::[] -> Names.string_of_id m - | d::tl -> (dirname tl)^"."^(Names.string_of_id d) - in (dirname mod_list, name) - *) + | None -> fallback_split_name n end module Edge = struct @@ -143,7 +164,7 @@ end * If not all, don't add nodes, and return an empty list. *) let add_gref_dpds opaque_access graph ~all n_gref todo = let gref = G.Node.gref n_gref in - debug (str "Add dpds " ++ Printer.pr_global gref); + debug (str "Add dpds " ++ pr_global_safe gref); let add_dpd dpd nb_use (g, td) = match G.get_node g dpd with | Some n -> let g = G.add_edge g n_gref n nb_use in g, td | None -> @@ -157,12 +178,15 @@ let add_gref_dpds opaque_access graph ~all n_gref todo = let data = Searchdepend.collect_dependance opaque_access gref in let graph, todo = Searchdepend.Data.fold add_dpd data (graph, todo) in graph, todo - with Searchdepend.NoDef gref -> (* nothing to do *) graph, todo + with + | Searchdepend.NoDef gref -> (* nothing to do *) graph, todo + | exn when CErrors.noncritical exn || CErrors.is_sync_anomaly exn -> + graph, todo (** add gref node and add it to the todo list * to process its dependencies later. *) let add_gref_only (graph, todo) gref = - debug (str "Add " ++ Printer.pr_global gref); + debug (str "Add " ++ pr_global_safe gref); let graph, n = G.add_node graph gref in let todo = n::todo in graph, todo @@ -184,17 +208,33 @@ module Out : sig val file : G.t -> unit end = struct - let add_cnst_attrib acc cnst = - let env = Global.env() in - let cb = Environ.lookup_constant cnst env in + let add_cnst_body_attrib acc cnst = + let cb = Searchdepend.ModLookup.lookup_constant cnst in let acc = match cb.Declarations.const_body with - | Declarations.OpaqueDef _ -> ("opaque", "yes")::("body", "yes")::acc - | Declarations.Def _ -> ("opaque", "no")::("body", "yes")::acc - | Declarations.Undef _ -> ("opaque", "yes")::("body", "no")::acc - | Declarations.Primitive _ -> ("prim", "yes")::("body", "no")::acc - | Declarations.Symbol _ -> ("symb", "yes")::("body", "no")::acc + | Declarations.OpaqueDef _ -> ("body", "yes")::acc + | Declarations.Def _ -> ("body", "yes")::acc + | Declarations.Undef _ -> ("body", "no")::acc + | Declarations.Primitive _ -> ("body", "no")::acc + | Declarations.Symbol _ -> ("body", "no")::acc in acc + let add_cnst_opaque_attrib acc cnst = + try + let env = Global.env() in + let cb = Environ.lookup_constant cnst env in + let acc = match cb.Declarations.const_body with + | Declarations.OpaqueDef _ -> ("opaque", "yes")::acc + | Declarations.Def _ -> ("opaque", "no")::acc + | Declarations.Undef _ -> ("opaque", "yes")::acc + | Declarations.Primitive _ -> ("prim", "yes")::acc + | Declarations.Symbol _ -> ("symb", "yes")::acc + in acc + with exn when CErrors.noncritical exn || CErrors.is_sync_anomaly exn -> acc + + let add_cnst_attrib acc cnst = + let acc = add_cnst_body_attrib acc cnst in + add_cnst_opaque_attrib acc cnst + let add_gref_attrib acc gref id = let is_prop = is_prop gref id in let acc = ("prop", if is_prop then "yes" else "no")::acc in diff --git a/searchdepend.mlg b/searchdepend.mlg index 2ad016337..3c06bd484 100644 --- a/searchdepend.mlg +++ b/searchdepend.mlg @@ -69,28 +69,202 @@ let collect_long_names avoid (c:Constr.t) (acc:Data.t) = exception NoDef of Names.GlobRef.t +(** Module structure lookup for accessing bodies hidden by module type constraints. + Based on the approach used by Print Assumptions in vernac/assumptions.ml *) +module ModLookup : sig + val lookup_constant : Names.Constant.t -> Declarations.constant_body + val get_constant_body : Global.indirect_accessor -> Names.Constant.t -> Constr.t option + val lookup_mind : Names.MutInd.t -> Declarations.mutual_inductive_body +end = struct +(* This module is copied verbatim from Rocq's assumptions.ml and is thus licensed under Rocq's license, the GNU Lesser General Public License Version 2.1 *) +open Util +open Names +open Declarations +open Mod_declarations + +(** For a constant c in a module sealed by an interface (M:T and + not M<:T), [Global.lookup_constant] may return a [constant_body] + without body. We fix this by looking in the implementation + of the module *) + +let modcache = ref (ModPath.Map.empty : structure_body ModPath.Map.t) + +let rec search_mod_label lab = function + | [] -> raise Not_found + | (l, SFBmodule mb) :: _ when Id.equal l lab -> mb + | _ :: fields -> search_mod_label lab fields + +let rec search_cst_label lab = function + | [] -> raise Not_found + | (l, SFBconst cb) :: _ when Id.equal l lab -> cb + | _ :: fields -> search_cst_label lab fields + +let rec search_mind_label lab = function + | [] -> raise Not_found + | (l, SFBmind mind) :: _ when Id.equal l lab -> mind + | _ :: fields -> search_mind_label lab fields + +(* TODO: using [empty_delta_resolver] below is probably slightly incorrect. But: + a) I don't see currently what should be used instead + b) this shouldn't be critical for Print Assumption. At worse some + constants will have a canonical name which is non-canonical, + leading to failures in [Global.lookup_constant], but our own + [lookup_constant] should work. +*) + +let rec fields_of_functor f subs mp0 args = function + | NoFunctor a -> f subs mp0 args a + | MoreFunctor (mbid,_,e) -> + let open Mod_subst in + match args with + | [] -> assert false (* we should only encounter applied functors *) + | mpa :: args -> + let subs = join (map_mbid mbid mpa (empty_delta_resolver mpa) (*TODO*)) subs in + fields_of_functor f subs mp0 args e + +let rec lookup_module_in_impl mp = + match mp with + | MPfile _ -> Global.lookup_module mp + | MPbound _ -> Global.lookup_module mp + | MPdot (mp',lab') -> + if ModPath.equal mp' (Global.current_modpath ()) then + Global.lookup_module mp + else + let fields = memoize_fields_of_mp mp' in + search_mod_label lab' fields + +and memoize_fields_of_mp mp = + try ModPath.Map.find mp !modcache + with Not_found -> + let l = fields_of_mp mp in + modcache := ModPath.Map.add mp l !modcache; + l + +and fields_of_mp mp = + let open Mod_subst in + let mb = lookup_module_in_impl mp in + let fields,inner_mp,subs = fields_of_mb empty_subst mp mb [] in + let delta_mb = mod_delta mb in + let subs = + (* XXX this code makes little sense, adding a delta_mb to subs if the root + does not coincide with mp used to be equivalent to a no-op and now fails + with an assertion failure. More likely than not, this means that we have + no idea about what we are doing. *) + if ModPath.equal inner_mp mp then subs + else if has_root_delta_resolver mp delta_mb then + add_mp inner_mp mp delta_mb subs + else + add_mp inner_mp mp (empty_delta_resolver mp) subs + in + Modops.subst_structure subs mp fields + +and fields_of_mb subs mp mb args = match Mod_declarations.mod_expr mb with + | Algebraic expr -> fields_of_expression subs mp args (mod_type mb) expr + | Struct (_, sign) -> + let sign = Modops.annotate_struct_body sign (mod_type mb) in + fields_of_signature subs mp args sign + | Abstract|FullStruct -> fields_of_signature subs mp args (mod_type mb) + +(** The Abstract case above corresponds to [Declare Module] *) + +and fields_of_signature x = + fields_of_functor + (fun subs mp0 args struc -> + assert (List.is_empty args); + (struc, mp0, subs)) x + +and fields_of_expr subs mp0 args = function + | MEident mp -> + let mp = Mod_subst.subst_mp subs mp in + let mb = lookup_module_in_impl mp in + fields_of_mb subs mp mb args + | MEapply (me1,mp2) -> fields_of_expr subs mp0 (mp2::args) me1 + | MEwith _ -> assert false (* no 'with' in [mod_expr] *) + +and fields_of_expression subs mp args mty me = + let me = Modops.annotate_module_expression me mty in + fields_of_functor fields_of_expr subs mp args me + +let lookup_constant_in_impl cst fallback = + try + let mp,lab = KerName.repr (Constant.canonical cst) in + let fields = memoize_fields_of_mp mp in + (* A module found this way is necessarily closed, in particular + our constant cannot be in an opened section : *) + search_cst_label lab fields + with Not_found -> + (* Either: + - The module part of the constant isn't registered yet : + we're still in it, so the [constant_body] found earlier + (if any) was a true axiom. + - The label has not been found in the structure. This is an error *) + match fallback with + | Some cb -> cb + | None -> + CErrors.anomaly + Pp.(str "Print Assumption: unknown constant " + ++ Constant.print cst ++ str ".") + +let lookup_constant cst = + let env = Global.env() in + if not (Environ.mem_constant cst env) + then lookup_constant_in_impl cst None + else + let cb = Environ.lookup_constant cst env in + if Declareops.constant_has_body cb then cb + else lookup_constant_in_impl cst (Some cb) + +let lookup_mind_in_impl mind = + try + let mp,lab = KerName.repr (MutInd.canonical mind) in + let fields = memoize_fields_of_mp mp in + search_mind_label lab fields + with Not_found -> + CErrors.anomaly + Pp.(str "Print Assumption: unknown inductive " + ++ MutInd.print mind ++ str ".") + +let lookup_mind mind = + let env = Global.env() in + if Environ.mem_mind mind env then Environ.lookup_mind mind env + else lookup_mind_in_impl mind + + +let get_constant_body access kn = + let cb = lookup_constant kn in + match cb.const_body with + | Undef _ | Primitive _ | Symbol _ -> None + | Def c -> Some c + | OpaqueDef o -> + match Global.force_proof access o with + | c, _ -> Some c + | exception e when CErrors.noncritical e -> None (* missing delayed body, e.g. in vok mode *) + +end + let collect_dependance opaque_access gref = let open Names in let open GlobRef in match gref with | VarRef _ -> assert false | ConstRef cst -> - let cb = Environ.lookup_constant cst (Global.env()) in + let cb = ModLookup.lookup_constant cst in let cl = (* Skip opaque bodies when access_opaque flag is unset *) if access_opaque () || not (Declareops.is_opaque cb) then - match Global.body_of_constant_body opaque_access cb with - | Some (e,_,_) -> [e] + match ModLookup.get_constant_body opaque_access cst with + | Some e -> [e] | None -> [] else [] in let cl = cb.Declarations.const_type :: cl in List.fold_right (collect_long_names []) cl Data.empty - | IndRef i | ConstructRef (i,_) -> - let _, indbody = Global.lookup_inductive i in + | IndRef (mind, n) | ConstructRef ((mind, n),_) -> + let mib = ModLookup.lookup_mind mind in + let indbody = mib.Declarations.mind_packets.(n) in let ca = indbody.Declarations.mind_user_lc in - Array.fold_right (collect_long_names [fst i]) ca Data.empty + Array.fold_right (collect_long_names [mind]) ca Data.empty let display_dependance ~opaque_access gref = let display d = diff --git a/tests/ModuleTypeLocked.cmd b/tests/ModuleTypeLocked.cmd new file mode 100644 index 000000000..7d54c620b --- /dev/null +++ b/tests/ModuleTypeLocked.cmd @@ -0,0 +1,9 @@ +Require Import dpdgraph.dpdgraph. + +Require ModuleTypeLocked. +Set DependGraph File "ModuleTypeLocked.dpd". +Print DependGraph ModuleTypeLocked.Foo.T. +Set DependGraph File "ModuleTypeLocked_regular.dpd". +Print DependGraph ModuleTypeLocked.Regular. +Set DependGraph File "ModuleTypeLocked_axiom.dpd". +Print DependGraph ModuleTypeLocked.Ax. diff --git a/tests/ModuleTypeLocked.dot.oracle b/tests/ModuleTypeLocked.dot.oracle new file mode 100644 index 000000000..93083987b --- /dev/null +++ b/tests/ModuleTypeLocked.dot.oracle @@ -0,0 +1,15 @@ +digraph tests/ModuleTypeLocked { + graph [ratio=0.5] + node [style=filled] +ModuleTypeLocked_Foo_T [label="T", URL=, peripheries=3, fillcolor="#F070D1"] ; +_nat [label="nat", URL=<.html#nat>, fillcolor="#E2CDFA"] ; +_O [label="O", URL=<.html#O>, fillcolor="#7FAAFF"] ; +_S [label="S", URL=<.html#S>, fillcolor="#7FAAFF"] ; + ModuleTypeLocked_Foo_T -> _nat [] ; + ModuleTypeLocked_Foo_T -> _O [] ; + ModuleTypeLocked_Foo_T -> _S [] ; +subgraph cluster_ModuleTypeLocked { label="ModuleTypeLocked"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_ModuleTypeLocked_Foo { label="Foo"; fillcolor="#FFFFA3"; labeljust=l; style=filled +ModuleTypeLocked_Foo_T; }; +}; +} /* END */ diff --git a/tests/ModuleTypeLocked.dpd.oracle b/tests/ModuleTypeLocked.dpd.oracle new file mode 100644 index 000000000..b6a5b6830 --- /dev/null +++ b/tests/ModuleTypeLocked.dpd.oracle @@ -0,0 +1,7 @@ +N: 1 "T" [opaque=yes, body=yes, kind=cnst, prop=no, path="ModuleTypeLocked.Foo", ]; +N: 2 "nat" [kind=inductive, prop=no, ]; +N: 3 "O" [kind=construct, prop=no, ]; +N: 4 "S" [kind=construct, prop=no, ]; +E: 1 2 [weight=1, ]; +E: 1 3 [weight=1, ]; +E: 1 4 [weight=1, ]; diff --git a/tests/ModuleTypeLocked.v b/tests/ModuleTypeLocked.v new file mode 100644 index 000000000..ad9236338 --- /dev/null +++ b/tests/ModuleTypeLocked.v @@ -0,0 +1,21 @@ +(* Test file for module type locked bodies *) +(* When a module implements a module type signature with `:`, the body + is hidden from the global environment's direct lookup. However, the body + still exists in the module structure and can be accessed (like Extraction + and Print Assumptions do). dpdgraph looks up the module structure to + correctly detect that such constants have a body, reporting body=yes. *) + +Module Type FooT. + Axiom T : nat. +End FooT. + +Module Foo : FooT. + (* This definition has a body, but it's hidden by the module type *) + Definition T := S O. +End Foo. + +(* A regular definition for comparison - body=yes expected *) +Definition Regular := S O. + +(* An axiom for comparison - body=no expected *) +Axiom Ax : nat. diff --git a/tests/NestedModules.cmd b/tests/NestedModules.cmd new file mode 100644 index 000000000..b85359dc6 --- /dev/null +++ b/tests/NestedModules.cmd @@ -0,0 +1,4 @@ +Load "NestedModules.v". +Require Import dpdgraph.dpdgraph. +Set DependGraph File "NestedModules.dpd". +Print DependGraph Flocq.Calc.Div.Fdiv_correct. diff --git a/tests/NestedModules.dot.oracle b/tests/NestedModules.dot.oracle new file mode 100644 index 000000000..25adcc638 --- /dev/null +++ b/tests/NestedModules.dot.oracle @@ -0,0 +1,12824 @@ +digraph tests/NestedModules { + graph [ratio=0.5] + node [style=filled] +OrderedRing_Rle_gt_cases [label="Rle_gt_cases", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rlt_trichotomy [label="Rlt_trichotomy", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rle_lt_eq [label="Rle_lt_eq", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Req_em [label="Req_em", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rle_refl [label="Rle_refl", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORle_refl [label="SORle_refl", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rneq_symm [label="Rneq_symm", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORlt_trichotomy [label="SORlt_trichotomy", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rlt_trans [label="Rlt_trans", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rle_antisymm [label="Rle_antisymm", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rle_trans [label="Rle_trans", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORle_trans [label="SORle_trans", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rle_lt_trans [label="Rle_lt_trans", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_cltb [label="cltb", URL=, fillcolor="#F070D1"] ; +RingMicromega_cneqb [label="cneqb", URL=, fillcolor="#F070D1"] ; +_andb [label="andb", URL=<.html#andb>, fillcolor="#F070D1"] ; +RingMicromega_rminus_morph_Proper [label="rminus_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_eval_pol_norm [label="eval_pol_norm", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rminus_eq_0 [label="Rminus_eq_0", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_eval_pexpr [label="eval_pexpr", URL=, fillcolor="#F070D1"] ; +RingMicromega_eval_pol_sub [label="eval_pol_sub", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_eval_op2 [label="eval_op2", URL=, fillcolor="#F070D1"] ; +RingMicromega_OpNEq [label="OpNEq", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_OpLe [label="OpLe", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_OpGe [label="OpGe", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_OpGt [label="OpGt", URL=, fillcolor="#7FAAFF"] ; +EnvRing_Psub_ok [label="Psub_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_pow_pos_add [label="pow_pos_add", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Pjump_add [label="Pjump_add", URL=, fillcolor="#7FFFD4"] ; +EnvRing_mkPX_ok [label="mkPX_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_PaddC_ok [label="PaddC_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Pjump_xO_tail [label="Pjump_xO_tail", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Pjump_pred_double [label="Pjump_pred_double", URL=, fillcolor="#7FFFD4"] ; +EnvRing_rsub_ext_Proper [label="rsub_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +EnvRing_ropp_ext_Proper [label="ropp_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +EnvRing_mkPinj_ok [label="mkPinj_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_PsubC_ok [label="PsubC_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_PsubX_ok [label="PsubX_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_env_morph [label="env_morph", URL=, fillcolor="#7FFFD4"] ; +Env_jump_pred_double [label="jump_pred_double", URL=, fillcolor="#7FFFD4"] ; +Env_jump_simpl [label="jump_simpl", URL=, fillcolor="#7FFFD4"] ; +Env_jump_add [label="jump_add", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Pphi0 [label="Pphi0", URL=, fillcolor="#7FFFD4"] ; +EnvRing_ceqb_spec [label="ceqb_spec", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Peq_spec [label="Peq_spec", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Peq_ok [label="Peq_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_PEeval [label="PEeval", URL=, fillcolor="#F070D1"] ; +OrderedRing_Rplus_0_l [label="Rplus_0_l", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_rminus_morph_Proper [label="rminus_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_SORpower [label="SORpower", URL=, fillcolor="#7FFFD4"] ; +EnvRing_norm_aux_spec [label="norm_aux_spec", URL=, fillcolor="#7FFFD4"] ; +EnvRing_mkX_ok [label="mkX_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_PExpr_ind [label="PExpr_ind", URL=, fillcolor="#7FFFD4"] ; +EnvRing_get_PEopp [label="get_PEopp", URL=, fillcolor="#F070D1"] ; +EnvRing_norm_aux_PEadd [label="norm_aux_PEadd", URL=, fillcolor="#7FFFD4"] ; +EnvRing_norm_aux_PEopp [label="norm_aux_PEopp", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Padd_ok [label="Padd_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Ppow_N_ok [label="Ppow_N_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Pmul_ok [label="Pmul_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_PEopp [label="PEopp", URL=, fillcolor="#7FAAFF"] ; +EnvRing_PEpow [label="PEpow", URL=, fillcolor="#7FAAFF"] ; +EnvRing_PmulC_ok [label="PmulC_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_PmulI_ok [label="PmulI_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_PmulC_aux_ok [label="PmulC_aux_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Pphi1 [label="Pphi1", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Ppow_pos_ok [label="Ppow_pos_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_PaddX_ok [label="PaddX_ok", URL=, fillcolor="#7FFFD4"] ; +Env_nth_pred_double [label="nth_pred_double", URL=, fillcolor="#7FFFD4"] ; +Env_nth_jump [label="nth_jump", URL=, fillcolor="#7FFFD4"] ; +Env_nth_spec [label="nth_spec", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_rminus_morph [label="rminus_morph", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_xnegate_correct [label="xnegate_correct", URL=, fillcolor="#7FFFD4"] ; +Tauto_eval_cnf_tt [label="eval_cnf_tt", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_xnegate [label="xnegate", URL=, fillcolor="#F070D1"] ; +OrderedRing_Req_dne [label="Req_dne", URL=, fillcolor="#7FFFD4"] ; +QMicromega_Qeval_expr [label="Qeval_expr", URL=, fillcolor="#F070D1"] ; +QMicromega_Qeval_pop2 [label="Qeval_pop2", URL=, fillcolor="#F070D1"] ; +QMicromega_Qeval_op2_hold [label="Qeval_op2_hold", URL=, fillcolor="#7FFFD4"] ; +QMicromega_Qeval_expr_ [label="Qeval_expr'", URL=, fillcolor="#F070D1"] ; +QMicromega_Qeval_expr_compat [label="Qeval_expr_compat", URL=, fillcolor="#7FFFD4"] ; +QMicromega_Qeval_op2 [label="Qeval_op2", URL=, fillcolor="#F070D1"] ; +QMicromega_Qeval_bop2 [label="Qeval_bop2", URL=, fillcolor="#F070D1"] ; +QMicromega_Qlt_bool [label="Qlt_bool", URL=, fillcolor="#F070D1"] ; +Z_ltb [label="ltb", URL=, fillcolor="#F070D1"] ; +QMicromega_QNpower [label="QNpower", URL=, fillcolor="#7FFFD4"] ; +QMicromega_pop2_bop2 [label="pop2_bop2", URL=, fillcolor="#7FFFD4"] ; +Bool_negb_true_iff [label="negb_true_iff", URL=, fillcolor="#7FFFD4"] ; +QMicromega_Qlt_bool_iff [label="Qlt_bool_iff", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qle_bool_iff [label="Qle_bool_iff", URL=, fillcolor="#7FFFD4"] ; +Z_leb_le [label="leb_le", URL=, fillcolor="#7FFFD4"] ; +Z_ltb_lt [label="ltb_lt", URL=, fillcolor="#7FFFD4"] ; +Tauto_e_rtyp [label="e_rtyp", URL=, fillcolor="#F070D1"] ; +Tauto_eval_f [label="eval_f", URL=, fillcolor="#F070D1"] ; +Tauto_eFF [label="eFF", URL=, fillcolor="#F070D1"] ; +Tauto_eOR [label="eOR", URL=, fillcolor="#F070D1"] ; +Tauto_eTT [label="eTT", URL=, fillcolor="#F070D1"] ; +Tauto_eAND [label="eAND", URL=, fillcolor="#F070D1"] ; +Tauto_eIFF [label="eIFF", URL=, fillcolor="#F070D1"] ; +Tauto_eIMPL [label="eIMPL", URL=, fillcolor="#F070D1"] ; +Tauto_GFormula [label="GFormula", URL=, fillcolor="#E2CDFA"] ; +_implb [label="implb", URL=<.html#implb>, fillcolor="#F070D1"] ; +Bool_eqb [label="eqb", URL=, fillcolor="#F070D1"] ; +_orb [label="orb", URL=<.html#orb>, fillcolor="#F070D1"] ; +RingMicromega_check_normalised_formulas [label="check_normalised_formulas", URL=, fillcolor="#F070D1"] ; +RingMicromega_Psatz [label="Psatz", URL=, fillcolor="#E2CDFA"] ; +RingMicromega_eval_Psatz [label="eval_Psatz", URL=, fillcolor="#F070D1"] ; +RingMicromega_pexpr_times_nformula [label="pexpr_times_nformula", URL=, fillcolor="#F070D1"] ; +RingMicromega_map_option2 [label="map_option2", URL=, fillcolor="#F070D1"] ; +ListDef_nth [label="nth", URL=, fillcolor="#F070D1"] ; +RingMicromega_nformula_times_nformula [label="nformula_times_nformula", URL=, fillcolor="#F070D1"] ; +RingMicromega_map_option [label="map_option", URL=, fillcolor="#F070D1"] ; +EnvRing_Psquare [label="Psquare", URL=, fillcolor="#F070D1"] ; +RingMicromega_OpMult [label="OpMult", URL=, fillcolor="#F070D1"] ; +RingMicromega_checker_nf_sound [label="checker_nf_sound", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_eval_Psatz_Sound [label="eval_Psatz_Sound", URL=, fillcolor="#7FFFD4"] ; +List_In [label="In", URL=, fillcolor="#F070D1"] ; +Refl_make_conj_impl [label="make_conj_impl", URL=, fillcolor="#7FFFD4"] ; +Refl_make_conj_in [label="make_conj_in", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_nformula_times_nformula_correct [label="nformula_times_nformula_correct", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_pexpr_times_nformula_correct [label="pexpr_times_nformula_correct", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Psquare_ok [label="Psquare_ok", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rtimes_square_nonneg [label="Rtimes_square_nonneg", URL=, fillcolor="#7FFFD4"] ; +List_nth_in_or_default [label="nth_in_or_default", URL=, fillcolor="#F070D1"] ; +RingMicromega_cltb_sound [label="cltb_sound", URL=, fillcolor="#7FFFD4"] ; +_eq_rect [label="eq_rect", URL=<.html#eq_rect>, fillcolor="#F070D1"] ; +RingMicromega_Psatz_ind [label="Psatz_ind", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_PsatzLet [label="PsatzLet", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_PsatzIn [label="PsatzIn", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_PsatzSquare [label="PsatzSquare", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_PsatzMulC [label="PsatzMulC", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_PsatzMulE [label="PsatzMulE", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_PsatzAdd [label="PsatzAdd", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_PsatzC [label="PsatzC", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_PsatzZ [label="PsatzZ", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_cleb_sound [label="cleb_sound", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_cneqb_sound [label="cneqb_sound", URL=, fillcolor="#7FFFD4"] ; +_andb_prop [label="andb_prop", URL=<.html#andb_prop>, fillcolor="#7FFFD4"] ; +RingMicromega_SORcneqb_morph [label="SORcneqb_morph", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_SORcleb_morph [label="SORcleb_morph", URL=, fillcolor="#7FFFD4"] ; +_list_rec [label="list_rec", URL=<.html#list_rec>, fillcolor="#F070D1"] ; +OrderedRing_Rtimes_neg_neg [label="Rtimes_neg_neg", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rtimes_0_l [label="Rtimes_0_l", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rtimes_pos_pos [label="Rtimes_pos_pos", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORtimes_pos_pos [label="SORtimes_pos_pos", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Ropp_pos_neg [label="Ropp_pos_neg", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Ropp_lt_mono [label="Ropp_lt_mono", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rtimes_0_r [label="Rtimes_0_r", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_OpMult_sound [label="OpMult_sound", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rtimes_neq_0 [label="Rtimes_neq_0", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rtimes_nonneg_nonneg [label="Rtimes_nonneg_nonneg", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rtimes_comm [label="Rtimes_comm", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rtimes_pos_neg [label="Rtimes_pos_neg", URL=, fillcolor="#7FFFD4"] ; +Tauto_cnf_checker_sound [label="cnf_checker_sound", URL=, fillcolor="#7FFFD4"] ; +Tauto_tauto_checker [label="tauto_checker", URL=, fillcolor="#F070D1"] ; +Tauto_xcnf_correct [label="xcnf_correct", URL=, fillcolor="#7FFFD4"] ; +Tauto_cnf_checker [label="cnf_checker", URL=, fillcolor="#F070D1"] ; +Tauto_xcnf [label="xcnf", URL=, fillcolor="#F070D1"] ; +Tauto_mk_impl [label="mk_impl", URL=, fillcolor="#F070D1"] ; +Tauto_mk_and [label="mk_and", URL=, fillcolor="#F070D1"] ; +Tauto_mk_iff [label="mk_iff", URL=, fillcolor="#F070D1"] ; +Tauto_TFormula [label="TFormula", URL=, fillcolor="#F070D1"] ; +Tauto_is_bool [label="is_bool", URL=, fillcolor="#F070D1"] ; +Tauto_mk_or [label="mk_or", URL=, fillcolor="#F070D1"] ; +Tauto_or_cnf_opt [label="or_cnf_opt", URL=, fillcolor="#F070D1"] ; +Tauto_and_cnf_opt [label="and_cnf_opt", URL=, fillcolor="#F070D1"] ; +Tauto_and_cnf [label="and_cnf", URL=, fillcolor="#F070D1"] ; +Tauto_is_cnf_ff [label="is_cnf_ff", URL=, fillcolor="#F070D1"] ; +Tauto_is_cnf_tt [label="is_cnf_tt", URL=, fillcolor="#F070D1"] ; +Tauto_or_cnf [label="or_cnf", URL=, fillcolor="#F070D1"] ; +Tauto_or_clause_cnf [label="or_clause_cnf", URL=, fillcolor="#F070D1"] ; +Tauto_xor_clause_cnf [label="xor_clause_cnf", URL=, fillcolor="#F070D1"] ; +List_fold_left [label="fold_left", URL=, fillcolor="#F070D1"] ; +Tauto_or_clause [label="or_clause", URL=, fillcolor="#F070D1"] ; +Tauto_add_term [label="add_term", URL=, fillcolor="#F070D1"] ; +Tauto_or_cnf_opt_correct [label="or_cnf_opt_correct", URL=, fillcolor="#7FFFD4"] ; +Tauto_GFormula_ind [label="GFormula_ind", URL=, fillcolor="#7FFFD4"] ; +Tauto_hold_eAND [label="hold_eAND", URL=, fillcolor="#7FFFD4"] ; +Tauto_xcnf_iff [label="xcnf_iff", URL=, fillcolor="#7FFFD4"] ; +Tauto_xcnf_impl [label="xcnf_impl", URL=, fillcolor="#7FFFD4"] ; +Tauto_or_cnf_correct [label="or_cnf_correct", URL=, fillcolor="#7FFFD4"] ; +Tauto_hold_eEQ [label="hold_eEQ", URL=, fillcolor="#7FFFD4"] ; +Tauto_hold_eFF [label="hold_eFF", URL=, fillcolor="#7FFFD4"] ; +Tauto_hold_eOR [label="hold_eOR", URL=, fillcolor="#7FFFD4"] ; +Tauto_hold_eTT [label="hold_eTT", URL=, fillcolor="#7FFFD4"] ; +Tauto_eval_cnf_app [label="eval_cnf_app", URL=, fillcolor="#7FFFD4"] ; +Tauto_is_bool_inv [label="is_bool_inv", URL=, fillcolor="#7FFFD4"] ; +Tauto_eval_cnf_and_opt [label="eval_cnf_and_opt", URL=, fillcolor="#7FFFD4"] ; +Tauto_mk_iff_is_bool [label="mk_iff_is_bool", URL=, fillcolor="#7FFFD4"] ; +Tauto_TT [label="TT", URL=, fillcolor="#7FAAFF"] ; +Tauto_FF [label="FF", URL=, fillcolor="#7FAAFF"] ; +Tauto_X [label="X", URL=, fillcolor="#7FAAFF"] ; +Tauto_AND [label="AND", URL=, fillcolor="#7FAAFF"] ; +Tauto_OR [label="OR", URL=, fillcolor="#7FAAFF"] ; +Tauto_NOT [label="NOT", URL=, fillcolor="#7FAAFF"] ; +Tauto_IMPL [label="IMPL", URL=, fillcolor="#7FAAFF"] ; +Tauto_IFF [label="IFF", URL=, fillcolor="#7FAAFF"] ; +Tauto_EQ [label="EQ", URL=, fillcolor="#7FAAFF"] ; +Tauto_and_cnf_opt_cnf_tt [label="and_cnf_opt_cnf_tt", URL=, fillcolor="#7FFFD4"] ; +Tauto_or_cnf_opt_cnf_ff_r [label="or_cnf_opt_cnf_ff_r", URL=, fillcolor="#7FFFD4"] ; +Tauto_and_cnf_opt_cnf_ff_r [label="and_cnf_opt_cnf_ff_r", URL=, fillcolor="#7FFFD4"] ; +Tauto_or_cnf_opt_cnf_ff [label="or_cnf_opt_cnf_ff", URL=, fillcolor="#7FFFD4"] ; +Tauto_is_cnf_ff_inv [label="is_cnf_ff_inv", URL=, fillcolor="#7FFFD4"] ; +Tauto_is_cnf_tt_cnf_ff [label="is_cnf_tt_cnf_ff", URL=, fillcolor="#7FFFD4"] ; +Tauto_is_cnf_tt_inv [label="is_cnf_tt_inv", URL=, fillcolor="#7FFFD4"] ; +Bool_orb_comm [label="orb_comm", URL=, fillcolor="#7FFFD4"] ; +Tauto_is_cnf_ff_cnf_ff [label="is_cnf_ff_cnf_ff", URL=, fillcolor="#7FFFD4"] ; +Tauto_if_cnf_tt [label="if_cnf_tt", URL=, fillcolor="#7FFFD4"] ; +_app [label="app", URL=<.html#app>, fillcolor="#F070D1"] ; +Refl_make_conj_rapp [label="make_conj_rapp", URL=, fillcolor="#7FFFD4"] ; +Refl_make_conj_app [label="make_conj_app", URL=, fillcolor="#7FFFD4"] ; +Bool_orb_true_iff [label="orb_true_iff", URL=, fillcolor="#7FFFD4"] ; +Tauto_or_clause_cnf_correct [label="or_clause_cnf_correct", URL=, fillcolor="#7FFFD4"] ; +Tauto_or_clause_correct [label="or_clause_correct", URL=, fillcolor="#7FFFD4"] ; +Tauto_eval_opt_clause [label="eval_opt_clause", URL=, fillcolor="#F070D1"] ; +Tauto_add_term_correct [label="add_term_correct", URL=, fillcolor="#7FFFD4"] ; +Tauto_hold_eIMPL [label="hold_eIMPL", URL=, fillcolor="#7FFFD4"] ; +Tauto_hold_eIFF_IMPL [label="hold_eIFF_IMPL", URL=, fillcolor="#7FFFD4"] ; +Tauto_hold_eIFF [label="hold_eIFF", URL=, fillcolor="#7FFFD4"] ; +Bool_eqb_true_iff [label="eqb_true_iff", URL=, fillcolor="#7FFFD4"] ; +Bool_andb_true_iff [label="andb_true_iff", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_eval_nformula_dec [label="eval_nformula_dec", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_0_l [label="Qmult_0_l", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_lt_compat_r [label="Qmult_lt_compat_r", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qle_trans [label="Qle_trans", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qlt_not_eq [label="Qlt_not_eq", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Q_dec [label="Q_dec", URL=, fillcolor="#F070D1"] ; +QArith_base_Qle_antisym [label="Qle_antisym", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qnot_le_lt [label="Qnot_le_lt", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_mk_SOR_theory [label="mk_SOR_theory", URL=, fillcolor="#7FAAFF"] ; +Z_nle_gt [label="nle_gt", URL=, fillcolor="#7FFFD4"] ; +Z_le_antisymm [label="le_antisymm", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_le_antisym [label="le_antisym", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_eq_neq [label="eq_neq", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_eq_refl [label="eq_refl", URL=, fillcolor="#7FFFD4"] ; +_Z_dec_ [label="Z_dec'", URL=<.html#Z_dec'>, fillcolor="#F070D1"] ; +Z_eq_dec [label="eq_dec", URL=, fillcolor="#F070D1"] ; +_not_Zeq_inf [label="not_Zeq_inf", URL=<.html#not_Zeq_inf>, fillcolor="#F070D1"] ; +_inleft [label="inleft", URL=<.html#inleft>, fillcolor="#7FAAFF"] ; +_inright [label="inright", URL=<.html#inright>, fillcolor="#7FAAFF"] ; +_Z_le_lt_eq_dec [label="Z_le_lt_eq_dec", URL=<.html#Z_le_lt_eq_dec>, fillcolor="#F070D1"] ; +Z_ge [label="ge", URL=, fillcolor="#F070D1"] ; +_Z_lt_ge_dec [label="Z_lt_ge_dec", URL=<.html#Z_lt_ge_dec>, fillcolor="#F070D1"] ; +Z_ge_le [label="ge_le", URL=, fillcolor="#7FFFD4"] ; +Z_ge_le_iff [label="ge_le_iff", URL=, fillcolor="#7FFFD4"] ; +_Z_lt_dec [label="Z_lt_dec", URL=<.html#Z_lt_dec>, fillcolor="#F070D1"] ; +_Zcompare_rec [label="Zcompare_rec", URL=<.html#Zcompare_rec>, fillcolor="#F070D1"] ; +_Zcompare_rect [label="Zcompare_rect", URL=<.html#Zcompare_rect>, fillcolor="#F070D1"] ; +Pos_eq_dec [label="eq_dec", URL=, fillcolor="#F070D1"] ; +_Z_rec [label="Z_rec", URL=<.html#Z_rec>, fillcolor="#F070D1"] ; +_sumbool_rec [label="sumbool_rec", URL=<.html#sumbool_rec>, fillcolor="#F070D1"] ; +_positive_rec [label="positive_rec", URL=<.html#positive_rec>, fillcolor="#F070D1"] ; +Z_lt_neq [label="lt_neq", URL=, fillcolor="#7FFFD4"] ; +Z_mul_shuffle1 [label="mul_shuffle1", URL=, fillcolor="#7FFFD4"] ; +Z_mul_pos_pos [label="mul_pos_pos", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qeq_bool_neq [label="Qeq_bool_neq", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qle_bool_imp_le [label="Qle_bool_imp_le", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_mk_SOR_addon [label="mk_SOR_addon", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_OpAdd_sound [label="OpAdd_sound", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_OpAdd [label="OpAdd", URL=, fillcolor="#F070D1"] ; +OrderedRing_Rplus_pos_pos [label="Rplus_pos_pos", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_nonneg_pos [label="Rplus_nonneg_pos", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_0_r [label="Rplus_0_r", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_nonneg_nonneg [label="Rplus_nonneg_nonneg", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_pos_nonneg [label="Rplus_pos_nonneg", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_lt_le_mono [label="Rplus_lt_le_mono", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_le_mono [label="Rplus_le_mono", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_le_lt_mono [label="Rplus_le_lt_mono", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_lt_mono [label="Rplus_lt_mono", URL=, fillcolor="#7FFFD4"] ; +ZifyInst_Inj_pos_Z [label="Inj_pos_Z", URL=, fillcolor="#F070D1"] ; +ZifyClasses_rew_iff [label="rew_iff", URL=, fillcolor="#7FFFD4"] ; +_Zmult_lt_compat2 [label="Zmult_lt_compat2", URL=<.html#Zmult_lt_compat2>, fillcolor="#7FFFD4"] ; +ZifyClasses_mkapp2 [label="mkapp2", URL=, fillcolor="#7FFFD4"] ; +Z_pow_add_r [label="pow_add_r", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_minus [label="Qpower_minus", URL=, fillcolor="#7FFFD4"] ; +Z_add_1_r [label="add_1_r", URL=, fillcolor="#7FFFD4"] ; +ZifyClasses_and_morph [label="and_morph", URL=, fillcolor="#7FFFD4"] ; +QExtra_Pos_log2floor_plus1_spec [label="Pos_log2floor_plus1_spec", URL=, fillcolor="#7FFFD4"] ; +Pos2Z_inj_succ [label="inj_succ", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_decomp_pos [label="Qpower_decomp_pos", URL=, fillcolor="#7FFFD4"] ; +Z_to_N [label="to_N", URL=, fillcolor="#F070D1"] ; +_Zmult_lt_reg_r [label="Zmult_lt_reg_r", URL=<.html#Zmult_lt_reg_r>, fillcolor="#7FFFD4"] ; +PosExtra_Pos_pow_1_r [label="Pos_pow_1_r", URL=, fillcolor="#7FFFD4"] ; +Pos_pow [label="pow", URL=, fillcolor="#F070D1"] ; +Pos2Z_pos_is_pos [label="pos_is_pos", URL=, fillcolor="#7FFFD4"] ; +Pos2Z_inj_pow [label="inj_pow", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_ZTautoChecker [label="ZTautoChecker", URL=, fillcolor="#F070D1"] ; +QArith_base_Qlt_shift_div_l [label="Qlt_shift_div_l", URL=, fillcolor="#7FFFD4"] ; +ZifyClasses_inj [label="inj", URL=, fillcolor="#F070D1"] ; +ZifyClasses_mkrel [label="mkrel", URL=, fillcolor="#7FFFD4"] ; +Z_pow_pos_nonneg [label="pow_pos_nonneg", URL=, fillcolor="#7FFFD4"] ; +Z_pow_nonneg [label="pow_nonneg", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_ZTautoChecker_sound [label="ZTautoChecker_sound", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_0_lt [label="Qpower_0_lt", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_ZArithProof [label="ZArithProof", URL=, fillcolor="#E2CDFA"] ; +ZMicromega_DoneProof [label="DoneProof", URL=, fillcolor="#7FAAFF"] ; +ZMicromega_RatProof [label="RatProof", URL=, fillcolor="#7FAAFF"] ; +ZMicromega_CutProof [label="CutProof", URL=, fillcolor="#7FAAFF"] ; +ZMicromega_ZWitness [label="ZWitness", URL=, fillcolor="#F070D1"] ; +QArith_base_Qlt_leneq [label="Qlt_leneq", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_not_0 [label="Qpower_not_0", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qnot_eq_sym [label="Qnot_eq_sym", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_0_le [label="Qpower_0_le", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qinv_le_0_compat [label="Qinv_le_0_compat", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_pos_positive [label="Qpower_pos_positive", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_le_0_compat [label="Qmult_le_0_compat", URL=, fillcolor="#7FFFD4"] ; +Z_mul_nonneg_nonneg [label="mul_nonneg_nonneg", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_le_refl [label="le_refl", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_0_r [label="Qmult_0_r", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_not_0_positive [label="Qpower_not_0_positive", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_integral [label="Qmult_integral", URL=, fillcolor="#7FFFD4"] ; +Z_eq_mul_0 [label="eq_mul_0", URL=, fillcolor="#7FFFD4"] ; +Z_mul_neg_neg [label="mul_neg_neg", URL=, fillcolor="#7FFFD4"] ; +Z_mul_neg_pos [label="mul_neg_pos", URL=, fillcolor="#7FFFD4"] ; +Z_mul_pos_neg [label="mul_pos_neg", URL=, fillcolor="#7FFFD4"] ; +Z_mul_lt_mono_neg_r [label="mul_lt_mono_neg_r", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_ZSORaddon [label="ZSORaddon", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_normalise_correct [label="normalise_correct", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zeval_formula [label="Zeval_formula", URL=, fillcolor="#F070D1"] ; +ZMicromega_normalise [label="normalise", URL=, fillcolor="#F070D1"] ; +ZMicromega_eval_nformula [label="eval_nformula", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zeval_nformula_dec [label="Zeval_nformula_dec", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zeval_formula_compat [label="Zeval_formula_compat", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zsor [label="Zsor", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_ZChecker [label="ZChecker", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zdeduce [label="Zdeduce", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zunsat [label="Zunsat", URL=, fillcolor="#F070D1"] ; +ZMicromega_ZChecker_sound [label="ZChecker_sound", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_negate [label="negate", URL=, fillcolor="#F070D1"] ; +ZMicromega_negate_correct [label="negate_correct", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_cnf_of_list_correct [label="cnf_of_list_correct", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_cnf_of_list [label="cnf_of_list", URL=, fillcolor="#F070D1"] ; +ZMicromega_xnnormalise [label="xnnormalise", URL=, fillcolor="#F070D1"] ; +ZMicromega_xnegate [label="xnegate", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zunsat_sound [label="Zunsat_sound", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_xnegate_correct [label="xnegate_correct", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_xnnormalise_correct [label="xnnormalise_correct", URL=, fillcolor="#7FFFD4"] ; +Z_lt_0_sub [label="lt_0_sub", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_eval_pol_sub [label="eval_pol_sub", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_eval_pol [label="eval_pol", URL=, fillcolor="#F070D1"] ; +ZMicromega_le_0_iff [label="le_0_iff", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_eval_pol_norm [label="eval_pol_norm", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zeval_formula_compat_ [label="Zeval_formula_compat'", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_psub [label="psub", URL=, fillcolor="#F070D1"] ; +ZMicromega_normZ [label="normZ", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zeval_formula_ [label="Zeval_formula'", URL=, fillcolor="#F070D1"] ; +Z_add_sub_assoc [label="add_sub_assoc", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_eval_expr [label="eval_expr", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zeval_expr_compat [label="Zeval_expr_compat", URL=, fillcolor="#7FFFD4"] ; +Z_gt [label="gt", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zeval_expr [label="Zeval_expr", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zeval_pop2 [label="Zeval_pop2", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zeval_op2 [label="Zeval_op2", URL=, fillcolor="#F070D1"] ; +Z_gt_lt [label="gt_lt", URL=, fillcolor="#7FFFD4"] ; +Z_le_ge [label="le_ge", URL=, fillcolor="#7FFFD4"] ; +Z_lt_gt [label="lt_gt", URL=, fillcolor="#7FFFD4"] ; +Z_gt_lt_iff [label="gt_lt_iff", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zeval_bop2 [label="Zeval_bop2", URL=, fillcolor="#F070D1"] ; +Z_geb [label="geb", URL=, fillcolor="#F070D1"] ; +Z_gtb [label="gtb", URL=, fillcolor="#F070D1"] ; +IntDef_Z_add [label="add", URL=, fillcolor="#F070D1"] ; +IntDef_Z_mul [label="mul", URL=, fillcolor="#F070D1"] ; +IntDef_Z_opp [label="opp", URL=, fillcolor="#F070D1"] ; +IntDef_Z_sub [label="sub", URL=, fillcolor="#F070D1"] ; +ZMicromega_ZNpower [label="ZNpower", URL=, fillcolor="#7FFFD4"] ; +_f_equal2 [label="f_equal2", URL=<.html#f_equal2>, fillcolor="#7FFFD4"] ; +IntDef_Z_pos_sub [label="pos_sub", URL=, fillcolor="#F070D1"] ; +IntDef_Z_pred_double [label="pred_double", URL=, fillcolor="#F070D1"] ; +IntDef_Z_double [label="double", URL=, fillcolor="#F070D1"] ; +IntDef_Z_succ_double [label="succ_double", URL=, fillcolor="#F070D1"] ; +Z_le_0_sub [label="le_0_sub", URL=, fillcolor="#7FFFD4"] ; +Z_sub_simpl_r [label="sub_simpl_r", URL=, fillcolor="#7FFFD4"] ; +Z_sub_sub_distr [label="sub_sub_distr", URL=, fillcolor="#7FFFD4"] ; +Z_opp_sub_distr [label="opp_sub_distr", URL=, fillcolor="#7FFFD4"] ; +Z_opp_add_distr [label="opp_add_distr", URL=, fillcolor="#7FFFD4"] ; +Z_opp_involutive [label="opp_involutive", URL=, fillcolor="#7FFFD4"] ; +Z_opp_pred [label="opp_pred", URL=, fillcolor="#7FFFD4"] ; +Z_eq_decidable [label="eq_decidable", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_eval_pol_Pc [label="eval_pol_Pc", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_eq_cnf [label="eq_cnf", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_lt_le_iff [label="lt_le_iff", URL=, fillcolor="#7FFFD4"] ; +Z_sub_1_r [label="sub_1_r", URL=, fillcolor="#7FFFD4"] ; +Z_opp_pos_neg [label="opp_pos_neg", URL=, fillcolor="#7FFFD4"] ; +Z_sub_opp_l [label="sub_opp_l", URL=, fillcolor="#7FFFD4"] ; +Z_opp_lt_mono [label="opp_lt_mono", URL=, fillcolor="#7FFFD4"] ; +Z_sub_opp_r [label="sub_opp_r", URL=, fillcolor="#7FFFD4"] ; +Z_add_opp_l [label="add_opp_l", URL=, fillcolor="#7FFFD4"] ; +Decidable_decidable [label="decidable", URL=, fillcolor="#F070D1"] ; +ZMicromega_eval_Psatz [label="eval_Psatz", URL=, fillcolor="#F070D1"] ; +ZMicromega_Private_Pos_neq_le_lt [label="Private_Pos_neq_le_lt", URL=, fillcolor="#7FFFD4"] ; +Pos_leb [label="leb", URL=, fillcolor="#F070D1"] ; +ZMicromega_max_var_nformulae [label="max_var_nformulae", URL=, fillcolor="#F070D1"] ; +ZMicromega_mk_eq_pos [label="mk_eq_pos", URL=, fillcolor="#F070D1"] ; +Z_leb_spec [label="leb_spec", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_eval_nformula_mk_eq_pos [label="eval_nformula_mk_eq_pos", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_nformula_of_cutting_plane [label="nformula_of_cutting_plane", URL=, fillcolor="#F070D1"] ; +Z_opp_nonneg_nonpos [label="opp_nonneg_nonpos", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_cutting_plane_sound [label="cutting_plane_sound", URL=, fillcolor="#7FFFD4"] ; +Pos_leb_spec [label="leb_spec", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_bound_var [label="bound_var", URL=, fillcolor="#F070D1"] ; +ZMicromega_agree_env_eval_nformulae [label="agree_env_eval_nformulae", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_genCuttingPlane [label="genCuttingPlane", URL=, fillcolor="#F070D1"] ; +Pos_eqb_neq [label="eqb_neq", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_popp [label="popp", URL=, fillcolor="#F070D1"] ; +ZMicromega_eval_nformula_bound_var [label="eval_nformula_bound_var", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_eval_Psatz_sound [label="eval_Psatz_sound", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Private_Pos_neq_lt [label="Private_Pos_neq_lt", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_eval_nformula_split [label="eval_nformula_split", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_agree_env [label="agree_env", URL=, fillcolor="#F070D1"] ; +ZMicromega_genCuttingPlaneNone [label="genCuttingPlaneNone", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_ZArithProof_ind [label="ZArithProof_ind", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_SplitProof [label="SplitProof", URL=, fillcolor="#7FAAFF"] ; +ZMicromega_deprecated_EnumProof [label="deprecated_EnumProof", URL=, fillcolor="#7FAAFF"] ; +ZMicromega_ExProof [label="ExProof", URL=, fillcolor="#7FAAFF"] ; +Z_gcd_opp_r [label="gcd_opp_r", URL=, fillcolor="#7FFFD4"] ; +Z_gtb_lt [label="gtb_lt", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zgcd_pol_correct_lt [label="Zgcd_pol_correct_lt", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zdiv_pol [label="Zdiv_pol", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zgcd_pol [label="Zgcd_pol", URL=, fillcolor="#F070D1"] ; +Z_eqb_neq [label="eqb_neq", URL=, fillcolor="#7FFFD4"] ; +Z_gcd [label="gcd", URL=, fillcolor="#F070D1"] ; +Z_add_move_0_l [label="add_move_0_l", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_makeCuttingPlane [label="makeCuttingPlane", URL=, fillcolor="#F070D1"] ; +Z_gcd_mul_diag_l [label="gcd_mul_diag_l", URL=, fillcolor="#7FFFD4"] ; +Z_divide [label="divide", URL=, fillcolor="#F070D1"] ; +Z_divide_mul_l [label="divide_mul_l", URL=, fillcolor="#7FFFD4"] ; +Z_gcd_unique_alt [label="gcd_unique_alt", URL=, fillcolor="#7FFFD4"] ; +Z_divide_refl [label="divide_refl", URL=, fillcolor="#7FFFD4"] ; +Z_gcd_unique [label="gcd_unique", URL=, fillcolor="#7FFFD4"] ; +Z_gcd_divide_l [label="gcd_divide_l", URL=, fillcolor="#7FFFD4"] ; +Z_gcd_divide_r [label="gcd_divide_r", URL=, fillcolor="#7FFFD4"] ; +Z_divide_antisym_nonneg [label="divide_antisym_nonneg", URL=, fillcolor="#7FFFD4"] ; +Z_gcd_nonneg [label="gcd_nonneg", URL=, fillcolor="#7FFFD4"] ; +Z_gcd_greatest [label="gcd_greatest", URL=, fillcolor="#7FFFD4"] ; +Pos_gcd_greatest [label="gcd_greatest", URL=, fillcolor="#7FFFD4"] ; +Z_divide_Zpos_Zneg_l [label="divide_Zpos_Zneg_l", URL=, fillcolor="#7FFFD4"] ; +Z_divide_Zpos_Zneg_r [label="divide_Zpos_Zneg_r", URL=, fillcolor="#7FFFD4"] ; +Z_divide_Zpos [label="divide_Zpos", URL=, fillcolor="#7FFFD4"] ; +Pos_gcd [label="gcd", URL=, fillcolor="#F070D1"] ; +Pos_divide [label="divide", URL=, fillcolor="#F070D1"] ; +Pos_size_nat [label="size_nat", URL=, fillcolor="#F070D1"] ; +Pos_gcdn [label="gcdn", URL=, fillcolor="#F070D1"] ; +Z_mul_opp_l [label="mul_opp_l", URL=, fillcolor="#7FFFD4"] ; +Z_add_opp_diag_l [label="add_opp_diag_l", URL=, fillcolor="#7FFFD4"] ; +Z_add_move_0_r [label="add_move_0_r", URL=, fillcolor="#7FFFD4"] ; +Z_sub_0_l [label="sub_0_l", URL=, fillcolor="#7FFFD4"] ; +Z_add_move_r [label="add_move_r", URL=, fillcolor="#7FFFD4"] ; +Z_add_move_l [label="add_move_l", URL=, fillcolor="#7FFFD4"] ; +_iff_stepl [label="iff_stepl", URL=<.html#iff_stepl>, fillcolor="#7FFFD4"] ; +Z_sub_cancel_r [label="sub_cancel_r", URL=, fillcolor="#7FFFD4"] ; +Z_mul_opp_r [label="mul_opp_r", URL=, fillcolor="#7FFFD4"] ; +Pos_gcdn_greatest [label="gcdn_greatest", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_decr [label="sub_decr", URL=, fillcolor="#7FFFD4"] ; +_plus_Sn_m [label="plus_Sn_m", URL=<.html#plus_Sn_m>, fillcolor="#7FFFD4"] ; +Pos_size_nat_monotone [label="size_nat_monotone", URL=, fillcolor="#7FFFD4"] ; +Pos_divide_mul_r [label="divide_mul_r", URL=, fillcolor="#7FFFD4"] ; +Pos_divide_xO_xI [label="divide_xO_xI", URL=, fillcolor="#7FFFD4"] ; +Pos_divide_xO_xO [label="divide_xO_xO", URL=, fillcolor="#7FFFD4"] ; +Pos_divide_add_cancel_l [label="divide_add_cancel_l", URL=, fillcolor="#7FFFD4"] ; +Pos_mul_lt_mono_r [label="mul_lt_mono_r", URL=, fillcolor="#7FFFD4"] ; +Pos_divide_mul_l [label="divide_mul_l", URL=, fillcolor="#7FFFD4"] ; +Z_eq_mul_1_nonneg_ [label="eq_mul_1_nonneg'", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_le_eq [label="le_eq", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_neq_eq [label="neq_eq", URL=, fillcolor="#7FFFD4"] ; +Z_mul_id_l [label="mul_id_l", URL=, fillcolor="#7FFFD4"] ; +Z_lt_ge_cases [label="lt_ge_cases", URL=, fillcolor="#7FFFD4"] ; +_and_comm [label="and_comm", URL=<.html#and_comm>, fillcolor="#7FFFD4"] ; +Z_eq_mul_1_nonneg [label="eq_mul_1_nonneg", URL=, fillcolor="#7FFFD4"] ; +Z_lt_0_1 [label="lt_0_1", URL=, fillcolor="#7FFFD4"] ; +Z_lt_1_2 [label="lt_1_2", URL=, fillcolor="#7FFFD4"] ; +Z_lt_1_mul_pos [label="lt_1_mul_pos", URL=, fillcolor="#7FFFD4"] ; +Z_lt_1_l [label="lt_1_l", URL=, fillcolor="#7FFFD4"] ; +Z_two_succ [label="two_succ", URL=, fillcolor="#7FFFD4"] ; +Z_ggcd_correct_divisors [label="ggcd_correct_divisors", URL=, fillcolor="#7FFFD4"] ; +Z_ggcd_gcd [label="ggcd_gcd", URL=, fillcolor="#7FFFD4"] ; +Z_ggcd [label="ggcd", URL=, fillcolor="#F070D1"] ; +Z_sgn [label="sgn", URL=, fillcolor="#F070D1"] ; +Pos_ggcd [label="ggcd", URL=, fillcolor="#F070D1"] ; +Pos_ggcdn [label="ggcdn", URL=, fillcolor="#F070D1"] ; +Pos_ggcd_gcd [label="ggcd_gcd", URL=, fillcolor="#7FFFD4"] ; +Pos_ggcdn_gcdn [label="ggcdn_gcdn", URL=, fillcolor="#7FFFD4"] ; +Pos_ggcd_correct_divisors [label="ggcd_correct_divisors", URL=, fillcolor="#7FFFD4"] ; +Pos_ggcdn_correct_divisors [label="ggcdn_correct_divisors", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_ceiling [label="ceiling", URL=, fillcolor="#F070D1"] ; +Z_div_eucl [label="div_eucl", URL=, fillcolor="#F070D1"] ; +Z_pos_div_eucl [label="pos_div_eucl", URL=, fillcolor="#F070D1"] ; +Bool_not_true_iff_false [label="not_true_iff_false", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_ZgcdM [label="ZgcdM", URL=, fillcolor="#F070D1"] ; +Z_max [label="max", URL=, fillcolor="#F070D1"] ; +Z_div [label="div", URL=, fillcolor="#F070D1"] ; +RingMicromega_PsubC_ok [label="PsubC_ok", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_psubC [label="psubC", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zgcd_pol_div [label="Zgcd_pol_div", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zdiv_pol_correct [label="Zdiv_pol_correct", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zdivide_pol_ind [label="Zdivide_pol_ind", URL=, fillcolor="#7FFFD4"] ; +Z_divide_div_mul_exact [label="divide_div_mul_exact", URL=, fillcolor="#7FFFD4"] ; +Z_div_mul [label="div_mul", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zdivide_pol [label="Zdivide_pol", URL=, fillcolor="#E2CDFA"] ; +Z_Private_OrderTac_Tac_le_neq_lt [label="le_neq_lt", URL=, fillcolor="#7FFFD4"] ; +Z_div_unique [label="div_unique", URL=, fillcolor="#7FFFD4"] ; +Z_div_mod_unique [label="div_mod_unique", URL=, fillcolor="#7FFFD4"] ; +Z_mod_pos_bound [label="mod_pos_bound", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_neq_sym [label="neq_sym", URL=, fillcolor="#7FFFD4"] ; +Z_div_mod [label="div_mod", URL=, fillcolor="#7FFFD4"] ; +Z_modulo [label="modulo", URL=, fillcolor="#F070D1"] ; +Z_mod_neg_bound [label="mod_neg_bound", URL=, fillcolor="#7FFFD4"] ; +Z_pos_div_eucl_bound [label="pos_div_eucl_bound", URL=, fillcolor="#7FFFD4"] ; +Z_pos_sub_lt [label="pos_sub_lt", URL=, fillcolor="#7FFFD4"] ; +Z_ltb_spec [label="ltb_spec", URL=, fillcolor="#7FFFD4"] ; +Z_succ_double_spec [label="succ_double_spec", URL=, fillcolor="#7FFFD4"] ; +Pos_le_succ_l [label="le_succ_l", URL=, fillcolor="#7FFFD4"] ; +Pos_succ_lt_mono [label="succ_lt_mono", URL=, fillcolor="#7FFFD4"] ; +Z_ltb_spec0 [label="ltb_spec0", URL=, fillcolor="#F070D1"] ; +Z_compare_ngt_iff [label="compare_ngt_iff", URL=, fillcolor="#7FFFD4"] ; +Z_compare_gt_iff [label="compare_gt_iff", URL=, fillcolor="#7FFFD4"] ; +Z_div_eucl_eq [label="div_eucl_eq", URL=, fillcolor="#7FFFD4"] ; +Z_mul_add_distr_l [label="mul_add_distr_l", URL=, fillcolor="#7FFFD4"] ; +Z_add_opp_diag_r [label="add_opp_diag_r", URL=, fillcolor="#7FFFD4"] ; +Z_mul_opp_comm [label="mul_opp_comm", URL=, fillcolor="#7FFFD4"] ; +Z_pos_div_eucl_eq [label="pos_div_eucl_eq", URL=, fillcolor="#7FFFD4"] ; +Pos_le_antisym [label="le_antisym", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +Pos_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_eq_cases [label="lt_eq_cases", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_le_iff [label="compare_le_iff", URL=, fillcolor="#7FFFD4"] ; +Z_pos_sub_gt [label="pos_sub_gt", URL=, fillcolor="#7FFFD4"] ; +Z_Private_NZDiv_div_mod_unique [label="div_mod_unique", URL=, fillcolor="#7FFFD4"] ; +Z_opp_inj_wd [label="opp_inj_wd", URL=, fillcolor="#7FFFD4"] ; +Z_opp_inj [label="opp_inj", URL=, fillcolor="#7FFFD4"] ; +Z_div_exact [label="div_exact", URL=, fillcolor="#7FFFD4"] ; +Z_divide_mul_r [label="divide_mul_r", URL=, fillcolor="#7FFFD4"] ; +Z_mod_divide [label="mod_divide", URL=, fillcolor="#7FFFD4"] ; +Z_mod_wd [label="mod_wd", URL=, fillcolor="#7FFFD4"] ; +Z_mod_mul [label="mod_mul", URL=, fillcolor="#7FFFD4"] ; +Z_mod_eq [label="mod_eq", URL=, fillcolor="#7FFFD4"] ; +Z_divide_wd [label="divide_wd", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Prop_ex_iff_morphism [label="ex_iff_morphism", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Prop_ex_iff_morphism_obligation_1 [label="ex_iff_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_ex_ind [label="ex_ind", URL=<.html#ex_ind>, fillcolor="#7FFFD4"] ; +ZMicromega_Zdivide_pol_one [label="Zdivide_pol_one", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zdivide_pol_sub [label="Zdivide_pol_sub", URL=, fillcolor="#7FFFD4"] ; +Z_max_spec [label="max_spec", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zdivide_pol_Zdivide [label="Zdivide_pol_Zdivide", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zdiv_Pc [label="Zdiv_Pc", URL=, fillcolor="#7FAAFF"] ; +ZMicromega_Zdiv_Pinj [label="Zdiv_Pinj", URL=, fillcolor="#7FAAFF"] ; +ZMicromega_Zdiv_PX [label="Zdiv_PX", URL=, fillcolor="#7FAAFF"] ; +Z_divide_trans [label="divide_trans", URL=, fillcolor="#7FFFD4"] ; +Z_max_l [label="max_l", URL=, fillcolor="#7FFFD4"] ; +Z_max_r [label="max_r", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_Zgcd_minus [label="Zgcd_minus", URL=, fillcolor="#7FFFD4"] ; +Z_divide_add_r [label="divide_add_r", URL=, fillcolor="#7FFFD4"] ; +Z_sub_move_r [label="sub_move_r", URL=, fillcolor="#7FFFD4"] ; +Z_gtb_ltb [label="gtb_ltb", URL=, fillcolor="#7FFFD4"] ; +Z_gcd_opp_l [label="gcd_opp_l", URL=, fillcolor="#7FFFD4"] ; +Z_gcd_comm [label="gcd_comm", URL=, fillcolor="#7FFFD4"] ; +Z_gcd_divide_iff [label="gcd_divide_iff", URL=, fillcolor="#7FFFD4"] ; +Z_divide_transitive [label="divide_transitive", URL=, fillcolor="#7FFFD4"] ; +Z_divide_opp_r [label="divide_opp_r", URL=, fillcolor="#7FFFD4"] ; +Z_le_ge_cases [label="le_ge_cases", URL=, fillcolor="#7FFFD4"] ; +Pos_max_1_l [label="max_1_l", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_max_var_nformulae_mono_aux_ [label="max_var_nformulae_mono_aux'", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_max_var_nformulae_mono_aux [label="max_var_nformulae_mono_aux", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_agree_env_subset [label="agree_env_subset", URL=, fillcolor="#7FFFD4"] ; +Pos_max [label="max", URL=, fillcolor="#F070D1"] ; +ZMicromega_max_var [label="max_var", URL=, fillcolor="#F070D1"] ; +_and_iff_compat_l [label="and_iff_compat_l", URL=<.html#and_iff_compat_l>, fillcolor="#7FFFD4"] ; +ZMicromega_agree_env_eval_nformula [label="agree_env_eval_nformula", URL=, fillcolor="#7FFFD4"] ; +Pos_le_refl [label="le_refl", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_agree_env_jump [label="agree_env_jump", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_agree_env_tail [label="agree_env_tail", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_max_var_acc [label="max_var_acc", URL=, fillcolor="#7FFFD4"] ; +Pos_le_max_l [label="le_max_l", URL=, fillcolor="#7FFFD4"] ; +Pos_le_max_r [label="le_max_r", URL=, fillcolor="#7FFFD4"] ; +_Pplus_one_succ_r [label="Pplus_one_succ_r", URL=<.html#Pplus_one_succ_r>, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_eq_lt [label="eq_lt", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_le_lt_trans [label="le_lt_trans", URL=, fillcolor="#7FFFD4"] ; +Pos_max_spec [label="max_spec", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_eq_sym [label="eq_sym", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_not_gt_le [label="not_gt_le", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +Pos_max_l [label="max_l", URL=, fillcolor="#7FFFD4"] ; +Pos_max_r [label="max_r", URL=, fillcolor="#7FFFD4"] ; +Pos_le_nlt [label="le_nlt", URL=, fillcolor="#7FFFD4"] ; +Pos_ge_le_iff [label="ge_le_iff", URL=, fillcolor="#7FFFD4"] ; +Pos_ge [label="ge", URL=, fillcolor="#F070D1"] ; +Pos_Private_Tac_trans [label="trans", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_interp_ord [label="interp_ord", URL=, fillcolor="#F070D1"] ; +Pos_Private_Tac_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +_Pplus_one_succ_l [label="Pplus_one_succ_l", URL=<.html#Pplus_one_succ_l>, fillcolor="#7FFFD4"] ; +Pos_add_max_distr_r [label="add_max_distr_r", URL=, fillcolor="#7FFFD4"] ; +Pos_add_max_distr_l [label="add_max_distr_l", URL=, fillcolor="#7FFFD4"] ; +Pos_add_le_mono_l [label="add_le_mono_l", URL=, fillcolor="#7FFFD4"] ; +Pos_max_monotone [label="max_monotone", URL=, fillcolor="#7FFFD4"] ; +Pos_max_mono [label="max_mono", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_le_antisym [label="le_antisym", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_eq_neq [label="eq_neq", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_neq_eq [label="neq_eq", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_not_neq_eq [label="not_neq_eq", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_eq_refl [label="eq_refl", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_le_neq_lt [label="le_neq_lt", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_not_ge_lt [label="not_ge_lt", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_eq_trans [label="eq_trans", URL=, fillcolor="#7FFFD4"] ; +Pos_add_le_mono_r [label="add_le_mono_r", URL=, fillcolor="#7FFFD4"] ; +Pos_le_trans [label="le_trans", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_le_trans [label="lt_le_trans", URL=, fillcolor="#7FFFD4"] ; +Pos_max_case_strong [label="max_case_strong", URL=, fillcolor="#F070D1"] ; +ZMicromega_F [label="F", URL=, fillcolor="#F070D1"] ; +Pos_Private_Dec_max_case_strong [label="max_case_strong", URL=, fillcolor="#F070D1"] ; +_CompSpec2Type [label="CompSpec2Type", URL=<.html#CompSpec2Type>, fillcolor="#F070D1"] ; +_CompareSpecT [label="CompareSpecT", URL=<.html#CompareSpecT>, fillcolor="#E2CDFA"] ; +_CompSpec [label="CompSpec", URL=<.html#CompSpec>, fillcolor="#F070D1"] ; +_CompSpecT [label="CompSpecT", URL=<.html#CompSpecT>, fillcolor="#F070D1"] ; +_CompareSpec2Type [label="CompareSpec2Type", URL=<.html#CompareSpec2Type>, fillcolor="#F070D1"] ; +_CompEqT [label="CompEqT", URL=<.html#CompEqT>, fillcolor="#7FAAFF"] ; +_CompLtT [label="CompLtT", URL=<.html#CompLtT>, fillcolor="#7FAAFF"] ; +_CompGtT [label="CompGtT", URL=<.html#CompGtT>, fillcolor="#7FAAFF"] ; +Pos_max_le_compat_r [label="max_le_compat_r", URL=, fillcolor="#7FFFD4"] ; +Pos_max_lub_iff [label="max_lub_iff", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_eq_le [label="eq_le", URL=, fillcolor="#7FFFD4"] ; +Pos_Private_Tac_lt_eq [label="lt_eq", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_nle [label="lt_nle", URL=, fillcolor="#7FFFD4"] ; +Pos_leb_spec0 [label="leb_spec0", URL=, fillcolor="#F070D1"] ; +Pos_compare_nge_iff [label="compare_nge_iff", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_nle_iff [label="compare_nle_iff", URL=, fillcolor="#7FFFD4"] ; +Pos_leb_le [label="leb_le", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_eval_pol_add [label="eval_pol_add", URL=, fillcolor="#7FFFD4"] ; +Bool_negb_false_iff [label="negb_false_iff", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_padd [label="padd", URL=, fillcolor="#F070D1"] ; +ZMicromega_Zdivide_ceiling [label="Zdivide_ceiling", URL=, fillcolor="#7FFFD4"] ; +Z_lt_le_pred [label="lt_le_pred", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_makeCuttingPlane_ns_sound [label="makeCuttingPlane_ns_sound", URL=, fillcolor="#7FFFD4"] ; +Z_div_unique_exact [label="div_unique_exact", URL=, fillcolor="#7FFFD4"] ; +Bool_andb_false_iff [label="andb_false_iff", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_padd [label="padd", URL=, fillcolor="#F070D1"] ; +RingMicromega_eval_pol_add [label="eval_pol_add", URL=, fillcolor="#7FFFD4"] ; +Z_sub_move_0_r [label="sub_move_0_r", URL=, fillcolor="#7FFFD4"] ; +Z_div_wd [label="div_wd", URL=, fillcolor="#7FFFD4"] ; +Z_le_sub_le_add_r [label="le_sub_le_add_r", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_narrow_interval_lower_bound [label="narrow_interval_lower_bound", URL=, fillcolor="#7FFFD4"] ; +Z_gtb_spec [label="gtb_spec", URL=, fillcolor="#7FFFD4"] ; +Z_add_nonneg_nonneg [label="add_nonneg_nonneg", URL=, fillcolor="#7FFFD4"] ; +Z_le_add_le_sub_l [label="le_add_le_sub_l", URL=, fillcolor="#7FFFD4"] ; +Z_le_add_le_sub_r [label="le_add_le_sub_r", URL=, fillcolor="#7FFFD4"] ; +Z_add_simpl_r [label="add_simpl_r", URL=, fillcolor="#7FFFD4"] ; +Z_sub_le_mono_r [label="sub_le_mono_r", URL=, fillcolor="#7FFFD4"] ; +_Fdiv_correct [label="Fdiv_correct", URL=<.html#Fdiv_correct>, peripheries=3, fillcolor="#7FFFD4"] ; +Z_mul_div_le [label="mul_div_le", URL=, fillcolor="#7FFFD4"] ; +Z_le [label="le", URL=, fillcolor="#F070D1"] ; +Z_lt_add_pos_r [label="lt_add_pos_r", URL=, fillcolor="#7FFFD4"] ; +_IZR [label="IZR", URL=<.html#IZR>, fillcolor="#F070D1"] ; +Z_lt_add_pos_l [label="lt_add_pos_l", URL=, fillcolor="#7FFFD4"] ; +_Rdiv [label="Rdiv", URL=<.html#Rdiv>, fillcolor="#F070D1"] ; +Z_eqb_spec [label="eqb_spec", URL=, fillcolor="#F070D1"] ; +Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_correct [label="Fdiv_correct", URL=, fillcolor="#FFB57F"] ; +Z_div_0_r [label="div_0_r", URL=, fillcolor="#7FFFD4"] ; +_Fdiv [label="Fdiv", URL=<.html#Fdiv>, fillcolor="#F070D1"] ; +Z_div_eucl_0_r [label="div_eucl_0_r", URL=, fillcolor="#7FFFD4"] ; +_F2R [label="F2R", URL=<.html#F2R>, fillcolor="#F070D1"] ; +Z_opp_le_mono [label="opp_le_mono", URL=, fillcolor="#7FFFD4"] ; +_cexp [label="cexp", URL=<.html#cexp>, fillcolor="#F070D1"] ; +Z_leb_spec0 [label="leb_spec0", URL=, fillcolor="#F070D1"] ; +_inbetween_float [label="inbetween_float", URL=<.html#inbetween_float>, fillcolor="#F070D1"] ; +Z_compare_nge_iff [label="compare_nge_iff", URL=, fillcolor="#7FFFD4"] ; +_Rlt [label="Rlt", URL=<.html#Rlt>, fillcolor="#F070D1"] ; +_prod [label="prod", URL=<.html#prod>, fillcolor="#E2CDFA"] ; +Z_compare_nle_iff [label="compare_nle_iff", URL=, fillcolor="#7FFFD4"] ; +_and [label="and", URL=<.html#and>, fillcolor="#E2CDFA"] ; +Pos_le_lt_trans [label="le_lt_trans", URL=, fillcolor="#7FFFD4"] ; +_Z [label="Z", URL=<.html#Z>, fillcolor="#E2CDFA"] ; +Z_le_neq [label="le_neq", URL=, fillcolor="#7FFFD4"] ; +_float [label="float", URL=<.html#float>, fillcolor="#E2CDFA"] ; +_Zsth [label="Zsth", URL=<.html#Zsth>, fillcolor="#7FFFD4"] ; +_radix [label="radix", URL=<.html#radix>, fillcolor="#E2CDFA"] ; +ZMicromega_Zeval_op2_hold [label="Zeval_op2_hold", URL=, fillcolor="#7FFFD4"] ; +SpecFloat_location [label="location", URL=, fillcolor="#E2CDFA"] ; +ZMicromega_pop2_bop2 [label="pop2_bop2", URL=, fillcolor="#7FFFD4"] ; +_Z0 [label="Z0", URL=<.html#Z0>, fillcolor="#7FAAFF"] ; +Z_geb_le [label="geb_le", URL=, fillcolor="#7FFFD4"] ; +_positive [label="positive", URL=<.html#positive>, fillcolor="#E2CDFA"] ; +Z_gtb_gt [label="gtb_gt", URL=, fillcolor="#7FFFD4"] ; +_comparison [label="comparison", URL=<.html#comparison>, fillcolor="#E2CDFA"] ; +Z_geb_leb [label="geb_leb", URL=, fillcolor="#7FFFD4"] ; +ZMicromega_xnormalise [label="xnormalise", URL=, fillcolor="#F070D1"] ; +Z_leb [label="leb", URL=, fillcolor="#F070D1"] ; +_bool [label="bool", URL=<.html#bool>, fillcolor="#E2CDFA"] ; +ZMicromega_xnormalise_correct [label="xnormalise_correct", URL=, fillcolor="#7FFFD4"] ; +_eq [label="eq", URL=<.html#eq>, fillcolor="#E2CDFA"] ; +ZMicromega_le_neg [label="le_neg", URL=, fillcolor="#7FFFD4"] ; +_true [label="true", URL=<.html#true>, fillcolor="#7FAAFF"] ; +Z_le_ind [label="le_ind", URL=, fillcolor="#7FFFD4"] ; +_Zpos [label="Zpos", URL=<.html#Zpos>, fillcolor="#7FAAFF"] ; +Z_pow_wd [label="pow_wd", URL=, fillcolor="#7FFFD4"] ; +_xO [label="xO", URL=<.html#xO>, fillcolor="#7FAAFF"] ; +Z_pow_neg_r [label="pow_neg_r", URL=, fillcolor="#7FFFD4"] ; +_xH [label="xH", URL=<.html#xH>, fillcolor="#7FAAFF"] ; +Z_pow_succ_r [label="pow_succ_r", URL=, fillcolor="#7FFFD4"] ; +Z_pow_0_r [label="pow_0_r", URL=, fillcolor="#7FFFD4"] ; +Z_compare [label="compare", URL=, fillcolor="#F070D1"] ; +_false [label="false", URL=<.html#false>, fillcolor="#7FAAFF"] ; +Pos_iter [label="iter", URL=, fillcolor="#F070D1"] ; +Pos_iter_add [label="iter_add", URL=, fillcolor="#7FFFD4"] ; +_CompOpp [label="CompOpp", URL=<.html#CompOpp>, fillcolor="#F070D1"] ; +Pos_iter_succ [label="iter_succ", URL=, fillcolor="#7FFFD4"] ; +PosDef_Pos_compare [label="compare", URL=, fillcolor="#F070D1"] ; +_Eq [label="Eq", URL=<.html#Eq>, fillcolor="#7FAAFF"] ; +Pos_iter_swap [label="iter_swap", URL=, fillcolor="#7FFFD4"] ; +_Lt [label="Lt", URL=<.html#Lt>, fillcolor="#7FAAFF"] ; +Pos_iter_swap_gen [label="iter_swap_gen", URL=, fillcolor="#7FFFD4"] ; +_Gt [label="Gt", URL=<.html#Gt>, fillcolor="#7FAAFF"] ; +ZifyClasses_InjTyp [label="InjTyp", URL=, fillcolor="#E2CDFA"] ; +PosDef_Pos_compare_cont [label="compare_cont", URL=, fillcolor="#F070D1"] ; +QArith_base_Qinv_lt_0_compat [label="Qinv_lt_0_compat", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_lt_0_le_reg_r [label="Qmult_lt_0_le_reg_r", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealLtProp [label="CRealLtProp", URL=, fillcolor="#F070D1"] ; +_R [label="R", URL=<.html#R>, fillcolor="#F070D1"] ; +QArith_base_Qlt_not_le [label="Qlt_not_le", URL=, fillcolor="#7FFFD4"] ; +_Rrepr [label="Rrepr", URL=<.html#Rrepr>, fillcolor="#F070D1"] ; +QArith_base_Qdiv_mult_l [label="Qdiv_mult_l", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_1_r [label="Qmult_1_r", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_DRealRepr [label="DRealRepr", URL=, fillcolor="#F070D1"] ; +Z_lt_nge [label="lt_nge", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_DReal [label="DReal", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CReal [label="CReal", URL=, fillcolor="#E2CDFA"] ; +Pos2Z_inj_pow_pos [label="inj_pow_pos", URL=, fillcolor="#7FFFD4"] ; +Datatypes_id [label="id", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_QCauchySeq [label="QCauchySeq", URL=, fillcolor="#F070D1"] ; +Pos_iter_invariant [label="iter_invariant", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_QBound [label="QBound", URL=, fillcolor="#F070D1"] ; +QArith_base_Q [label="Q", URL=, fillcolor="#E2CDFA"] ; +Pos_iter_ind [label="iter_ind", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qlt [label="Qlt", URL=, fillcolor="#F070D1"] ; +_ID [label="ID", URL=<.html#ID>, fillcolor="#F070D1"] ; +Qpower_Qpower_decomp_positive [label="Qpower_decomp_positive", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs [label="Qabs", URL=, fillcolor="#F070D1"] ; +Pos_pow_1_r [label="pow_1_r", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qpower [label="Qpower", URL=, fillcolor="#F070D1"] ; +QArith_base_Qmake [label="Qmake", URL=, fillcolor="#7FAAFF"] ; +Pos2Z_inj [label="inj", URL=, fillcolor="#7FFFD4"] ; +Z_pow_twice_r [label="pow_twice_r", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qinv [label="Qinv", URL=, fillcolor="#F070D1"] ; +Z_pow_1_r [label="pow_1_r", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qpower_positive [label="Qpower_positive", URL=, fillcolor="#F070D1"] ; +_pow_pos [label="pow_pos", URL=<.html#pow_pos>, fillcolor="#F070D1"] ; +Z_add_neg_neg [label="add_neg_neg", URL=, fillcolor="#7FFFD4"] ; +Pos_pow_succ_r [label="pow_succ_r", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult [label="Qmult", URL=, fillcolor="#F070D1"] ; +ZifyClasses_rew_iff_rev [label="rew_iff_rev", URL=, fillcolor="#7FFFD4"] ; +Pos_mul [label="mul", URL=, fillcolor="#F070D1"] ; +Z_mul [label="mul", URL=, fillcolor="#F070D1"] ; +ZifyClasses_mkapp [label="mkapp", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qden [label="Qden", URL=, fillcolor="#F070D1"] ; +_Fnorm [label="Fnorm", URL=<.html#Fnorm>, fillcolor="#F070D1"] ; +QArith_base_Qnum [label="Qnum", URL=, fillcolor="#F070D1"] ; +_PCond [label="PCond", URL=<.html#PCond>, fillcolor="#F070D1"] ; +PosDef_Pos_mul [label="mul", URL=, fillcolor="#F070D1"] ; +_denum [label="denum", URL=<.html#denum>, fillcolor="#F070D1"] ; +_Zneg [label="Zneg", URL=<.html#Zneg>, fillcolor="#7FAAFF"] ; +Qfield_Qfield_field_lemma1 [label="Qfield_field_lemma1", URL=, fillcolor="#7FFFD4"] ; +PosDef_Pos_add [label="add", URL=, fillcolor="#F070D1"] ; +_FEeval [label="FEeval", URL=<.html#FEeval>, fillcolor="#F070D1"] ; +PosDef_Pos_succ [label="succ", URL=, fillcolor="#F070D1"] ; +_Fcons2 [label="Fcons2", URL=<.html#Fcons2>, fillcolor="#F070D1"] ; +_xI [label="xI", URL=<.html#xI>, fillcolor="#7FAAFF"] ; +_condition [label="condition", URL=<.html#condition>, fillcolor="#F070D1"] ; +Pos_add [label="add", URL=, fillcolor="#F070D1"] ; +Qpower_Qpower_opp [label="Qpower_opp", URL=, fillcolor="#7FFFD4"] ; +Pos_succ [label="succ", URL=, fillcolor="#F070D1"] ; +Qfield_Qfield_lemma5 [label="Qfield_lemma5", URL=, fillcolor="#7FFFD4"] ; +Z_abs [label="abs", URL=, fillcolor="#F070D1"] ; +Qpower_Qpower_plus [label="Qpower_plus", URL=, fillcolor="#7FFFD4"] ; +_num [label="num", URL=<.html#num>, fillcolor="#F070D1"] ; +Z_lt [label="lt", URL=, fillcolor="#F070D1"] ; +QArith_base_Qminus [label="Qminus", URL=, fillcolor="#F070D1"] ; +_Fapp [label="Fapp", URL=<.html#Fapp>, fillcolor="#F070D1"] ; +_linear [label="linear", URL=<.html#linear>, fillcolor="#E2CDFA"] ; +QArith_base_Qopp [label="Qopp", URL=, fillcolor="#F070D1"] ; +_FEX [label="FEX", URL=<.html#FEX>, fillcolor="#7FAAFF"] ; +QArith_base_Qplus [label="Qplus", URL=, fillcolor="#F070D1"] ; +_FEmul [label="FEmul", URL=<.html#FEmul>, fillcolor="#7FAAFF"] ; +Z_add [label="add", URL=, fillcolor="#F070D1"] ; +_FEinv [label="FEinv", URL=<.html#FEinv>, fillcolor="#7FAAFF"] ; +Z_pos_sub [label="pos_sub", URL=, fillcolor="#F070D1"] ; +_FEdiv [label="FEdiv", URL=<.html#FEdiv>, fillcolor="#7FAAFF"] ; +PosDef_Pos_pred_double [label="pred_double", URL=, fillcolor="#F070D1"] ; +_mk_linear [label="mk_linear", URL=<.html#mk_linear>, fillcolor="#7FAAFF"] ; +Z_pred_double [label="pred_double", URL=, fillcolor="#F070D1"] ; +Z_double [label="double", URL=, fillcolor="#F070D1"] ; +Qpower_Qpower_plus_positive [label="Qpower_plus_positive", URL=, fillcolor="#7FFFD4"] ; +Z_succ_double [label="succ_double", URL=, fillcolor="#F070D1"] ; +QArith_base_Qinv_mult_distr [label="Qinv_mult_distr", URL=, fillcolor="#7FFFD4"] ; +Z_opp [label="opp", URL=, fillcolor="#F070D1"] ; +Qfield_Qfield_ring_lemma1 [label="Qfield_ring_lemma1", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_isLowerCut [label="isLowerCut", URL=, fillcolor="#F070D1"] ; +Qpower_Qpower_minus_positive [label="Qpower_minus_positive", URL=, fillcolor="#7FFFD4"] ; +_sig [label="sig", URL=<.html#sig>, fillcolor="#E2CDFA"] ; +QArith_base_Qinv_comp [label="Qinv_comp", URL=, fillcolor="#7FFFD4"] ; +_FEc [label="FEc", URL=<.html#FEc>, fillcolor="#7FAAFF"] ; +_not [label="not", URL=<.html#not>, fillcolor="#F070D1"] ; +QArith_base_Qle [label="Qle", URL=, fillcolor="#F070D1"] ; +QArith_base_Qdiv_comp [label="Qdiv_comp", URL=, fillcolor="#7FFFD4"] ; +_or [label="or", URL=<.html#or>, fillcolor="#E2CDFA"] ; +QArith_base_Qeq_dec [label="Qeq_dec", URL=, fillcolor="#F070D1"] ; +_False [label="False", URL=<.html#False>, fillcolor="#E2CDFA"] ; +QArith_base_Qpower_positive_comp [label="Qpower_positive_comp", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_positive_0 [label="Qpower_positive_0", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_CReal_of_DReal_cauchy [label="CReal_of_DReal_cauchy", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qeq_eq_bool [label="Qeq_eq_bool", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_CReal_of_DReal_bound [label="CReal_of_DReal_bound", URL=, fillcolor="#7FFFD4"] ; +_Pcond_simpl_complete [label="Pcond_simpl_complete", URL=<.html#Pcond_simpl_complete>, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_CReal_of_DReal_scale [label="CReal_of_DReal_scale", URL=, fillcolor="#F070D1"] ; +_F2AF [label="F2AF", URL=<.html#F2AF>, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_CReal_of_DReal_seq [label="CReal_of_DReal_seq", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_mkCReal [label="mkCReal", URL=, fillcolor="#7FAAFF"] ; +_Finv_l [label="Finv_l", URL=<.html#Finv_l>, fillcolor="#7FFFD4"] ; +_proj1_sig [label="proj1_sig", URL=<.html#proj1_sig>, fillcolor="#F070D1"] ; +_F_1_neq_0 [label="F_1_neq_0", URL=<.html#F_1_neq_0>, fillcolor="#7FFFD4"] ; +Nat_pow [label="pow", URL=, fillcolor="#F070D1"] ; +_Fdiv_def [label="Fdiv_def", URL=<.html#Fdiv_def>, fillcolor="#7FFFD4"] ; +_almost_field_theory [label="almost_field_theory", URL=<.html#almost_field_theory>, fillcolor="#E2CDFA"] ; +ClassicalDedekindReals_DRealQlimExp2 [label="DRealQlimExp2", URL=, fillcolor="#F070D1"] ; +_mk_afield [label="mk_afield", URL=<.html#mk_afield>, fillcolor="#7FAAFF"] ; +Z_to_nat [label="to_nat", URL=, fillcolor="#F070D1"] ; +Pos_of_nat [label="of_nat", URL=, fillcolor="#F070D1"] ; +_AF_AR [label="AF_AR", URL=<.html#AF_AR>, fillcolor="#7FFFD4"] ; +_O [label="O", URL=<.html#O>, fillcolor="#7FAAFF"] ; +_AFinv_l [label="AFinv_l", URL=<.html#AFinv_l>, fillcolor="#7FFFD4"] ; +_S [label="S", URL=<.html#S>, fillcolor="#7FAAFF"] ; +_PFcons2_fcons_inv [label="PFcons2_fcons_inv", URL=<.html#PFcons2_fcons_inv>, fillcolor="#7FFFD4"] ; +_nat [label="nat", URL=<.html#nat>, fillcolor="#E2CDFA"] ; +_fcons_ok [label="fcons_ok", URL=<.html#fcons_ok>, fillcolor="#7FFFD4"] ; +PosDef_Pos_to_nat [label="to_nat", URL=, fillcolor="#F070D1"] ; +Setoid_Seq_sym [label="Seq_sym", URL=, fillcolor="#7FFFD4"] ; +PosDef_Pos_iter_op [label="iter_op", URL=, fillcolor="#F070D1"] ; +_ARopp_zero [label="ARopp_zero", URL=<.html#ARopp_zero>, fillcolor="#7FFFD4"] ; +Init_Nat_add [label="add", URL=, fillcolor="#F070D1"] ; +Setoid_Seq_trans [label="Seq_trans", URL=, fillcolor="#7FFFD4"] ; +Nat_succ_pred_pos [label="succ_pred_pos", URL=, fillcolor="#7FFFD4"] ; +_AF_1_neq_0 [label="AF_1_neq_0", URL=<.html#AF_1_neq_0>, fillcolor="#7FFFD4"] ; +_PEsimp_ok [label="PEsimp_ok", URL=<.html#PEsimp_ok>, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_DRealQlim [label="DRealQlim", URL=, fillcolor="#F070D1"] ; +Nat_pred [label="pred", URL=, fillcolor="#F070D1"] ; +_PFcons1_fcons_inv [label="PFcons1_fcons_inv", URL=<.html#PFcons1_fcons_inv>, fillcolor="#7FFFD4"] ; +_Fcons1 [label="Fcons1", URL=<.html#Fcons1>, fillcolor="#F070D1"] ; +_False_ind [label="False_ind", URL=<.html#False_ind>, fillcolor="#7FFFD4"] ; +_lt [label="lt", URL=<.html#lt>, fillcolor="#F070D1"] ; +_PEsimp [label="PEsimp", URL=<.html#PEsimp>, fillcolor="#F070D1"] ; +_eq_ind [label="eq_ind", URL=<.html#eq_ind>, fillcolor="#7FFFD4"] ; +_NPEadd [label="NPEadd", URL=<.html#NPEadd>, fillcolor="#F070D1"] ; +Nat_neq_0_lt_0 [label="neq_0_lt_0", URL=, fillcolor="#7FFFD4"] ; +_NPEmul [label="NPEmul", URL=<.html#NPEmul>, fillcolor="#F070D1"] ; +Nat_pow_nonzero [label="pow_nonzero", URL=, fillcolor="#7FFFD4"] ; +_NPEopp [label="NPEopp", URL=<.html#NPEopp>, fillcolor="#F070D1"] ; +_True [label="True", URL=<.html#True>, fillcolor="#E2CDFA"] ; +_NPEpow [label="NPEpow", URL=<.html#NPEpow>, fillcolor="#F070D1"] ; +_eq_refl [label="eq_refl", URL=<.html#eq_refl>, fillcolor="#7FAAFF"] ; +_NPEsub [label="NPEsub", URL=<.html#NPEsub>, fillcolor="#F070D1"] ; +_I [label="I", URL=<.html#I>, fillcolor="#7FAAFF"] ; +N_eqb [label="eqb", URL=, fillcolor="#F070D1"] ; +_exist [label="exist", URL=<.html#exist>, fillcolor="#7FAAFF"] ; +_Fcons0 [label="Fcons0", URL=<.html#Fcons0>, fillcolor="#F070D1"] ; +Nat_le_0_l [label="le_0_l", URL=, fillcolor="#7FFFD4"] ; +_absurd_PCond [label="absurd_PCond", URL=<.html#absurd_PCond>, fillcolor="#F070D1"] ; +Nat_Private_NZPow_pow_nonzero [label="pow_nonzero", URL=, fillcolor="#7FFFD4"] ; +_field_is_integral_domain [label="field_is_integral_domain", URL=<.html#field_is_integral_domain>, fillcolor="#7FFFD4"] ; +_ropp_neq_0 [label="ropp_neq_0", URL=<.html#ropp_neq_0>, fillcolor="#7FFFD4"] ; +Nat_Private_NZPow_pow_eq_0 [label="pow_eq_0", URL=, fillcolor="#7FFFD4"] ; +_le [label="le", URL=<.html#le>, fillcolor="#E2CDFA"] ; +_PFcons0_fcons_inv [label="PFcons0_fcons_inv", URL=<.html#PFcons0_fcons_inv>, fillcolor="#7FFFD4"] ; +Nat_le_ind [label="le_ind", URL=, fillcolor="#7FFFD4"] ; +_ceqb_spec_ [label="ceqb_spec'", URL=<.html#ceqb_spec'>, fillcolor="#F070D1"] ; +Nat_lt_0_1 [label="lt_0_1", URL=, fillcolor="#7FFFD4"] ; +_absurd_PCond_bottom [label="absurd_PCond_bottom", URL=<.html#absurd_PCond_bottom>, fillcolor="#7FFFD4"] ; +Field_theory_ropp_ext_Proper [label="ropp_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_1_2 [label="lt_1_2", URL=, fillcolor="#7FFFD4"] ; +Nat_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +_PEpow_nz [label="PEpow_nz", URL=<.html#PEpow_nz>, fillcolor="#7FFFD4"] ; +_pow_pos_nz [label="pow_pos_nz", URL=<.html#pow_pos_nz>, fillcolor="#7FFFD4"] ; +Nat_eq_mul_0 [label="eq_mul_0", URL=, fillcolor="#7FFFD4"] ; +Basics_flip [label="flip", URL=, fillcolor="#F070D1"] ; +_PCond_cons [label="PCond_cons", URL=<.html#PCond_cons>, fillcolor="#7FFFD4"] ; +Field_theory_rmul_ext_Proper [label="rmul_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +Basics_impl [label="impl", URL=, fillcolor="#F070D1"] ; +Nat_Private_OrderTac_Tac_eq_lt [label="eq_lt", URL=, fillcolor="#7FFFD4"] ; +_PEsub_ext [label="PEsub_ext", URL=<.html#PEsub_ext>, fillcolor="#7FFFD4"] ; +Morphisms_subrelation_proper [label="subrelation_proper", URL=, fillcolor="#7FFFD4"] ; +_PEadd_ext [label="PEadd_ext", URL=<.html#PEadd_ext>, fillcolor="#7FFFD4"] ; +Nat_pow_wd [label="pow_wd", URL=, fillcolor="#7FFFD4"] ; +_NPEadd_ok [label="NPEadd_ok", URL=<.html#NPEadd_ok>, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_lt_eq [label="lt_eq", URL=, fillcolor="#7FFFD4"] ; +_NPEequiv [label="NPEequiv", URL=<.html#NPEequiv>, fillcolor="#F070D1"] ; +Morphisms_reflexive_reflexive_proxy [label="reflexive_reflexive_proxy", URL=, fillcolor="#7FFFD4"] ; +_NPEmul_ok [label="NPEmul_ok", URL=<.html#NPEmul_ok>, fillcolor="#7FFFD4"] ; +Morphisms_subrelation_refl [label="subrelation_refl", URL=, fillcolor="#7FFFD4"] ; +_NPEopp_ok [label="NPEopp_ok", URL=<.html#NPEopp_ok>, fillcolor="#7FFFD4"] ; +Nat_mul [label="mul", URL=, fillcolor="#F070D1"] ; +_NPEpow_ok [label="NPEpow_ok", URL=<.html#NPEpow_ok>, fillcolor="#7FFFD4"] ; +Morphisms_Reflexive_partial_app_morphism [label="Reflexive_partial_app_morphism", URL=, fillcolor="#7FFFD4"] ; +_NPEsub_ok [label="NPEsub_ok", URL=<.html#NPEsub_ok>, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +_NPEequiv_eq [label="NPEequiv_eq", URL=<.html#NPEequiv_eq>, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_eq_sym [label="eq_sym", URL=, fillcolor="#7FFFD4"] ; +_PEmul_ext [label="PEmul_ext", URL=<.html#PEmul_ext>, fillcolor="#7FFFD4"] ; +_iff [label="iff", URL=<.html#iff>, fillcolor="#F070D1"] ; +_PEopp_ext [label="PEopp_ext", URL=<.html#PEopp_ext>, fillcolor="#7FFFD4"] ; +Morphisms_Proper [label="Proper", URL=, fillcolor="#F070D1"] ; +_PEpow_ext [label="PEpow_ext", URL=<.html#PEpow_ext>, fillcolor="#7FFFD4"] ; +_pow_N_ext [label="pow_N_ext", URL=<.html#pow_N_ext>, fillcolor="#7FFFD4"] ; +Morphisms_PER_morphism [label="PER_morphism", URL=, fillcolor="#7FFFD4"] ; +Morphisms_respectful [label="respectful", URL=, fillcolor="#F070D1"] ; +_pow_ext [label="pow_ext", URL=<.html#pow_ext>, fillcolor="#7FFFD4"] ; +Morphisms_trans_co_eq_inv_impl_morphism [label="trans_co_eq_inv_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +_NPEeval_ext [label="NPEeval_ext", URL=<.html#NPEeval_ext>, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_not_neq_eq [label="not_neq_eq", URL=, fillcolor="#7FFFD4"] ; +_ceqb_spec [label="ceqb_spec", URL=<.html#ceqb_spec>, fillcolor="#7FFFD4"] ; +_rsub_0_l [label="rsub_0_l", URL=<.html#rsub_0_l>, fillcolor="#7FFFD4"] ; +RelationClasses_reflexivity [label="reflexivity", URL=, fillcolor="#7FFFD4"] ; +_rsub_0_r [label="rsub_0_r", URL=<.html#rsub_0_r>, fillcolor="#7FFFD4"] ; +Morphisms_eq_proper_proxy [label="eq_proper_proxy", URL=, fillcolor="#7FFFD4"] ; +Field_theory_rsub_ext_Proper [label="rsub_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_iff_Transitive [label="iff_Transitive", URL=, fillcolor="#7FFFD4"] ; +_Rring_ring_lemma1 [label="Rring_ring_lemma1", URL=<.html#Rring_ring_lemma1>, fillcolor="#7FFFD4"] ; +RelationClasses_Equivalence_PER [label="Equivalence_PER", URL=, fillcolor="#7FFFD4"] ; +Field_theory_radd_ext_Proper [label="radd_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_iff_Reflexive [label="iff_Reflexive", URL=, fillcolor="#7FFFD4"] ; +Morphisms_iff_flip_impl_subrelation [label="iff_flip_impl_subrelation", URL=, fillcolor="#7FFFD4"] ; +N_div_eucl [label="div_eucl", URL=, fillcolor="#F070D1"] ; +Morphisms_reflexive_proper_proxy [label="reflexive_proper_proxy", URL=, fillcolor="#7FFFD4"] ; +_Nopp [label="Nopp", URL=<.html#Nopp>, fillcolor="#F070D1"] ; +Morphisms_Prop_iff_iff_iff_impl_morphism [label="iff_iff_iff_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +_Nsub [label="Nsub", URL=<.html#Nsub>, fillcolor="#F070D1"] ; +Nat_pow_succ_r [label="pow_succ_r", URL=, fillcolor="#7FFFD4"] ; +_SRsub [label="SRsub", URL=<.html#SRsub>, fillcolor="#F070D1"] ; +Nat_pow_0_r [label="pow_0_r", URL=, fillcolor="#7FFFD4"] ; +_SRopp [label="SRopp", URL=<.html#SRopp>, fillcolor="#F070D1"] ; +_gen_phiN_morph [label="gen_phiN_morph", URL=<.html#gen_phiN_morph>, fillcolor="#7FFFD4"] ; +RelationClasses_Equivalence_Reflexive [label="Equivalence_Reflexive", URL=, fillcolor="#7FFFD4"] ; +Morphisms_subrelation_respectful [label="subrelation_respectful", URL=, fillcolor="#7FFFD4"] ; +_gen_phiN [label="gen_phiN", URL=<.html#gen_phiN>, fillcolor="#F070D1"] ; +_tt [label="tt", URL=<.html#tt>, fillcolor="#7FAAFF"] ; +_SRth_ARth [label="SRth_ARth", URL=<.html#SRth_ARth>, fillcolor="#7FFFD4"] ; +Relation_Definitions_relation [label="relation", URL=, fillcolor="#F070D1"] ; +_ARth_SRth [label="ARth_SRth", URL=<.html#ARth_SRth>, fillcolor="#7FFFD4"] ; +RelationClasses_subrelation [label="subrelation", URL=, fillcolor="#F070D1"] ; +_SReqe_Reqe [label="SReqe_Reqe", URL=<.html#SReqe_Reqe>, fillcolor="#7FFFD4"] ; +RelationClasses_Reflexive [label="Reflexive", URL=, fillcolor="#F070D1"] ; +_Ntriv_div_th [label="Ntriv_div_th", URL=<.html#Ntriv_div_th>, fillcolor="#7FFFD4"] ; +_mk_seqe [label="mk_seqe", URL=<.html#mk_seqe>, fillcolor="#7FAAFF"] ; +RelationClasses_Equivalence [label="Equivalence", URL=, fillcolor="#E2CDFA"] ; +N_mul_comm [label="mul_comm", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_Symmetric [label="Symmetric", URL=, fillcolor="#F070D1"] ; +N_div_eucl_spec [label="div_eucl_spec", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_Transitive [label="Transitive", URL=, fillcolor="#F070D1"] ; +Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 [label="iff_iff_iff_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +N_add_cancel_r [label="add_cancel_r", URL=, fillcolor="#7FFFD4"] ; +N_mul_0_l [label="mul_0_l", URL=, fillcolor="#7FFFD4"] ; +_and_ind [label="and_ind", URL=<.html#and_ind>, fillcolor="#7FFFD4"] ; +_conj [label="conj", URL=<.html#conj>, fillcolor="#7FAAFF"] ; +N_mul_0_r [label="mul_0_r", URL=, fillcolor="#7FFFD4"] ; +N_mul_wd [label="mul_wd", URL=, fillcolor="#7FFFD4"] ; +Morphisms_ReflexiveProxy [label="ReflexiveProxy", URL=, fillcolor="#F070D1"] ; +N_mul_succ_l [label="mul_succ_l", URL=, fillcolor="#7FFFD4"] ; +Morphisms_ProperProxy [label="ProperProxy", URL=, fillcolor="#F070D1"] ; +N_mul_succ_r [label="mul_succ_r", URL=, fillcolor="#7FFFD4"] ; +_iff_refl [label="iff_refl", URL=<.html#iff_refl>, fillcolor="#7FFFD4"] ; +N_add_cancel_l [label="add_cancel_l", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_Equivalence_Transitive [label="Equivalence_Transitive", URL=, fillcolor="#7FFFD4"] ; +_SRmul_ext [label="SRmul_ext", URL=<.html#SRmul_ext>, fillcolor="#7FFFD4"] ; +RelationClasses_Equivalence_Symmetric [label="Equivalence_Symmetric", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_PER [label="PER", URL=, fillcolor="#E2CDFA"] ; +_SRopp_ext [label="SRopp_ext", URL=<.html#SRopp_ext>, fillcolor="#7FFFD4"] ; +RelationClasses_Build_PER [label="Build_PER", URL=, fillcolor="#7FAAFF"] ; +_SRadd_ext [label="SRadd_ext", URL=<.html#SRadd_ext>, fillcolor="#7FFFD4"] ; +_sring_eq_ext [label="sring_eq_ext", URL=<.html#sring_eq_ext>, fillcolor="#E2CDFA"] ; +_iff_trans [label="iff_trans", URL=<.html#iff_trans>, fillcolor="#7FFFD4"] ; +_semi_ring_theory [label="semi_ring_theory", URL=<.html#semi_ring_theory>, fillcolor="#E2CDFA"] ; +Nat_Private_OrderTac_IsTotal_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +_mk_srt [label="mk_srt", URL=<.html#mk_srt>, fillcolor="#7FAAFF"] ; +Nat_Private_OrderTac_IsTotal_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_IsTotal_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +_SRmul_0_l [label="SRmul_0_l", URL=<.html#SRmul_0_l>, fillcolor="#7FFFD4"] ; +Morphisms_iff_impl_subrelation [label="iff_impl_subrelation", URL=, fillcolor="#7FFFD4"] ; +_SRmul_1_l [label="SRmul_1_l", URL=<.html#SRmul_1_l>, fillcolor="#7FFFD4"] ; +Nat_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +_SRopp_add [label="SRopp_add", URL=<.html#SRopp_add>, fillcolor="#7FFFD4"] ; +Nat_lt_wd [label="lt_wd", URL=, fillcolor="#7FFFD4"] ; +_SRopp_mul_l [label="SRopp_mul_l", URL=<.html#SRopp_mul_l>, fillcolor="#7FFFD4"] ; +PeanoNat_Nat_lt_wd_obligation_1 [label="lt_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_SRadd_assoc [label="SRadd_assoc", URL=<.html#SRadd_assoc>, fillcolor="#7FFFD4"] ; +_eq_ind_r [label="eq_ind_r", URL=<.html#eq_ind_r>, fillcolor="#7FFFD4"] ; +_SRsub_def [label="SRsub_def", URL=<.html#SRsub_def>, fillcolor="#7FFFD4"] ; +_eq_sym [label="eq_sym", URL=<.html#eq_sym>, fillcolor="#7FFFD4"] ; +_SRadd_0_l [label="SRadd_0_l", URL=<.html#SRadd_0_l>, fillcolor="#7FFFD4"] ; +Nat_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +_SRmul_assoc [label="SRmul_assoc", URL=<.html#SRmul_assoc>, fillcolor="#7FFFD4"] ; +Nat_lt_trichotomy [label="lt_trichotomy", URL=, fillcolor="#7FFFD4"] ; +_SRdistr_l [label="SRdistr_l", URL=<.html#SRdistr_l>, fillcolor="#7FFFD4"] ; +_or_ind [label="or_ind", URL=<.html#or_ind>, fillcolor="#7FFFD4"] ; +_SRmul_comm [label="SRmul_comm", URL=<.html#SRmul_comm>, fillcolor="#7FFFD4"] ; +Nat_le_gt_cases [label="le_gt_cases", URL=, fillcolor="#7FFFD4"] ; +_SRadd_comm [label="SRadd_comm", URL=<.html#SRadd_comm>, fillcolor="#7FFFD4"] ; +Nat_lt_eq_cases [label="lt_eq_cases", URL=, fillcolor="#7FFFD4"] ; +_gen_phiN_add [label="gen_phiN_add", URL=<.html#gen_phiN_add>, fillcolor="#7FFFD4"] ; +Morphisms_Prop_or_iff_morphism [label="or_iff_morphism", URL=, fillcolor="#7FFFD4"] ; +_gen_phiN_sub [label="gen_phiN_sub", URL=<.html#gen_phiN_sub>, fillcolor="#7FFFD4"] ; +_or_introl [label="or_introl", URL=<.html#or_introl>, fillcolor="#7FAAFF"] ; +_R_setoid4_Reflexive [label="R_setoid4_Reflexive", URL=<.html#R_setoid4_Reflexive>, fillcolor="#7FFFD4"] ; +_or_intror [label="or_intror", URL=<.html#or_intror>, fillcolor="#7FAAFF"] ; +N_eqb_eq [label="eqb_eq", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Prop_or_iff_morphism_obligation_1 [label="or_iff_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_gen_phiN_mult [label="gen_phiN_mult", URL=<.html#gen_phiN_mult>, fillcolor="#7FFFD4"] ; +RelationClasses_iff_equivalence [label="iff_equivalence", URL=, fillcolor="#7FFFD4"] ; +_gen_phiN1 [label="gen_phiN1", URL=<.html#gen_phiN1>, fillcolor="#F070D1"] ; +Morphisms_trans_sym_co_inv_impl_morphism [label="trans_sym_co_inv_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +_R_setoid4 [label="R_setoid4", URL=<.html#R_setoid4>, fillcolor="#7FFFD4"] ; +_same_genN [label="same_genN", URL=<.html#same_genN>, fillcolor="#7FFFD4"] ; +RelationClasses_iff_Symmetric [label="iff_Symmetric", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_symmetry [label="symmetry", URL=, fillcolor="#7FFFD4"] ; +_R_setoid4_Transitive [label="R_setoid4_Transitive", URL=<.html#R_setoid4_Transitive>, fillcolor="#7FFFD4"] ; +_rmul_ext4_Proper [label="rmul_ext4_Proper", URL=<.html#rmul_ext4_Proper>, fillcolor="#7FFFD4"] ; +Nat_compare [label="compare", URL=, fillcolor="#F070D1"] ; +_radd_ext4_Proper [label="radd_ext4_Proper", URL=<.html#radd_ext4_Proper>, fillcolor="#7FFFD4"] ; +Nat_compare_eq_iff [label="compare_eq_iff", URL=, fillcolor="#7FFFD4"] ; +Pos_eqb_spec [label="eqb_spec", URL=, fillcolor="#F070D1"] ; +Nat_compare_le_iff [label="compare_le_iff", URL=, fillcolor="#7FFFD4"] ; +_pow_pos_0 [label="pow_pos_0", URL=<.html#pow_pos_0>, fillcolor="#7FFFD4"] ; +Nat_compare_lt_iff [label="compare_lt_iff", URL=, fillcolor="#7FFFD4"] ; +_pow_pos_1 [label="pow_pos_1", URL=<.html#pow_pos_1>, fillcolor="#7FFFD4"] ; +_nat_ind [label="nat_ind", URL=<.html#nat_ind>, fillcolor="#7FFFD4"] ; +_pow_pos_cst [label="pow_pos_cst", URL=<.html#pow_pos_cst>, fillcolor="#7FFFD4"] ; +_le_0_n [label="le_0_n", URL=<.html#le_0_n>, fillcolor="#7FFFD4"] ; +_le_S_n [label="le_S_n", URL=<.html#le_S_n>, fillcolor="#7FFFD4"] ; +N_eqb_spec [label="eqb_spec", URL=, fillcolor="#F070D1"] ; +_pow_pos_mul_l [label="pow_pos_mul_l", URL=<.html#pow_pos_mul_l>, fillcolor="#7FFFD4"] ; +_le_n_S [label="le_n_S", URL=<.html#le_n_S>, fillcolor="#7FFFD4"] ; +_le_ind [label="le_ind", URL=<.html#le_ind>, fillcolor="#7FFFD4"] ; +QArith_base_Qinv_involutive [label="Qinv_involutive", URL=, fillcolor="#7FFFD4"] ; +_le_n [label="le_n", URL=<.html#le_n>, fillcolor="#7FAAFF"] ; +_FExpr [label="FExpr", URL=<.html#FExpr>, fillcolor="#E2CDFA"] ; +_le_S [label="le_S", URL=<.html#le_S>, fillcolor="#7FAAFF"] ; +_Field_correct [label="Field_correct", URL=<.html#Field_correct>, fillcolor="#7FFFD4"] ; +_le_pred [label="le_pred", URL=<.html#le_pred>, fillcolor="#7FFFD4"] ; +_AFdiv_def [label="AFdiv_def", URL=<.html#AFdiv_def>, fillcolor="#7FFFD4"] ; +Init_Nat_pred [label="pred", URL=, fillcolor="#F070D1"] ; +_Fnorm_crossproduct [label="Fnorm_crossproduct", URL=<.html#Fnorm_crossproduct>, fillcolor="#7FFFD4"] ; +_f_equal_nat [label="f_equal_nat", URL=<.html#f_equal_nat>, fillcolor="#7FFFD4"] ; +_Pcond_Fnorm [label="Pcond_Fnorm", URL=<.html#Pcond_Fnorm>, fillcolor="#7FFFD4"] ; +_eq_add_S [label="eq_add_S", URL=<.html#eq_add_S>, fillcolor="#7FFFD4"] ; +_cross_product_eq [label="cross_product_eq", URL=<.html#cross_product_eq>, fillcolor="#7FFFD4"] ; +_f_equal [label="f_equal", URL=<.html#f_equal>, fillcolor="#7FFFD4"] ; +_Fnorm_FEeval_PEeval [label="Fnorm_FEeval_PEeval", URL=<.html#Fnorm_FEeval_PEeval>, fillcolor="#7FFFD4"] ; +_iff_sym [label="iff_sym", URL=<.html#iff_sym>, fillcolor="#7FFFD4"] ; +_PCond_app [label="PCond_app", URL=<.html#PCond_app>, fillcolor="#7FFFD4"] ; +Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 [label="trans_sym_co_inv_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_and_assoc [label="and_assoc", URL=<.html#and_assoc>, fillcolor="#7FFFD4"] ; +_rdiv1 [label="rdiv1", URL=<.html#rdiv1>, fillcolor="#7FFFD4"] ; +RelationClasses_PER_Symmetric [label="PER_Symmetric", URL=, fillcolor="#7FFFD4"] ; +_rdiv5 [label="rdiv5", URL=<.html#rdiv5>, fillcolor="#7FFFD4"] ; +RelationClasses_PER_Transitive [label="PER_Transitive", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_transitivity [label="transitivity", URL=, fillcolor="#7FFFD4"] ; +_rdiv6 [label="rdiv6", URL=<.html#rdiv6>, fillcolor="#7FFFD4"] ; +RelationClasses_Build_Equivalence [label="Build_Equivalence", URL=, fillcolor="#7FAAFF"] ; +_split [label="split", URL=<.html#split>, fillcolor="#F070D1"] ; +Nat_lt_succ_r [label="lt_succ_r", URL=, fillcolor="#7FFFD4"] ; +_FExpr_ind [label="FExpr_ind", URL=<.html#FExpr_ind>, fillcolor="#7FFFD4"] ; +_rdiv2b [label="rdiv2b", URL=<.html#rdiv2b>, fillcolor="#7FFFD4"] ; +Nat_le_succ_l [label="le_succ_l", URL=, fillcolor="#7FFFD4"] ; +_rdiv3b [label="rdiv3b", URL=<.html#rdiv3b>, fillcolor="#7FFFD4"] ; +Nat_central_induction [label="central_induction", URL=, fillcolor="#7FFFD4"] ; +_rdiv4b [label="rdiv4b", URL=<.html#rdiv4b>, fillcolor="#7FFFD4"] ; +Nat_le_refl [label="le_refl", URL=, fillcolor="#7FFFD4"] ; +_rdiv7b [label="rdiv7b", URL=<.html#rdiv7b>, fillcolor="#7FFFD4"] ; +Nat_le_wd [label="le_wd", URL=, fillcolor="#7FFFD4"] ; +Nat_succ_wd [label="succ_wd", URL=, fillcolor="#7FFFD4"] ; +_rsplit_common [label="rsplit_common", URL=<.html#rsplit_common>, fillcolor="#F070D1"] ; +PeanoNat_Nat_succ_wd_obligation_1 [label="succ_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_rdiv_ext [label="rdiv_ext", URL=<.html#rdiv_ext>, fillcolor="#7FFFD4"] ; +_rinv_ext_Proper [label="rinv_ext_Proper", URL=<.html#rinv_ext_Proper>, fillcolor="#7FFFD4"] ; +Nat_bi_induction [label="bi_induction", URL=, fillcolor="#7FFFD4"] ; +_split_ok_l [label="split_ok_l", URL=<.html#split_ok_l>, fillcolor="#7FFFD4"] ; +Nat_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +Nat_succ_inj_wd [label="succ_inj_wd", URL=, fillcolor="#7FFFD4"] ; +_split_ok_r [label="split_ok_r", URL=<.html#split_ok_r>, fillcolor="#7FFFD4"] ; +_rsplit_right [label="rsplit_right", URL=<.html#rsplit_right>, fillcolor="#F070D1"] ; +Morphisms_per_partial_app_morphism [label="per_partial_app_morphism", URL=, fillcolor="#7FFFD4"] ; +_rsplit_left [label="rsplit_left", URL=<.html#rsplit_left>, fillcolor="#F070D1"] ; +Nat_nle_succ_diag_l [label="nle_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +_pow_pos_div [label="pow_pos_div", URL=<.html#pow_pos_div>, fillcolor="#7FFFD4"] ; +_or_cancel_r [label="or_cancel_r", URL=<.html#or_cancel_r>, fillcolor="#7FFFD4"] ; +_FEO [label="FEO", URL=<.html#FEO>, fillcolor="#7FAAFF"] ; +_or_iff_compat_r [label="or_iff_compat_r", URL=<.html#or_iff_compat_r>, fillcolor="#7FFFD4"] ; +_FEI [label="FEI", URL=<.html#FEI>, fillcolor="#7FAAFF"] ; +Nat_neq_succ_diag_l [label="neq_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +_FEadd [label="FEadd", URL=<.html#FEadd>, fillcolor="#7FAAFF"] ; +Nat_nlt_succ_diag_l [label="nlt_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +_FEsub [label="FEsub", URL=<.html#FEsub>, fillcolor="#7FAAFF"] ; +Nat_lt_le_incl [label="lt_le_incl", URL=, fillcolor="#7FFFD4"] ; +_FEopp [label="FEopp", URL=<.html#FEopp>, fillcolor="#7FAAFF"] ; +Nat_lt_succ_diag_r [label="lt_succ_diag_r", URL=, fillcolor="#7FFFD4"] ; +_FEpow [label="FEpow", URL=<.html#FEpow>, fillcolor="#7FAAFF"] ; +Morphisms_per_partial_app_morphism_obligation_1 [label="per_partial_app_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Nat_succ_inj [label="succ_inj", URL=, fillcolor="#7FFFD4"] ; +_rdiv4 [label="rdiv4", URL=<.html#rdiv4>, fillcolor="#7FFFD4"] ; +Morphisms_trans_co_impl_morphism [label="trans_co_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +_rmul_reg_l [label="rmul_reg_l", URL=<.html#rmul_reg_l>, fillcolor="#7FFFD4"] ; +_rdiv_simpl [label="rdiv_simpl", URL=<.html#rdiv_simpl>, fillcolor="#7FFFD4"] ; +Nat_pred_succ [label="pred_succ", URL=, fillcolor="#7FFFD4"] ; +_rsplit [label="rsplit", URL=<.html#rsplit>, fillcolor="#E2CDFA"] ; +Nat_pred_wd [label="pred_wd", URL=, fillcolor="#7FFFD4"] ; +_split_aux [label="split_aux", URL=<.html#split_aux>, fillcolor="#F070D1"] ; +PeanoNat_Nat_pred_wd_obligation_1 [label="pred_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Morphisms_trans_co_impl_morphism_obligation_1 [label="trans_co_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_split_aux_ok [label="split_aux_ok", URL=<.html#split_aux_ok>, fillcolor="#7FFFD4"] ; +Nat_compare_refl [label="compare_refl", URL=, fillcolor="#7FFFD4"] ; +_PE_1_r [label="PE_1_r", URL=<.html#PE_1_r>, fillcolor="#7FFFD4"] ; +_split_aux_ok1 [label="split_aux_ok1", URL=<.html#split_aux_ok1>, fillcolor="#7FFFD4"] ; +Morphisms_Prop_not_iff_morphism [label="not_iff_morphism", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Prop_not_iff_morphism_obligation_1 [label="not_iff_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_PEpow_mul_l [label="PEpow_mul_l", URL=<.html#PEpow_mul_l>, fillcolor="#7FFFD4"] ; +Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 [label="trans_co_eq_inv_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_PEpow_mul_r [label="PEpow_mul_r", URL=<.html#PEpow_mul_r>, fillcolor="#7FFFD4"] ; +_PEpow_0_r [label="PEpow_0_r", URL=<.html#PEpow_0_r>, fillcolor="#7FFFD4"] ; +Morphisms_PER_morphism_obligation_1 [label="PER_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_StrictOrder_Irreflexive [label="StrictOrder_Irreflexive", URL=, fillcolor="#7FFFD4"] ; +_PEpow_1_l [label="PEpow_1_l", URL=<.html#PEpow_1_l>, fillcolor="#7FFFD4"] ; +_mk_rsplit [label="mk_rsplit", URL=<.html#mk_rsplit>, fillcolor="#7FAAFF"] ; +Nat_Private_OrderTac_IsTotal_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +_pow_pos_mul_r [label="pow_pos_mul_r", URL=<.html#pow_pos_mul_r>, fillcolor="#7FFFD4"] ; +Nat_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_StrictOrder [label="StrictOrder", URL=, fillcolor="#E2CDFA"] ; +_pow_pos_add_r [label="pow_pos_add_r", URL=<.html#pow_pos_add_r>, fillcolor="#7FFFD4"] ; +Field_theory_rmul_ext [label="rmul_ext", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_Irreflexive [label="Irreflexive", URL=, fillcolor="#F070D1"] ; +RelationClasses_complement [label="complement", URL=, fillcolor="#F070D1"] ; +_PE_1_l [label="PE_1_l", URL=<.html#PE_1_l>, fillcolor="#7FFFD4"] ; +Nat_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +_Z_pos_sub_gt [label="Z_pos_sub_gt", URL=<.html#Z_pos_sub_gt>, fillcolor="#7FFFD4"] ; +RelationClasses_Build_StrictOrder [label="Build_StrictOrder", URL=, fillcolor="#7FAAFF"] ; +_PEpow_add_r [label="PEpow_add_r", URL=<.html#PEpow_add_r>, fillcolor="#7FFFD4"] ; +_isIn_ok [label="isIn_ok", URL=<.html#isIn_ok>, fillcolor="#7FFFD4"] ; +Morphisms_impl_pars [label="impl_pars", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_asymm [label="lt_asymm", URL=, fillcolor="#7FFFD4"] ; +_PEpow_1_r [label="PEpow_1_r", URL=<.html#PEpow_1_r>, fillcolor="#7FFFD4"] ; +Morphisms_Params [label="Params", URL=, fillcolor="#E2CDFA"] ; +_NtoZ [label="NtoZ", URL=<.html#NtoZ>, fillcolor="#F070D1"] ; +Morphisms_Build_Params [label="Build_Params", URL=, fillcolor="#7FAAFF"] ; +_ZtoN [label="ZtoN", URL=<.html#ZtoN>, fillcolor="#F070D1"] ; +_isIn [label="isIn", URL=<.html#isIn>, fillcolor="#F070D1"] ; +Nat_add [label="add", URL=, fillcolor="#F070D1"] ; +Nat_Private_OrderTac_Tac_trans [label="trans", URL=, fillcolor="#7FFFD4"] ; +_default_isIn [label="default_isIn", URL=<.html#default_isIn>, fillcolor="#F070D1"] ; +OrdersTac_OEQ [label="OEQ", URL=, fillcolor="#7FAAFF"] ; +_PExpr_eq [label="PExpr_eq", URL=<.html#PExpr_eq>, fillcolor="#F070D1"] ; +OrdersTac_OLT [label="OLT", URL=, fillcolor="#7FAAFF"] ; +_default_isIn_ok [label="default_isIn_ok", URL=<.html#default_isIn_ok>, fillcolor="#7FFFD4"] ; +RelationClasses_StrictOrder_Transitive [label="StrictOrder_Transitive", URL=, fillcolor="#7FFFD4"] ; +_PExpr_eq_spec [label="PExpr_eq_spec", URL=<.html#PExpr_eq_spec>, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_IsTotal_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +_PExpr_eq_semi_ok [label="PExpr_eq_semi_ok", URL=<.html#PExpr_eq_semi_ok>, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_interp_ord [label="interp_ord", URL=, fillcolor="#F070D1"] ; +_if_true [label="if_true", URL=<.html#if_true>, fillcolor="#7FFFD4"] ; +OrdersTac_trans_ord [label="trans_ord", URL=, fillcolor="#F070D1"] ; +_rdiv7 [label="rdiv7", URL=<.html#rdiv7>, fillcolor="#7FFFD4"] ; +OrdersTac_ord [label="ord", URL=, fillcolor="#E2CDFA"] ; +_rdiv_r_r [label="rdiv_r_r", URL=<.html#rdiv_r_r>, fillcolor="#7FFFD4"] ; +OrdersTac_OLE [label="OLE", URL=, fillcolor="#7FAAFF"] ; +Field_theory_radd_ext [label="radd_ext", URL=, fillcolor="#7FFFD4"] ; +_split_nz_l [label="split_nz_l", URL=<.html#split_nz_l>, fillcolor="#7FFFD4"] ; +Nat_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +_split_nz_r [label="split_nz_r", URL=<.html#split_nz_r>, fillcolor="#7FFFD4"] ; +PeanoNat_Nat_pow_wd_obligation_1 [label="pow_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +ZifyClasses_mkinj [label="mkinj", URL=, fillcolor="#7FAAFF"] ; +Init_Unconvertible [label="Unconvertible", URL=, fillcolor="#F070D1"] ; +_unit [label="unit", URL=<.html#unit>, fillcolor="#E2CDFA"] ; +_Z_gt_le_dec [label="Z_gt_le_dec", URL=<.html#Z_gt_le_dec>, fillcolor="#F070D1"] ; +Nat_lt_neq [label="lt_neq", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_CReal_of_DReal_seq_max_prec_1 [label="CReal_of_DReal_seq_max_prec_1", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_wd [label="mul_wd", URL=, fillcolor="#7FFFD4"] ; +_Z_gt_dec [label="Z_gt_dec", URL=<.html#Z_gt_dec>, fillcolor="#F070D1"] ; +Nat_mul_neg_neg [label="mul_neg_neg", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qle_minus_iff [label="Qle_minus_iff", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_neg_pos [label="mul_neg_pos", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_wd [label="Qabs_wd", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_0_l [label="mul_0_l", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_triangle [label="Qabs_triangle", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_0_r [label="mul_0_r", URL=, fillcolor="#7FFFD4"] ; +Z_abs_mul [label="abs_mul", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_pos_neg [label="mul_pos_neg", URL=, fillcolor="#7FFFD4"] ; +Z_abs_triangle [label="abs_triangle", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_pos_pos [label="mul_pos_pos", URL=, fillcolor="#7FFFD4"] ; +Z_abs_eq [label="abs_eq", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_lt_mono_pos_r [label="mul_lt_mono_pos_r", URL=, fillcolor="#7FFFD4"] ; +Z_add_nonpos_nonpos [label="add_nonpos_nonpos", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_lt_mono_pos_l [label="mul_lt_mono_pos_l", URL=, fillcolor="#7FFFD4"] ; +Z_abs_neq [label="abs_neq", URL=, fillcolor="#7FFFD4"] ; +Z_opp_nonpos_nonneg [label="opp_nonpos_nonneg", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_comm [label="mul_comm", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_succ_l [label="mul_succ_l", URL=, fillcolor="#7FFFD4"] ; +Z_abs_wd [label="abs_wd", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_succ_r [label="mul_succ_r", URL=, fillcolor="#7FFFD4"] ; +Z_abs_opp [label="abs_opp", URL=, fillcolor="#7FFFD4"] ; +Z_eq_refl [label="eq_refl", URL=, fillcolor="#7FFFD4"] ; +Nat_add_cancel_r [label="add_cancel_r", URL=, fillcolor="#7FFFD4"] ; +Z_mul_nonneg_nonpos [label="mul_nonneg_nonpos", URL=, fillcolor="#7FFFD4"] ; +Nat_add_comm [label="add_comm", URL=, fillcolor="#7FFFD4"] ; +Z_mul_opp_opp [label="mul_opp_opp", URL=, fillcolor="#7FFFD4"] ; +Nat_add_cancel_l [label="add_cancel_l", URL=, fillcolor="#7FFFD4"] ; +Z_mul_le_mono_nonpos_r [label="mul_le_mono_nonpos_r", URL=, fillcolor="#7FFFD4"] ; +Nat_add_wd [label="add_wd", URL=, fillcolor="#7FFFD4"] ; +Z_mul_le_mono_nonpos_l [label="mul_le_mono_nonpos_l", URL=, fillcolor="#7FFFD4"] ; +Nat_add_succ_l [label="add_succ_l", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_eq_le [label="eq_le", URL=, fillcolor="#7FFFD4"] ; +Nat_add_0_l [label="add_0_l", URL=, fillcolor="#7FFFD4"] ; +PeanoNat_Nat_add_wd_obligation_1 [label="add_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_wd_Proper [label="Qabs_wd_Proper", URL=, fillcolor="#7FFFD4"] ; +Nat_add_succ_r [label="add_succ_r", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_Qpower_2_invneg_le_pow [label="Qpower_2_invneg_le_pow", URL=, fillcolor="#7FFFD4"] ; +Nat_add_0_r [label="add_0_r", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_case [label="Qabs_case", URL=, fillcolor="#F070D1"] ; +Nat_add_assoc [label="add_assoc", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qlt_le_trans [label="Qlt_le_trans", URL=, fillcolor="#7FFFD4"] ; +_plus_n_Sm [label="plus_n_Sm", URL=<.html#plus_n_Sm>, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_UpperAboveLower [label="UpperAboveLower", URL=, fillcolor="#7FFFD4"] ; +_eq_trans [label="eq_trans", URL=<.html#eq_trans>, fillcolor="#7FFFD4"] ; +Qpower_Qpower_le_compat_l [label="Qpower_le_compat_l", URL=, fillcolor="#7FFFD4"] ; +_plus_n_O [label="plus_n_O", URL=<.html#plus_n_O>, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_le_l [label="Qmult_le_l", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_ind [label="lt_ind", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_1_le [label="Qpower_1_le", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_1_le_pos [label="Qpower_1_le_pos", URL=, fillcolor="#7FFFD4"] ; +Pos2Z_neg_is_neg [label="neg_is_neg", URL=, fillcolor="#7FFFD4"] ; +Nat_add_lt_mono [label="add_lt_mono", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Prop_all_iff_morphism [label="all_iff_morphism", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_le_1_compat [label="Qmult_le_1_compat", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_not_ge_lt [label="not_ge_lt", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_le_r [label="Qmult_le_r", URL=, fillcolor="#7FFFD4"] ; +_all [label="all", URL=<.html#all>, fillcolor="#F070D1"] ; +QArith_base_Qmult_le_compat_r [label="Qmult_le_compat_r", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Prop_all_iff_morphism_obligation_1 [label="all_iff_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_case_subproof [label="Qabs_case_subproof", URL=, fillcolor="#7FFFD4"] ; +Morphisms_pointwise_relation [label="pointwise_relation", URL=, fillcolor="#F070D1"] ; +Qabs_Qabs_case_subproof0 [label="Qabs_case_subproof0", URL=, fillcolor="#7FFFD4"] ; +Nat_add_lt_mono_l [label="add_lt_mono_l", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_case_subproof1 [label="Qabs_case_subproof1", URL=, fillcolor="#7FFFD4"] ; +Z2Nat_id [label="id", URL=, fillcolor="#7FFFD4"] ; +Nat_add_lt_mono_r [label="add_lt_mono_r", URL=, fillcolor="#7FFFD4"] ; +Nat_succ_lt_mono [label="succ_lt_mono", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv [label="Qpower_2_neg_eq_natpow_inv", URL=, fillcolor="#7FFFD4"] ; +Nat_right_induction [label="right_induction", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_frac_l [label="Qmult_frac_l", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_exists_pred [label="lt_exists_pred", URL=, fillcolor="#7FFFD4"] ; +Nat2Pos_inj_mul [label="inj_mul", URL=, fillcolor="#7FFFD4"] ; +Nat_strong_right_induction [label="strong_right_induction", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_minus_pos [label="Qpower_minus_pos", URL=, fillcolor="#7FFFD4"] ; +_ex [label="ex", URL=<.html#ex>, fillcolor="#E2CDFA"] ; +Nat_pow_succ_r_ [label="pow_succ_r'", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_le_lt_trans [label="le_lt_trans", URL=, fillcolor="#7FFFD4"] ; +Nat2Z_inj_succ [label="inj_succ", URL=, fillcolor="#7FFFD4"] ; +_well_founded_induction [label="well_founded_induction", URL=<.html#well_founded_induction>, fillcolor="#F070D1"] ; +QArith_base_Qinv_pos [label="Qinv_pos", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_not_gt_le [label="not_gt_le", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qpower_comp [label="Qpower_comp", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_wf [label="lt_wf", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qinv_power [label="Qinv_power", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qinv_power_positive [label="Qinv_power_positive", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Prop_Acc_pt_morphism [label="Acc_pt_morphism", URL=, fillcolor="#7FFFD4"] ; +_well_founded [label="well_founded", URL=<.html#well_founded>, fillcolor="#F070D1"] ; +Z2N_id [label="id", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_lt_succ_r [label="lt_lt_succ_r", URL=, fillcolor="#7FFFD4"] ; +_Z_N_nat [label="Z_N_nat", URL=<.html#Z_N_nat>, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_seq [label="seq", URL=, fillcolor="#F070D1"] ; +Nat_Rlt_wd [label="Rlt_wd", URL=, fillcolor="#7FFFD4"] ; +_inbetween [label="inbetween", URL=<.html#inbetween>, fillcolor="#E2CDFA"] ; +_Acc [label="Acc", URL=<.html#Acc>, fillcolor="#E2CDFA"] ; +_Float [label="Float", URL=<.html#Float>, fillcolor="#7FAAFF"] ; +_Acc_intro [label="Acc_intro", URL=<.html#Acc_intro>, fillcolor="#7FAAFF"] ; +Morphisms_Prop_and_iff_morphism [label="and_iff_morphism", URL=, fillcolor="#7FFFD4"] ; +_Rcompare [label="Rcompare", URL=<.html#Rcompare>, fillcolor="#F070D1"] ; +Morphisms_Prop_and_iff_morphism_obligation_1 [label="and_iff_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_Rplus [label="Rplus", URL=<.html#Rplus>, fillcolor="#F070D1"] ; +SpecFloat_loc_Exact [label="loc_Exact", URL=, fillcolor="#7FAAFF"] ; +_Acc_inv [label="Acc_inv", URL=<.html#Acc_inv>, fillcolor="#7FFFD4"] ; +SpecFloat_loc_Inexact [label="loc_Inexact", URL=, fillcolor="#7FAAFF"] ; +Morphisms_proper_sym_impl_iff [label="proper_sym_impl_iff", URL=, fillcolor="#7FFFD4"] ; +_well_founded_induction_type [label="well_founded_induction_type", URL=<.html#well_founded_induction_type>, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CReal_plus [label="CReal_plus", URL=, fillcolor="#F070D1"] ; +_Rabst [label="Rabst", URL=<.html#Rabst>, fillcolor="#F070D1"] ; +_Acc_rect [label="Acc_rect", URL=<.html#Acc_rect>, fillcolor="#F070D1"] ; +Nat_le_preorder [label="le_preorder", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_DRealAbstr [label="DRealAbstr", URL=, fillcolor="#F070D1"] ; +QArith_base_Qlt_le_dec [label="Qlt_le_dec", URL=, fillcolor="#F070D1"] ; +RelationClasses_PreOrder_Reflexive [label="PreOrder_Reflexive", URL=, fillcolor="#7FFFD4"] ; +Nat_le_le_succ_r [label="le_le_succ_r", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_DRealAbstr_aux [label="DRealAbstr_aux", URL=, fillcolor="#7FFFD4"] ; +Nat_le_succ_r [label="le_succ_r", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_red_seq [label="CReal_red_seq", URL=, fillcolor="#7FFFD4"] ; +_ex_intro [label="ex_intro", URL=<.html#ex_intro>, fillcolor="#7FAAFF"] ; +CMorphisms_reflexive_proper_proxy [label="reflexive_proper_proxy", URL=, fillcolor="#F070D1"] ; +RelationClasses_PreOrder [label="PreOrder", URL=, fillcolor="#E2CDFA"] ; +Qfield_Qfield_field_lemma2 [label="Qfield_field_lemma2", URL=, fillcolor="#7FFFD4"] ; +CMorphisms_subrelation_respectful [label="subrelation_respectful", URL=, fillcolor="#F070D1"] ; +Nat_le_trans [label="le_trans", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_Build_PreOrder [label="Build_PreOrder", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyReals_inject_Q [label="inject_Q", URL=, fillcolor="#F070D1"] ; +CMorphisms_subrelation_proper [label="subrelation_proper", URL=, fillcolor="#F070D1"] ; +Nat_mul_lt_mono_neg_r [label="mul_lt_mono_neg_r", URL=, fillcolor="#7FFFD4"] ; +Nat_mul_lt_mono_neg_l [label="mul_lt_mono_neg_l", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealLt_asym [label="CRealLt_asym", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_succ_l [label="lt_succ_l", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_inject_Q_plus [label="inject_Q_plus", URL=, fillcolor="#7FFFD4"] ; +Nat_order_induction_0 [label="order_induction_0", URL=, fillcolor="#7FFFD4"] ; +QExtra_Qbound_ltabs_ZExp2 [label="Qbound_ltabs_ZExp2", URL=, fillcolor="#F070D1"] ; +Nat_mul_lt_pred [label="mul_lt_pred", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealLt_morph [label="CRealLt_morph", URL=, fillcolor="#F070D1"] ; +Nat_le_lt_add_lt [label="le_lt_add_lt", URL=, fillcolor="#7FFFD4"] ; +CMorphisms_iffT_arrow_subrelation [label="iffT_arrow_subrelation", URL=, fillcolor="#F070D1"] ; +CMorphisms_subrelation_refl [label="subrelation_refl", URL=, fillcolor="#F070D1"] ; +Nat_nlt_ge [label="nlt_ge", URL=, fillcolor="#7FFFD4"] ; +Nat_add_le_mono [label="add_le_mono", URL=, fillcolor="#7FFFD4"] ; +ConstructiveRcomplete_Rfloor [label="Rfloor", URL=, fillcolor="#F070D1"] ; +CRelationClasses_iffT [label="iffT", URL=, fillcolor="#F070D1"] ; +Nat_add_le_mono_l [label="add_le_mono_l", URL=, fillcolor="#7FFFD4"] ; +CRelationClasses_arrow [label="arrow", URL=, fillcolor="#F070D1"] ; +Nat_add_le_mono_r [label="add_le_mono_r", URL=, fillcolor="#7FFFD4"] ; +Nat_succ_le_mono [label="succ_le_mono", URL=, fillcolor="#7FFFD4"] ; +_display_pow_linear [label="display_pow_linear", URL=<.html#display_pow_linear>, fillcolor="#F070D1"] ; +Nat_order_induction [label="order_induction", URL=, fillcolor="#7FFFD4"] ; +CMorphisms_Reflexive_partial_app_morphism [label="Reflexive_partial_app_morphism", URL=, fillcolor="#F070D1"] ; +Nat_left_induction [label="left_induction", URL=, fillcolor="#7FFFD4"] ; +_eq_rec [label="eq_rec", URL=<.html#eq_rec>, fillcolor="#F070D1"] ; +Nat_strong_left_induction [label="strong_left_induction", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_inject_Q_cauchy [label="inject_Q_cauchy", URL=, fillcolor="#7FFFD4"] ; +Nat_eq_le_incl [label="eq_le_incl", URL=, fillcolor="#7FFFD4"] ; +CRelationClasses_Equivalence_Symmetric [label="Equivalence_Symmetric", URL=, fillcolor="#F070D1"] ; +Nat_gt_wf [label="gt_wf", URL=, fillcolor="#7FFFD4"] ; +QExtra_Qbound_ltabs_ZExp2_spec [label="Qbound_ltabs_ZExp2_spec", URL=, fillcolor="#7FFFD4"] ; +CRelationClasses_symmetry [label="symmetry", URL=, fillcolor="#F070D1"] ; +Nat_Rgt_wd [label="Rgt_wd", URL=, fillcolor="#7FFFD4"] ; +Init_Nat_mul [label="mul", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CRealLe_not_lt [label="CRealLe_not_lt", URL=, fillcolor="#7FFFD4"] ; +PeanoNat_Nat_mul_wd_obligation_1 [label="mul_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qinv_minus_distr [label="Qinv_minus_distr", URL=, fillcolor="#7FFFD4"] ; +CMorphisms_respectful [label="respectful", URL=, fillcolor="#F070D1"] ; +RelationClasses_eq_equivalence [label="eq_equivalence", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_eq_Reflexive [label="eq_Reflexive", URL=, fillcolor="#7FFFD4"] ; +CRelationClasses_Equivalence_Reflexive [label="Equivalence_Reflexive", URL=, fillcolor="#F070D1"] ; +RelationClasses_eq_Transitive [label="eq_Transitive", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealEq [label="CRealEq", URL=, fillcolor="#F070D1"] ; +RelationClasses_eq_Symmetric [label="eq_Symmetric", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealLe [label="CRealLe", URL=, fillcolor="#F070D1"] ; +Nat_two_succ [label="two_succ", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealLt [label="CRealLt", URL=, fillcolor="#F070D1"] ; +Nat_one_succ [label="one_succ", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qminus_comp [label="Qminus_comp", URL=, fillcolor="#7FFFD4"] ; +Nat_neq_succ_0 [label="neq_succ_0", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealEq_relT [label="CRealEq_relT", URL=, fillcolor="#F070D1"] ; +Nat_pred_0 [label="pred_0", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_Qpower_2_neg_le_one [label="Qpower_2_neg_le_one", URL=, fillcolor="#7FFFD4"] ; +_sigT [label="sigT", URL=<.html#sigT>, fillcolor="#E2CDFA"] ; +Nat_lt_0_succ [label="lt_0_succ", URL=, fillcolor="#7FFFD4"] ; +Nat_case_analysis [label="case_analysis", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealEq_sym [label="CRealEq_sym", URL=, fillcolor="#7FFFD4"] ; +Nat_induction [label="induction", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealEq_trans [label="CRealEq_trans", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Pphi_pow [label="Pphi_pow", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CRealEq_refl [label="CRealEq_refl", URL=, fillcolor="#7FFFD4"] ; +CRelationClasses_Equivalence [label="Equivalence", URL=, fillcolor="#E2CDFA"] ; +Qfield_Qfield_ring_lemma2 [label="Qfield_ring_lemma2", URL=, fillcolor="#7FFFD4"] ; +CRelationClasses_Build_Equivalence [label="Build_Equivalence", URL=, fillcolor="#7FAAFF"] ; +QArith_base_Qplus_comp [label="Qplus_comp", URL=, fillcolor="#7FFFD4"] ; +CRelationClasses_Reflexive [label="Reflexive", URL=, fillcolor="#F070D1"] ; +QArith_base_Qplus_lt_l [label="Qplus_lt_l", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_lowerCutAbove [label="lowerCutAbove", URL=, fillcolor="#F070D1"] ; +CRelationClasses_Transitive [label="Transitive", URL=, fillcolor="#F070D1"] ; +ClassicalDedekindReals_lowerCutBelow [label="lowerCutBelow", URL=, fillcolor="#F070D1"] ; +CRelationClasses_crelation [label="crelation", URL=, fillcolor="#F070D1"] ; +SetoidTactics_default_relation [label="default_relation", URL=, fillcolor="#F070D1"] ; +CRelationClasses_Symmetric [label="Symmetric", URL=, fillcolor="#F070D1"] ; +ClassicalDedekindReals_DRealQlim_rec [label="DRealQlim_rec", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CRealLe_refl [label="CRealLe_refl", URL=, fillcolor="#7FFFD4"] ; +Z_of_N [label="of_N", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CRealLt_dec [label="CRealLt_dec", URL=, fillcolor="#F070D1"] ; +_sum [label="sum", URL=<.html#sum>, fillcolor="#E2CDFA"] ; +_get_sign_None [label="get_sign_None", URL=<.html#get_sign_None>, fillcolor="#F070D1"] ; +Qminmax_Q_OT_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_cauchy [label="cauchy", URL=, fillcolor="#7FFFD4"] ; +Nat2Z_inj_mul [label="inj_mul", URL=, fillcolor="#7FFFD4"] ; +QExtra_QarchimedeanExp2_Z [label="QarchimedeanExp2_Z", URL=, fillcolor="#F070D1"] ; +Z_min [label="min", URL=, fillcolor="#F070D1"] ; +Qminmax_Q_OT_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +Pos_succ_of_nat [label="succ_of_nat", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_Qlt_condition [label="Qabs_Qlt_condition", URL=, fillcolor="#7FFFD4"] ; +_ring_subst_niter [label="ring_subst_niter", URL=<.html#ring_subst_niter>, fillcolor="#F070D1"] ; +Z_min_spec [label="min_spec", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qinv_lt_contravar [label="Qinv_lt_contravar", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PEeval [label="PEeval", URL=, fillcolor="#F070D1"] ; +_inl [label="inl", URL=<.html#inl>, fillcolor="#7FAAFF"] ; +Pos_to_nat [label="to_nat", URL=, fillcolor="#F070D1"] ; +_inr [label="inr", URL=<.html#inr>, fillcolor="#7FAAFF"] ; +QArith_base_Qlt_le_weak [label="Qlt_le_weak", URL=, fillcolor="#7FFFD4"] ; +_positive_nat_Z [label="positive_nat_Z", URL=<.html#positive_nat_Z>, fillcolor="#7FFFD4"] ; +QArith_base_Qlt_shift_div_r [label="Qlt_shift_div_r", URL=, fillcolor="#7FFFD4"] ; +Z_of_nat [label="of_nat", URL=, fillcolor="#F070D1"] ; +QArith_base_Qmult_lt_l [label="Qmult_lt_l", URL=, fillcolor="#7FFFD4"] ; +SetoidTactics_equivalence_default [label="equivalence_default", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_lt_r [label="Qmult_lt_r", URL=, fillcolor="#7FFFD4"] ; +PosDef_Pos_of_succ_nat [label="of_succ_nat", URL=, fillcolor="#F070D1"] ; +Z_min_l [label="min_l", URL=, fillcolor="#7FFFD4"] ; +_triv_div [label="triv_div", URL=<.html#triv_div>, fillcolor="#F070D1"] ; +Z_min_r [label="min_r", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qle_Qabs [label="Qle_Qabs", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qeq [label="Qeq", URL=, fillcolor="#F070D1"] ; +Qfield_Qopp_opp [label="Qopp_opp", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qarchimedean [label="Qarchimedean", URL=, fillcolor="#F070D1"] ; +Ring_polynom_norm_subst [label="norm_subst", URL=, fillcolor="#F070D1"] ; +QArith_base_Qopp_lt_compat [label="Qopp_lt_compat", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_opp [label="Qabs_opp", URL=, fillcolor="#7FFFD4"] ; +Qminmax_Q_Proper_instance_0 [label="Proper_instance_0", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qopp_le_compat [label="Qopp_le_compat", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qeq_bool [label="Qeq_bool", URL=, fillcolor="#F070D1"] ; +Z_mul_1_r [label="mul_1_r", URL=, fillcolor="#7FFFD4"] ; +CMorphisms_ProperProxy [label="ProperProxy", URL=, fillcolor="#F070D1"] ; +CMorphisms_Proper [label="Proper", URL=, fillcolor="#F070D1"] ; +_IDphi [label="IDphi", URL=<.html#IDphi>, fillcolor="#F070D1"] ; +Ring_polynom_mk_monpol_list [label="mk_monpol_list", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Pphi_dev [label="Pphi_dev", URL=, fillcolor="#F070D1"] ; +Z_mul_comm [label="mul_comm", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CRealRing_ring_lemma2 [label="CRealRing_ring_lemma2", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Mon [label="Mon", URL=, fillcolor="#E2CDFA"] ; +ConstructiveCauchyReals_CReal_minus [label="CReal_minus", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Pol [label="Pol", URL=, fillcolor="#E2CDFA"] ; +CMorphisms_iffT_flip_arrow_subrelation [label="iffT_flip_arrow_subrelation", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PExpr [label="PExpr", URL=, fillcolor="#E2CDFA"] ; +ConstructiveCauchyReals_inject_Z [label="inject_Z", URL=, fillcolor="#F070D1"] ; +_list [label="list", URL=<.html#list>, fillcolor="#E2CDFA"] ; +CRelationClasses_flip [label="flip", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Pc [label="Pc", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyReals_CReal_opp [label="CReal_opp", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Pinj [label="Pinj", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyRealsMult_CRealArchimedean [label="CRealArchimedean", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PX [label="PX", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyReals_CReal_plus_morph_T [label="CReal_plus_morph_T", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PEX [label="PEX", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyReals_opp_inject_Q [label="opp_inject_Q", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PEadd [label="PEadd", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyRealsMult_CReal_mult [label="CReal_mult", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PEsub [label="PEsub", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyReals_CReal_plus_comm [label="CReal_plus_comm", URL=, fillcolor="#7FFFD4"] ; +_nil [label="nil", URL=<.html#nil>, fillcolor="#7FAAFF"] ; +ConstructiveCauchyReals_inject_Q_morph_T [label="inject_Q_morph_T", URL=, fillcolor="#F070D1"] ; +_cons [label="cons", URL=<.html#cons>, fillcolor="#7FAAFF"] ; +ConstructiveCauchyReals_CReal_plus_lt_reg_r [label="CReal_plus_lt_reg_r", URL=, fillcolor="#F070D1"] ; +_existT [label="existT", URL=<.html#existT>, fillcolor="#7FAAFF"] ; +_N [label="N", URL=<.html#N>, fillcolor="#E2CDFA"] ; +Z_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_plus_lt_reg_l [label="CReal_plus_lt_reg_l", URL=, fillcolor="#F070D1"] ; +Z_mul_wd [label="mul_wd", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_plus_bound [label="CReal_plus_bound", URL=, fillcolor="#7FFFD4"] ; +Z_mul_succ_l [label="mul_succ_l", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_plus_scale [label="CReal_plus_scale", URL=, fillcolor="#F070D1"] ; +Z_mul_succ_r [label="mul_succ_r", URL=, fillcolor="#7FFFD4"] ; +Qreduction_Qred_correct [label="Qred_correct", URL=, fillcolor="#7FFFD4"] ; +Z_succ [label="succ", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CReal_plus_cauchy [label="CReal_plus_cauchy", URL=, fillcolor="#7FFFD4"] ; +Z_bi_induction [label="bi_induction", URL=, fillcolor="#7FFFD4"] ; +Qreduction_Qred [label="Qred", URL=, fillcolor="#F070D1"] ; +Z_to_pos [label="to_pos", URL=, fillcolor="#F070D1"] ; +Z_add_cancel_r [label="add_cancel_r", URL=, fillcolor="#7FFFD4"] ; +Z_mul_0_l [label="mul_0_l", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_plus_seq [label="CReal_plus_seq", URL=, fillcolor="#F070D1"] ; +Z_mul_0_r [label="mul_0_r", URL=, fillcolor="#7FFFD4"] ; +Z2Pos_id [label="id", URL=, fillcolor="#7FFFD4"] ; +Z_mul_pos_cancel_l [label="mul_pos_cancel_l", URL=, fillcolor="#7FFFD4"] ; +Z_add_0_r [label="add_0_r", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_scale [label="scale", URL=, fillcolor="#F070D1"] ; +Z_add_wd [label="add_wd", URL=, fillcolor="#7FFFD4"] ; +Z_succ_inj_wd [label="succ_inj_wd", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_bound [label="bound", URL=, fillcolor="#7FFFD4"] ; +Z_add_succ_l [label="add_succ_l", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealEq_diff [label="CRealEq_diff", URL=, fillcolor="#7FFFD4"] ; +Z_add_0_l [label="add_0_l", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_Qle_condition [label="Qabs_Qle_condition", URL=, fillcolor="#7FFFD4"] ; +Z_Private_BootStrap_add_assoc [label="add_assoc", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_mult_seq [label="CReal_mult_seq", URL=, fillcolor="#F070D1"] ; +Z_Private_BootStrap_add_comm [label="add_comm", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_mult_bound [label="CReal_mult_bound", URL=, fillcolor="#7FFFD4"] ; +Pos_add_comm [label="add_comm", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_mult_scale [label="CReal_mult_scale", URL=, fillcolor="#F070D1"] ; +_positive_ind [label="positive_ind", URL=<.html#positive_ind>, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_mult_cauchy [label="CReal_mult_cauchy", URL=, fillcolor="#7FFFD4"] ; +PosDef_Pos_add_carry [label="add_carry", URL=, fillcolor="#F070D1"] ; +Qabs_Qabs_nonneg [label="Qabs_nonneg", URL=, fillcolor="#7FFFD4"] ; +Pos_add_carry_spec [label="add_carry_spec", URL=, fillcolor="#7FFFD4"] ; +Qpower_Qpower_0_r [label="Qpower_0_r", URL=, fillcolor="#7FFFD4"] ; +Pos_add_carry [label="add_carry", URL=, fillcolor="#F070D1"] ; +Qabs_Qabs_Qmult [label="Qabs_Qmult", URL=, fillcolor="#7FFFD4"] ; +Z_Private_BootStrap_opp_inj [label="opp_inj", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_lt_compat_nonneg [label="Qmult_lt_compat_nonneg", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_impl_Reflexive [label="impl_Reflexive", URL=, fillcolor="#7FFFD4"] ; +Z_Private_BootStrap_add_assoc_pos [label="add_assoc_pos", URL=, fillcolor="#7FFFD4"] ; +Z_Private_BootStrap_opp_add_distr [label="opp_add_distr", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_inverse_impl_rewrite_relation [label="inverse_impl_rewrite_relation", URL=, fillcolor="#7FFFD4"] ; +Z_pos_sub_opp [label="pos_sub_opp", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_flip_Reflexive [label="flip_Reflexive", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_impl_Reflexive_obligation_1 [label="impl_Reflexive_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Pos_add_assoc [label="add_assoc", URL=, fillcolor="#7FFFD4"] ; +Z_Private_BootStrap_pos_sub_add [label="pos_sub_add", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_plus_proper_r [label="CReal_plus_proper_r", URL=, fillcolor="#7FFFD4"] ; +Z_Private_BootStrap_add_0_r [label="add_0_r", URL=, fillcolor="#7FFFD4"] ; +Qround_Qlt_floor [label="Qlt_floor", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_gt [label="lt_gt", URL=, fillcolor="#7FFFD4"] ; +QArith_base_inject_Z [label="inject_Z", URL=, fillcolor="#F070D1"] ; +_eq_rec_r [label="eq_rec_r", URL=<.html#eq_rec_r>, fillcolor="#F070D1"] ; +Pos_add_compare_mono_r [label="add_compare_mono_r", URL=, fillcolor="#7FFFD4"] ; +Pos_add_sub_assoc [label="add_sub_assoc", URL=, fillcolor="#7FFFD4"] ; +Qround_Qfloor_le [label="Qfloor_le", URL=, fillcolor="#7FFFD4"] ; +PosDef_Pos_sub [label="sub", URL=, fillcolor="#F070D1"] ; +Qround_Qfloor [label="Qfloor", URL=, fillcolor="#F070D1"] ; +Pos_sub_add_distr [label="sub_add_distr", URL=, fillcolor="#7FFFD4"] ; +Z_lt_add_lt_sub_r [label="lt_add_lt_sub_r", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_add_r [label="lt_add_r", URL=, fillcolor="#7FFFD4"] ; +_Z_div_mod_eq_full [label="Z_div_mod_eq_full", URL=<.html#Z_div_mod_eq_full>, fillcolor="#7FFFD4"] ; +Z_sub_lt_mono_r [label="sub_lt_mono_r", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_equivalence_rewrite_relation [label="equivalence_rewrite_relation", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_opp_bound [label="CReal_opp_bound", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_add [label="sub_add", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_opp_scale [label="CReal_opp_scale", URL=, fillcolor="#F070D1"] ; +Morphisms_rewrite_relation_eq_dom [label="rewrite_relation_eq_dom", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_opp_cauchy [label="CReal_opp_cauchy", URL=, fillcolor="#7FFFD4"] ; +Pos_add_sub [label="add_sub", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_opp_seq [label="CReal_opp_seq", URL=, fillcolor="#F070D1"] ; +CRelationClasses_subrelation [label="subrelation", URL=, fillcolor="#F070D1"] ; +Pos_add_lt_mono_r [label="add_lt_mono_r", URL=, fillcolor="#7FFFD4"] ; +Morphisms_reflexive_proper [label="reflexive_proper", URL=, fillcolor="#7FFFD4"] ; +_prod_rect [label="prod_rect", URL=<.html#prod_rect>, fillcolor="#F070D1"] ; +Pos_compare_spec [label="compare_spec", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealEq_rel_Symmetric [label="CRealEq_rel_Symmetric", URL=, fillcolor="#7FFFD4"] ; +Pos_compare [label="compare", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyRealsMult_CReal_isRing [label="CReal_isRing", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_sub_distr [label="sub_sub_distr", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealEq_rel_Reflexive [label="CRealEq_rel_Reflexive", URL=, fillcolor="#7FFFD4"] ; +Morphisms_reflexive_eq_dom_reflexive [label="reflexive_eq_dom_reflexive", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_plus_morph_Proper [label="CReal_plus_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +Z_pos_sub_spec [label="pos_sub_spec", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_mult_morph_Proper [label="CReal_mult_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +Pos_gt [label="gt", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CRealEq_rel_Transitive [label="CRealEq_rel_Transitive", URL=, fillcolor="#7FFFD4"] ; +Pos_lt [label="lt", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyRealsMult_CReal_opp_morph_Proper [label="CReal_opp_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +_CompareSpec [label="CompareSpec", URL=<.html#CompareSpec>, fillcolor="#E2CDFA"] ; +Ring_polynom_ring_rw_correct [label="ring_rw_correct", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_RewriteRelation [label="RewriteRelation", URL=, fillcolor="#E2CDFA"] ; +Ring_polynom_Pphi_dev_ok [label="Pphi_dev_ok", URL=, fillcolor="#7FFFD4"] ; +Pos_sub [label="sub", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkmult_pow [label="mkmult_pow", URL=, fillcolor="#F070D1"] ; +Pos_sub_mask_diag [label="sub_mask_diag", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mkmult_pow_ok [label="mkmult_pow_ok", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_mask [label="sub_mask", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkpow [label="mkpow", URL=, fillcolor="#F070D1"] ; +Pos_pred_double [label="pred_double", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkopp_pow [label="mkopp_pow", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkopp_pow_ok [label="mkopp_pow_ok", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_xI_xI [label="compare_xI_xI", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mkpow_ok [label="mkpow_ok", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_xI_xO [label="compare_xI_xO", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_xO_xI [label="compare_xO_xI", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_isRingExt [label="CReal_isRingExt", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_xO_xO [label="compare_xO_xO", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_plus_morph [label="CReal_plus_morph", URL=, fillcolor="#7FFFD4"] ; +Pos_succ_double_mask [label="succ_double_mask", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CReal_plus_opp_r [label="CReal_plus_opp_r", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_xI_xI [label="sub_xI_xI", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_plus_eq_reg_l [label="CReal_plus_eq_reg_l", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_xI_xO [label="sub_xI_xO", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_mult_proper_l [label="CReal_mult_proper_l", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_xO_xI [label="sub_xO_xI", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_mult_comm [label="CReal_mult_comm", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_xO_xO [label="sub_xO_xO", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_plus_opp_l [label="CReal_plus_opp_l", URL=, fillcolor="#7FFFD4"] ; +Pos_switch_Eq [label="switch_Eq", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CRealEq_rel [label="CRealEq_rel", URL=, fillcolor="#7FFFD4"] ; +Pos_mask [label="mask", URL=, fillcolor="#E2CDFA"] ; +ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l [label="CReal_mult_plus_distr_l", URL=, fillcolor="#7FFFD4"] ; +Pos_IsNul [label="IsNul", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyRealsMult_CReal_opp_mult_distr_r [label="CReal_opp_mult_distr_r", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_mask_pos [label="sub_mask_pos", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_mult_proper_0_l [label="CReal_mult_proper_0_l", URL=, fillcolor="#7FFFD4"] ; +Pos_double_mask [label="double_mask", URL=, fillcolor="#F070D1"] ; +QArith_base_Qmult_le_compat_nonneg [label="Qmult_le_compat_nonneg", URL=, fillcolor="#7FFFD4"] ; +Pos_IsPos [label="IsPos", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyRealsMult_Weaken_Qle_QpowerFac [label="Weaken_Qle_QpowerFac", URL=, fillcolor="#7FFFD4"] ; +Pos_IsNeg [label="IsNeg", URL=, fillcolor="#7FAAFF"] ; +RelationClasses_PreOrder_Transitive [label="PreOrder_Transitive", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_mask_pos_ [label="sub_mask_pos'", URL=, fillcolor="#7FFFD4"] ; +Z_Proper_instance_0 [label="Proper_instance_0", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_iff_add [label="lt_iff_add", URL=, fillcolor="#7FFFD4"] ; +Z_Private_Tac_eq_le [label="eq_le", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_mask_pos_iff [label="sub_mask_pos_iff", URL=, fillcolor="#7FFFD4"] ; +Z_Private_Tac_eq_lt [label="eq_lt", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_mask_add_diag_l [label="sub_mask_add_diag_l", URL=, fillcolor="#7FFFD4"] ; +Z_Private_Tac_le_eq [label="le_eq", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_mask_add [label="sub_mask_add", URL=, fillcolor="#7FFFD4"] ; +Z_Private_Tac_lt_eq [label="lt_eq", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_mask_spec [label="sub_mask_spec", URL=, fillcolor="#7FFFD4"] ; +Z_Private_Tac_le_lt_trans [label="le_lt_trans", URL=, fillcolor="#7FFFD4"] ; +Pos_SubMaskSpec [label="SubMaskSpec", URL=, fillcolor="#E2CDFA"] ; +Z_Private_Tac_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +PosDef_Pos_IsNul [label="IsNul", URL=, fillcolor="#7FAAFF"] ; +Z_Private_Tac_eq_sym [label="eq_sym", URL=, fillcolor="#7FFFD4"] ; +PosDef_Pos_IsNeg [label="IsNeg", URL=, fillcolor="#7FAAFF"] ; +Z_Private_Tac_not_gt_le [label="not_gt_le", URL=, fillcolor="#7FFFD4"] ; +Z_Private_Tac_trans [label="trans", URL=, fillcolor="#7FFFD4"] ; +Pos_add_xI_pred_double [label="add_xI_pred_double", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_mask_carry_spec [label="sub_mask_carry_spec", URL=, fillcolor="#7FFFD4"] ; +Z_Private_Tac_interp_ord [label="interp_ord", URL=, fillcolor="#F070D1"] ; +Pos_succ_pred_double [label="succ_pred_double", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_Weaken_Qle_QpowerAddExp [label="Weaken_Qle_QpowerAddExp", URL=, fillcolor="#7FFFD4"] ; +Z_max_comm [label="max_comm", URL=, fillcolor="#7FFFD4"] ; +Pos_add_succ_r [label="add_succ_r", URL=, fillcolor="#7FFFD4"] ; +Pos_add_1_l [label="add_1_l", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_red_scale [label="CReal_red_scale", URL=, fillcolor="#7FFFD4"] ; +Z_Private_Tac_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +Pos_add_1_r [label="add_1_r", URL=, fillcolor="#7FFFD4"] ; +Pos_pred_mask [label="pred_mask", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CReal_plus_lt_compat_l [label="CReal_plus_lt_compat_l", URL=, fillcolor="#F070D1"] ; +Pos_sub_mask_carry [label="sub_mask_carry", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CRealLt_above [label="CRealLt_above", URL=, fillcolor="#F070D1"] ; +Pos_SubIsNul [label="SubIsNul", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyReals_CRealLt_aboveSig_ [label="CRealLt_aboveSig'", URL=, fillcolor="#7FFFD4"] ; +Pos_SubIsPos [label="SubIsPos", URL=, fillcolor="#7FAAFF"] ; +ConstructiveCauchyReals_CRealLt_aboveSig [label="CRealLt_aboveSig", URL=, fillcolor="#7FFFD4"] ; +Pos_SubIsNeg [label="SubIsNeg", URL=, fillcolor="#7FAAFF"] ; +Z_le_min_l [label="le_min_l", URL=, fillcolor="#7FFFD4"] ; +Pos_double_pred_mask [label="double_pred_mask", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CReal_plus_assoc [label="CReal_plus_assoc", URL=, fillcolor="#7FFFD4"] ; +Pos_pred [label="pred", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CReal_plus_0_l [label="CReal_plus_0_l", URL=, fillcolor="#7FFFD4"] ; +Pos_add_no_neutral [label="add_no_neutral", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_mult_1_l [label="CReal_mult_1_l", URL=, fillcolor="#7FFFD4"] ; +Pos_add_cancel_l [label="add_cancel_l", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_plus_proper_l [label="CReal_plus_proper_l", URL=, fillcolor="#7FFFD4"] ; +Pos_add_reg_l [label="add_reg_l", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_mult_assoc [label="CReal_mult_assoc", URL=, fillcolor="#7FFFD4"] ; +Pos_add_reg_r [label="add_reg_r", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_Weaken_Qle_QpowerRemSubExp [label="Weaken_Qle_QpowerRemSubExp", URL=, fillcolor="#7FFFD4"] ; +Pos_succ_inj [label="succ_inj", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealLt_above_same [label="CRealLt_above_same", URL=, fillcolor="#7FFFD4"] ; +Pos_add_carry_add [label="add_carry_add", URL=, fillcolor="#7FFFD4"] ; +_Field_rw_pow_correct [label="Field_rw_pow_correct", URL=<.html#Field_rw_pow_correct>, fillcolor="#7FFFD4"] ; +_not_eq_sym [label="not_eq_sym", URL=<.html#not_eq_sym>, fillcolor="#7FFFD4"] ; +_Z_lt_le_dec [label="Z_lt_le_dec", URL=<.html#Z_lt_le_dec>, fillcolor="#F070D1"] ; +_total_order_T [label="total_order_T", URL=<.html#total_order_T>, fillcolor="#F070D1"] ; +Pos_succ_not_1 [label="succ_not_1", URL=, fillcolor="#7FFFD4"] ; +Pos_mask2cmp [label="mask2cmp", URL=, fillcolor="#F070D1"] ; +_Rquot1 [label="Rquot1", URL=<.html#Rquot1>, fillcolor="#7FFFD4"] ; +Pos_compare_sub_mask [label="compare_sub_mask", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealLtForget [label="CRealLtForget", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_mask_neg_iff [label="sub_mask_neg_iff", URL=, fillcolor="#7FFFD4"] ; +_Rlt_def [label="Rlt_def", URL=<.html#Rlt_def>, fillcolor="#7FFFD4"] ; +Pos_sub_mask_add_diag_r [label="sub_mask_add_diag_r", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealLt_lpo_dec [label="CRealLt_lpo_dec", URL=, fillcolor="#F070D1"] ; +Pos_compare_cont_spec [label="compare_cont_spec", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qle_not_lt [label="Qle_not_lt", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_cont [label="compare_cont", URL=, fillcolor="#F070D1"] ; +ConstructiveExtra_Z_inj_nat [label="Z_inj_nat", URL=, fillcolor="#F070D1"] ; +Pos_sub_mask_nul_iff [label="sub_mask_nul_iff", URL=, fillcolor="#7FFFD4"] ; +ConstructiveExtra_Z_inj_nat_id [label="Z_inj_nat_id", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_eq_iff [label="compare_eq_iff", URL=, fillcolor="#7FFFD4"] ; +ConstructiveExtra_Z_inj_nat_rev [label="Z_inj_nat_rev", URL=, fillcolor="#F070D1"] ; +Pos2Nat_is_pos [label="is_pos", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_lt_iff [label="compare_lt_iff", URL=, fillcolor="#7FFFD4"] ; +Pos_xI_succ_xO [label="xI_succ_xO", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_antisym [label="compare_antisym", URL=, fillcolor="#7FFFD4"] ; +ConstructiveExtra_Pos_pred_double_inj [label="Pos_pred_double_inj", URL=, fillcolor="#7FFFD4"] ; +_CompOpp_iff [label="CompOpp_iff", URL=<.html#CompOpp_iff>, fillcolor="#7FFFD4"] ; +_CompEq [label="CompEq", URL=<.html#CompEq>, fillcolor="#7FAAFF"] ; +Z_le_ngt [label="le_ngt", URL=, fillcolor="#7FFFD4"] ; +_CompLt [label="CompLt", URL=<.html#CompLt>, fillcolor="#7FAAFF"] ; +ClassicalDedekindReals_DRealQuot1 [label="DRealQuot1", URL=, fillcolor="#7FFFD4"] ; +_CompGt [label="CompGt", URL=<.html#CompGt>, fillcolor="#7FAAFF"] ; +ConstructiveCauchyReals_CReal_le_lt_trans [label="CReal_le_lt_trans", URL=, fillcolor="#F070D1"] ; +ClassicalDedekindReals_DRealReprQ [label="DRealReprQ", URL=, fillcolor="#F070D1"] ; +_CompOpp_involutive [label="CompOpp_involutive", URL=<.html#CompOpp_involutive>, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_DRealReprQup [label="DRealReprQup", URL=, fillcolor="#7FFFD4"] ; +_CompOpp_inj [label="CompOpp_inj", URL=<.html#CompOpp_inj>, fillcolor="#7FFFD4"] ; +Pos_compare_cont_antisym [label="compare_cont_antisym", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_Rle [label="Rle", URL=, fillcolor="#F070D1"] ; +RelationClasses_Build_RewriteRelation [label="Build_RewriteRelation", URL=, fillcolor="#7FAAFF"] ; +ClassicalDedekindReals_Rle_antisym [label="Rle_antisym", URL=, fillcolor="#7FFFD4"] ; +Pos_peano_ind [label="peano_ind", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_isLowerCut_hprop [label="isLowerCut_hprop", URL=, fillcolor="#7FFFD4"] ; +FunctionalExtensionality_functional_extensionality [label="functional_extensionality", URL=, fillcolor="#7FFFD4"] ; +Pos_add_lt_mono_l [label="add_lt_mono_l", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_succ_diag_r [label="lt_succ_diag_r", URL=, fillcolor="#7FFFD4"] ; +FunctionalExtensionality_functional_extensionality_dep [label="functional_extensionality_dep", URL=, fillcolor="#FFB57F"] ; +HLevels_forall_hprop [label="forall_hprop", URL=, fillcolor="#7FFFD4"] ; +Pos_add_compare_mono_l [label="add_compare_mono_l", URL=, fillcolor="#7FFFD4"] ; +Eqdep_dec_eq_proofs_unicity_on [label="eq_proofs_unicity_on", URL=, fillcolor="#7FFFD4"] ; +Pos_add_succ_l [label="add_succ_l", URL=, fillcolor="#7FFFD4"] ; +HLevels_impl_hprop [label="impl_hprop", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_succ_succ [label="compare_succ_succ", URL=, fillcolor="#7FFFD4"] ; +HLevels_not_hprop [label="not_hprop", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_succ_l [label="compare_succ_l", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_succ_r [label="compare_succ_r", URL=, fillcolor="#7FFFD4"] ; +HLevelsBase_and_hprop [label="and_hprop", URL=, fillcolor="#7FFFD4"] ; +Pos_peano_rect [label="peano_rect", URL=, fillcolor="#F070D1"] ; +HLevelsBase_IsHProp [label="IsHProp", URL=, fillcolor="#F070D1"] ; +PosDef_Pos_sub_mask [label="sub_mask", URL=, fillcolor="#F070D1"] ; +Eqdep_dec_nu_constant [label="nu_constant", URL=, fillcolor="#7FFFD4"] ; +PosDef_Pos_mask [label="mask", URL=, fillcolor="#E2CDFA"] ; +Eqdep_dec_nu_left_inv_on [label="nu_left_inv_on", URL=, fillcolor="#7FFFD4"] ; +Eqdep_dec_trans_sym_eq [label="trans_sym_eq", URL=, fillcolor="#7FFFD4"] ; +PosDef_Pos_double_pred_mask [label="double_pred_mask", URL=, fillcolor="#F070D1"] ; +PosDef_Pos_double_mask [label="double_mask", URL=, fillcolor="#F070D1"] ; +ClassicalDedekindReals_DRealOpen [label="DRealOpen", URL=, fillcolor="#F070D1"] ; +PosDef_Pos_succ_double_mask [label="succ_double_mask", URL=, fillcolor="#F070D1"] ; +QExtra_QarchimedeanLowExp2_Z [label="QarchimedeanLowExp2_Z", URL=, fillcolor="#F070D1"] ; +PosDef_Pos_IsPos [label="IsPos", URL=, fillcolor="#7FAAFF"] ; +QExtra_Qlowbound_lt_ZExp2_spec [label="Qlowbound_lt_ZExp2_spec", URL=, fillcolor="#7FFFD4"] ; +Pos_gt_lt_iff [label="gt_lt_iff", URL=, fillcolor="#7FFFD4"] ; +QExtra_Qlowbound_ltabs_ZExp2 [label="Qlowbound_ltabs_ZExp2", URL=, fillcolor="#F070D1"] ; +Z_succ_wd [label="succ_wd", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_pos [label="Qabs_pos", URL=, fillcolor="#7FFFD4"] ; +Z_succ_inj [label="succ_inj", URL=, fillcolor="#7FFFD4"] ; +QExtra_Qlowbound_ltabs_ZExp2_inv [label="Qlowbound_ltabs_ZExp2_inv", URL=, fillcolor="#7FFFD4"] ; +Z_pred [label="pred", URL=, fillcolor="#F070D1"] ; +ZifyInst_Inj_Z_Z [label="Inj_Z_Z", URL=, fillcolor="#F070D1"] ; +Z_pred_succ [label="pred_succ", URL=, fillcolor="#7FFFD4"] ; +Pos2Z_add_pos_neg [label="add_pos_neg", URL=, fillcolor="#7FFFD4"] ; +Z_pred_wd [label="pred_wd", URL=, fillcolor="#7FFFD4"] ; +Pos2Nat_inj_le [label="inj_le", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_lowerUpper [label="lowerUpper", URL=, fillcolor="#7FFFD4"] ; +Z_eq [label="eq", URL=, fillcolor="#F070D1"] ; +Z_Private_BootStrap_add_opp_diag_r [label="add_opp_diag_r", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qlt_minus_iff [label="Qlt_minus_iff", URL=, fillcolor="#7FFFD4"] ; +Z_pos_sub_diag [label="pos_sub_diag", URL=, fillcolor="#7FFFD4"] ; +Z_lt_sub_lt_add_r [label="lt_sub_lt_add_r", URL=, fillcolor="#7FFFD4"] ; +Pos2Nat_inj_compare [label="inj_compare", URL=, fillcolor="#7FFFD4"] ; +Pos_compare_refl [label="compare_refl", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_1_succ [label="lt_1_succ", URL=, fillcolor="#7FFFD4"] ; +Pos_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +Pos_succ_pred_or [label="succ_pred_or", URL=, fillcolor="#7FFFD4"] ; +Z_add_comm [label="add_comm", URL=, fillcolor="#7FFFD4"] ; +Nat_compare_succ [label="compare_succ", URL=, fillcolor="#7FFFD4"] ; +Z_add_cancel_l [label="add_cancel_l", URL=, fillcolor="#7FFFD4"] ; +Pos2Nat_inj_1 [label="inj_1", URL=, fillcolor="#7FFFD4"] ; +Z_add_succ_r [label="add_succ_r", URL=, fillcolor="#7FFFD4"] ; +Z_succ_pred [label="succ_pred", URL=, fillcolor="#7FFFD4"] ; +Nat_compare_gt_iff [label="compare_gt_iff", URL=, fillcolor="#7FFFD4"] ; +Z_peano_ind [label="peano_ind", URL=, fillcolor="#7FFFD4"] ; +Nat_compare_antisym [label="compare_antisym", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_linear_order_T [label="linear_order_T", URL=, fillcolor="#F070D1"] ; +Z_add_assoc [label="add_assoc", URL=, fillcolor="#7FFFD4"] ; +Z_Private_BootStrap_mul_1_l [label="mul_1_l", URL=, fillcolor="#7FFFD4"] ; +_mag [label="mag", URL=<.html#mag>, fillcolor="#FACDEF"] ; +Z_Private_BootStrap_mul_add_distr_r [label="mul_add_distr_r", URL=, fillcolor="#7FFFD4"] ; +_mag_val [label="mag_val", URL=<.html#mag_val>, fillcolor="#F070D1"] ; +_mag_prop [label="mag_prop", URL=<.html#mag_prop>, fillcolor="#E2CDFA"] ; +Z_Private_BootStrap_mul_0_r [label="mul_0_r", URL=, fillcolor="#7FFFD4"] ; +Z_Private_BootStrap_mul_opp_r [label="mul_opp_r", URL=, fillcolor="#7FFFD4"] ; +_Rle [label="Rle", URL=<.html#Rle>, fillcolor="#F070D1"] ; +Z_Private_BootStrap_mul_add_distr_pos [label="mul_add_distr_pos", URL=, fillcolor="#7FFFD4"] ; +_bpow [label="bpow", URL=<.html#bpow>, fillcolor="#F070D1"] ; +Pos_mul_add_distr_r [label="mul_add_distr_r", URL=, fillcolor="#7FFFD4"] ; +_Rabs [label="Rabs", URL=<.html#Rabs>, fillcolor="#F070D1"] ; +Pos_mul_sub_distr_r [label="mul_sub_distr_r", URL=, fillcolor="#7FFFD4"] ; +_Rge [label="Rge", URL=<.html#Rge>, fillcolor="#F070D1"] ; +Pos_mul_compare_mono_r [label="mul_compare_mono_r", URL=, fillcolor="#7FFFD4"] ; +_Rcase_abs [label="Rcase_abs", URL=<.html#Rcase_abs>, fillcolor="#F070D1"] ; +Pos_mul_comm [label="mul_comm", URL=, fillcolor="#7FFFD4"] ; +_Ropp [label="Ropp", URL=<.html#Ropp>, fillcolor="#F070D1"] ; +Pos_mul_compare_mono_l [label="mul_compare_mono_l", URL=, fillcolor="#7FFFD4"] ; +_Rle_ge [label="Rle_ge", URL=<.html#Rle_ge>, fillcolor="#7FFFD4"] ; +Pos_gt_lt [label="gt_lt", URL=, fillcolor="#7FFFD4"] ; +_Rnot_le_lt [label="Rnot_le_lt", URL=<.html#Rnot_le_lt>, fillcolor="#7FFFD4"] ; +Pos_add_lt_mono [label="add_lt_mono", URL=, fillcolor="#7FFFD4"] ; +_Rle_dec [label="Rle_dec", URL=<.html#Rle_dec>, fillcolor="#F070D1"] ; +Pos_mul_1_r [label="mul_1_r", URL=, fillcolor="#7FFFD4"] ; +_Rlt_not_le [label="Rlt_not_le", URL=<.html#Rlt_not_le>, fillcolor="#7FFFD4"] ; +Pos_mul_xI_r [label="mul_xI_r", URL=, fillcolor="#7FFFD4"] ; +_Rnot_lt_le [label="Rnot_lt_le", URL=<.html#Rnot_lt_le>, fillcolor="#7FFFD4"] ; +Pos_mul_xO_r [label="mul_xO_r", URL=, fillcolor="#7FFFD4"] ; +_Rlt_dec [label="Rlt_dec", URL=<.html#Rlt_dec>, fillcolor="#F070D1"] ; +Pos_mul_sub_distr_l [label="mul_sub_distr_l", URL=, fillcolor="#7FFFD4"] ; +_Rgt [label="Rgt", URL=<.html#Rgt>, fillcolor="#F070D1"] ; +Pos_mul_add_distr_l [label="mul_add_distr_l", URL=, fillcolor="#7FFFD4"] ; +_Rge_not_lt [label="Rge_not_lt", URL=<.html#Rge_not_lt>, fillcolor="#7FFFD4"] ; +Pos_mul_lt_mono_l [label="mul_lt_mono_l", URL=, fillcolor="#7FFFD4"] ; +_Rge_le [label="Rge_le", URL=<.html#Rge_le>, fillcolor="#7FFFD4"] ; +Ring_polynom_mon_of_pol [label="mon_of_pol", URL=, fillcolor="#F070D1"] ; +_Rle_not_lt [label="Rle_not_lt", URL=<.html#Rle_not_lt>, fillcolor="#7FFFD4"] ; +_option [label="option", URL=<.html#option>, fillcolor="#E2CDFA"] ; +_Rlt_not_eq [label="Rlt_not_eq", URL=<.html#Rlt_not_eq>, fillcolor="#7FFFD4"] ; +_pair [label="pair", URL=<.html#pair>, fillcolor="#7FAAFF"] ; +_Rlt_asym [label="Rlt_asym", URL=<.html#Rlt_asym>, fillcolor="#7FFFD4"] ; +Ring_polynom_P0 [label="P0", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyReals_CRealLtEpsilon [label="CRealLtEpsilon", URL=, fillcolor="#F070D1"] ; +ConstructiveExtra_constructive_indefinite_ground_description_Z [label="constructive_indefinite_ground_description_Z", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Peq [label="Peq", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkVmon [label="mkVmon", URL=, fillcolor="#F070D1"] ; +ConstructiveEpsilon_constructive_indefinite_ground_description [label="constructive_indefinite_ground_description", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkZmon [label="mkZmon", URL=, fillcolor="#F070D1"] ; +ConstructiveEpsilon_P_ [label="P'", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mon0 [label="mon0", URL=, fillcolor="#7FAAFF"] ; +ConstructiveEpsilon_P__decidable [label="P'_decidable", URL=, fillcolor="#F070D1"] ; +_Some [label="Some", URL=<.html#Some>, fillcolor="#7FAAFF"] ; +ConstructiveEpsilon_constructive_indefinite_ground_description_nat [label="constructive_indefinite_ground_description_nat", URL=, fillcolor="#F070D1"] ; +_None [label="None", URL=<.html#None>, fillcolor="#7FAAFF"] ; +ConstructiveEpsilon_rel_ls_post [label="rel_ls_post", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_zmon [label="zmon", URL=, fillcolor="#7FAAFF"] ; +ConstructiveEpsilon_linear_search_from_0_conform [label="linear_search_from_0_conform", URL=, fillcolor="#F070D1"] ; +ConstructiveEpsilon_rel_ls [label="rel_ls", URL=, fillcolor="#E2CDFA"] ; +Ring_polynom_zmon_pred [label="zmon_pred", URL=, fillcolor="#F070D1"] ; +Ring_polynom_vmon [label="vmon", URL=, fillcolor="#7FAAFF"] ; +ConstructiveEpsilon_linear_search_conform [label="linear_search_conform", URL=, fillcolor="#F070D1"] ; +Z_one_succ [label="one_succ", URL=, fillcolor="#7FFFD4"] ; +ConstructiveEpsilon_O_witness [label="O_witness", URL=, fillcolor="#7FFFD4"] ; +ConstructiveEpsilon_before_witness [label="before_witness", URL=, fillcolor="#E2CDFA"] ; +Z_eqb [label="eqb", URL=, fillcolor="#F070D1"] ; +ConstructiveEpsilon_stop [label="stop", URL=, fillcolor="#7FAAFF"] ; +PosDef_Pos_eqb [label="eqb", URL=, fillcolor="#F070D1"] ; +ConstructiveEpsilon_next [label="next", URL=, fillcolor="#7FAAFF"] ; +Qminmax_Q_Private_Tac_eq_le [label="eq_le", URL=, fillcolor="#7FFFD4"] ; +ConstructiveEpsilon_inv_before_witness [label="inv_before_witness", URL=, fillcolor="#7FFFD4"] ; +Qminmax_Q_Private_Tac_eq_lt [label="eq_lt", URL=, fillcolor="#7FFFD4"] ; +ConstructiveEpsilon_Rstop [label="Rstop", URL=, fillcolor="#7FAAFF"] ; +Qminmax_Q_Private_Tac_le_eq [label="le_eq", URL=, fillcolor="#7FFFD4"] ; +ConstructiveEpsilon_Rnext [label="Rnext", URL=, fillcolor="#7FAAFF"] ; +Qminmax_Q_Private_Tac_lt_eq [label="lt_eq", URL=, fillcolor="#7FFFD4"] ; +ConstructiveEpsilon_rel_ls_ind [label="rel_ls_ind", URL=, fillcolor="#7FFFD4"] ; +Qminmax_Q_Private_Tac_le_lt_trans [label="le_lt_trans", URL=, fillcolor="#7FFFD4"] ; +Qminmax_Q_Private_Tac_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +_Rlt_irrefl [label="Rlt_irrefl", URL=<.html#Rlt_irrefl>, fillcolor="#7FFFD4"] ; +Qminmax_Q_Private_Tac_eq_sym [label="eq_sym", URL=, fillcolor="#7FFFD4"] ; +_Rtotal_order [label="Rtotal_order", URL=<.html#Rtotal_order>, fillcolor="#7FFFD4"] ; +Qminmax_Q_Private_Tac_not_gt_le [label="not_gt_le", URL=, fillcolor="#7FFFD4"] ; +RinvImpl_Rinv [label="Rinv", URL=, fillcolor="#F070D1"] ; +_radix_val [label="radix_val", URL=<.html#radix_val>, fillcolor="#F070D1"] ; +Qminmax_Q_OT_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +Qminmax_Q_OT_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +_Req_appart_dec [label="Req_appart_dec", URL=<.html#Req_appart_dec>, fillcolor="#F070D1"] ; +QOrderedType_Q_as_OT_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +_Rrepr_appart_0 [label="Rrepr_appart_0", URL=<.html#Rrepr_appart_0>, fillcolor="#F070D1"] ; +QArith_base_Qle_lteq [label="Qle_lteq", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_inv [label="CReal_inv", URL=, fillcolor="#F070D1"] ; +_R0 [label="R0", URL=<.html#R0>, fillcolor="#F070D1"] ; +QArith_base_Qeq_alt [label="Qeq_alt", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qle_alt [label="Qle_alt", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CReal_appart [label="CReal_appart", URL=, fillcolor="#F070D1"] ; +QArith_base_Qlt_alt [label="Qlt_alt", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_inv_pos [label="CReal_inv_pos", URL=, fillcolor="#F070D1"] ; +QArith_base_Qcompare [label="Qcompare", URL=, fillcolor="#F070D1"] ; +ConstructiveCauchyRealsMult_CReal_neg_lt_pos [label="CReal_neg_lt_pos", URL=, fillcolor="#F070D1"] ; +Z_compare_eq_iff [label="compare_eq_iff", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_neg_lt_pos_subproof [label="CReal_neg_lt_pos_subproof", URL=, fillcolor="#7FFFD4"] ; +Qminmax_Q_OT_compare_spec [label="compare_spec", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy [label="CReal_inv_pos_cauchy", URL=, fillcolor="#7FFFD4"] ; +QOrderedType_Q_as_OT_compare_spec [label="compare_spec", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_inv_pos_seq [label="CReal_inv_pos_seq", URL=, fillcolor="#F070D1"] ; +QArith_base_Qcompare_spec [label="Qcompare_spec", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_inv_pos_bound [label="CReal_inv_pos_bound", URL=, fillcolor="#7FFFD4"] ; +Z_compare_spec [label="compare_spec", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_inv_pos_scale [label="CReal_inv_pos_scale", URL=, fillcolor="#F070D1"] ; +Z_compare_antisym [label="compare_antisym", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CRealLowerBound [label="CRealLowerBound", URL=, fillcolor="#F070D1"] ; +Z_compare_lt_iff [label="compare_lt_iff", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CRealLowerBoundSpec [label="CRealLowerBoundSpec", URL=, fillcolor="#7FFFD4"] ; +Qminmax_Q_OT_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyRealsMult_CReal_inv_pos_cm [label="CReal_inv_pos_cm", URL=, fillcolor="#F070D1"] ; +QOrderedType_Q_as_OT_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_Qinv [label="Qabs_Qinv", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qlt_trans [label="Qlt_trans", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qle_shift_div_l [label="Qle_shift_div_l", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qlt_irrefl [label="Qlt_irrefl", URL=, fillcolor="#7FFFD4"] ; +Qabs_Qabs_gt [label="Qabs_gt", URL=, fillcolor="#7FFFD4"] ; +Z_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_div_r [label="Qmult_div_r", URL=, fillcolor="#7FFFD4"] ; +Z_compare_refl [label="compare_refl", URL=, fillcolor="#7FFFD4"] ; +_Rquot2 [label="Rquot2", URL=<.html#Rquot2>, fillcolor="#7FFFD4"] ; +QArith_base_Qle_lt_trans [label="Qle_lt_trans", URL=, fillcolor="#7FFFD4"] ; +ConstructiveCauchyReals_CRealLtProp_morph_Proper [label="CRealLtProp_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +Z_mul_le_mono_pos_r [label="mul_le_mono_pos_r", URL=, fillcolor="#7FFFD4"] ; +ConstructiveRcomplete_CRealLtDisjunctEpsilon [label="CRealLtDisjunctEpsilon", URL=, fillcolor="#F070D1"] ; +Z_mul_lt_mono_pos_r [label="mul_lt_mono_pos_r", URL=, fillcolor="#7FFFD4"] ; +_R0_def [label="R0_def", URL=<.html#R0_def>, fillcolor="#7FFFD4"] ; +Z_mul_shuffle0 [label="mul_shuffle0", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_DRealQuot2 [label="DRealQuot2", URL=, fillcolor="#7FFFD4"] ; +Z_le_lt_trans [label="le_lt_trans", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_DRealAbstrFalse [label="DRealAbstrFalse", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_le_lt_trans [label="le_lt_trans", URL=, fillcolor="#7FFFD4"] ; +_Z_ge_lt_dec [label="Z_ge_lt_dec", URL=<.html#Z_ge_lt_dec>, fillcolor="#F070D1"] ; +Z_Private_OrderTac_Tac_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +_Z_le_gt_dec [label="Z_le_gt_dec", URL=<.html#Z_le_gt_dec>, fillcolor="#F070D1"] ; +Z_Private_OrderTac_Tac_not_ge_lt [label="not_ge_lt", URL=, fillcolor="#7FFFD4"] ; +Nat2Z_is_nonneg [label="is_nonneg", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_IsTotal_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_DRealAbstrFalse__ [label="DRealAbstrFalse''", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_IsTotal_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +_Z_le_dec [label="Z_le_dec", URL=<.html#Z_le_dec>, fillcolor="#F070D1"] ; +Z_Private_OrderTac_IsTotal_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +_Z_ge_dec [label="Z_ge_dec", URL=<.html#Z_ge_dec>, fillcolor="#F070D1"] ; +Z_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +_Fexp [label="Fexp", URL=<.html#Fexp>, fillcolor="#F070D1"] ; +Z_lt_trichotomy [label="lt_trichotomy", URL=, fillcolor="#7FFFD4"] ; +_Fnum [label="Fnum", URL=<.html#Fnum>, fillcolor="#F070D1"] ; +Z_le_gt_cases [label="le_gt_cases", URL=, fillcolor="#7FFFD4"] ; +_Rmult [label="Rmult", URL=<.html#Rmult>, fillcolor="#F070D1"] ; +Z_lt_eq_cases [label="lt_eq_cases", URL=, fillcolor="#7FFFD4"] ; +_Zdigits [label="Zdigits", URL=<.html#Zdigits>, fillcolor="#F070D1"] ; +Z_compare_le_iff [label="compare_le_iff", URL=, fillcolor="#7FFFD4"] ; +_Fdiv_core [label="Fdiv_core", URL=<.html#Fdiv_core>, fillcolor="#F070D1"] ; +_new_location [label="new_location", URL=<.html#new_location>, fillcolor="#F070D1"] ; +Z_lt_succ_r [label="lt_succ_r", URL=, fillcolor="#7FFFD4"] ; +Z_le_succ_l [label="le_succ_l", URL=, fillcolor="#7FFFD4"] ; +Z_even [label="even", URL=, fillcolor="#F070D1"] ; +_new_location_odd [label="new_location_odd", URL=<.html#new_location_odd>, fillcolor="#F070D1"] ; +Z_central_induction [label="central_induction", URL=, fillcolor="#7FFFD4"] ; +_new_location_even [label="new_location_even", URL=<.html#new_location_even>, fillcolor="#F070D1"] ; +Z_le_refl [label="le_refl", URL=, fillcolor="#7FFFD4"] ; +Z_le_wd [label="le_wd", URL=, fillcolor="#7FFFD4"] ; +_Zdigits_aux [label="Zdigits_aux", URL=<.html#Zdigits_aux>, fillcolor="#F070D1"] ; +Z_lt_wd [label="lt_wd", URL=, fillcolor="#7FFFD4"] ; +_digits2_Pnat [label="digits2_Pnat", URL=<.html#digits2_Pnat>, fillcolor="#FACDEF"] ; +Z_nle_succ_diag_l [label="nle_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv [label="Fdiv", URL=, fillcolor="#F070D1"] ; +Z_neq_succ_diag_l [label="neq_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_core [label="Fdiv_core", URL=, fillcolor="#F070D1"] ; +Z_nlt_succ_diag_l [label="nlt_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +_IPR [label="IPR", URL=<.html#IPR>, fillcolor="#F070D1"] ; +Z_lt_le_incl [label="lt_le_incl", URL=, fillcolor="#7FFFD4"] ; +_IPR_2 [label="IPR_2", URL=<.html#IPR_2>, fillcolor="#F070D1"] ; +Z_lt_succ_diag_r [label="lt_succ_diag_r", URL=, fillcolor="#7FFFD4"] ; +_R1 [label="R1", URL=<.html#R1>, fillcolor="#F070D1"] ; +Z_compare_sub [label="compare_sub", URL=, fillcolor="#7FFFD4"] ; +Z_sub [label="sub", URL=, fillcolor="#F070D1"] ; +Z_sub_succ_r [label="sub_succ_r", URL=, fillcolor="#7FFFD4"] ; +Z_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_IsTotal_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +Z_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +Z_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +Z_lt_asymm [label="lt_asymm", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_trans [label="trans", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_IsTotal_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_interp_ord [label="interp_ord", URL=, fillcolor="#F070D1"] ; +Z_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +Z_mul_assoc [label="mul_assoc", URL=, fillcolor="#7FFFD4"] ; +Z_mul_add_distr_r [label="mul_add_distr_r", URL=, fillcolor="#7FFFD4"] ; +Z_mul_lt_mono_pos_l [label="mul_lt_mono_pos_l", URL=, fillcolor="#7FFFD4"] ; +Z_lt_ind [label="lt_ind", URL=, fillcolor="#7FFFD4"] ; +Z_add_lt_mono [label="add_lt_mono", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +Z_add_lt_mono_l [label="add_lt_mono_l", URL=, fillcolor="#7FFFD4"] ; +Z_add_lt_mono_r [label="add_lt_mono_r", URL=, fillcolor="#7FFFD4"] ; +Z_succ_lt_mono [label="succ_lt_mono", URL=, fillcolor="#7FFFD4"] ; +Z_right_induction [label="right_induction", URL=, fillcolor="#7FFFD4"] ; +Z_lt_exists_pred [label="lt_exists_pred", URL=, fillcolor="#7FFFD4"] ; +Z_strong_right_induction [label="strong_right_induction", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_not_gt_le [label="not_gt_le", URL=, fillcolor="#7FFFD4"] ; +Z_lt_wf [label="lt_wf", URL=, fillcolor="#7FFFD4"] ; +Z_Rlt_wd [label="Rlt_wd", URL=, fillcolor="#7FFFD4"] ; +Z_lt_lt_succ_r [label="lt_lt_succ_r", URL=, fillcolor="#7FFFD4"] ; +Z_le_preorder [label="le_preorder", URL=, fillcolor="#7FFFD4"] ; +Z_le_le_succ_r [label="le_le_succ_r", URL=, fillcolor="#7FFFD4"] ; +Z_le_succ_r [label="le_succ_r", URL=, fillcolor="#7FFFD4"] ; +Z_le_trans [label="le_trans", URL=, fillcolor="#7FFFD4"] ; +Z_mul_le_mono_pos_l [label="mul_le_mono_pos_l", URL=, fillcolor="#7FFFD4"] ; +Z_mul_cancel_l [label="mul_cancel_l", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_eq_lt [label="eq_lt", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_lt_eq [label="lt_eq", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_eq_sym [label="eq_sym", URL=, fillcolor="#7FFFD4"] ; +Z_mul_lt_mono_neg_l [label="mul_lt_mono_neg_l", URL=, fillcolor="#7FFFD4"] ; +Z_lt_gt_cases [label="lt_gt_cases", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_not_neq_eq [label="not_neq_eq", URL=, fillcolor="#7FFFD4"] ; +Z_Private_OrderTac_Tac_eq_trans [label="eq_trans", URL=, fillcolor="#7FFFD4"] ; +Z_lt_succ_l [label="lt_succ_l", URL=, fillcolor="#7FFFD4"] ; +Z_order_induction_0 [label="order_induction_0", URL=, fillcolor="#7FFFD4"] ; +Z_mul_lt_pred [label="mul_lt_pred", URL=, fillcolor="#7FFFD4"] ; +Z_le_lt_add_lt [label="le_lt_add_lt", URL=, fillcolor="#7FFFD4"] ; +Z_nlt_ge [label="nlt_ge", URL=, fillcolor="#7FFFD4"] ; +Z_add_le_mono [label="add_le_mono", URL=, fillcolor="#7FFFD4"] ; +Z_add_le_mono_l [label="add_le_mono_l", URL=, fillcolor="#7FFFD4"] ; +Z_add_le_mono_r [label="add_le_mono_r", URL=, fillcolor="#7FFFD4"] ; +Z_succ_le_mono [label="succ_le_mono", URL=, fillcolor="#7FFFD4"] ; +Z_order_induction [label="order_induction", URL=, fillcolor="#7FFFD4"] ; +Z_left_induction [label="left_induction", URL=, fillcolor="#7FFFD4"] ; +Z_strong_left_induction [label="strong_left_induction", URL=, fillcolor="#7FFFD4"] ; +Z_eq_le_incl [label="eq_le_incl", URL=, fillcolor="#7FFFD4"] ; +Z_gt_wf [label="gt_wf", URL=, fillcolor="#7FFFD4"] ; +Z_Rgt_wd [label="Rgt_wd", URL=, fillcolor="#7FFFD4"] ; +Qminmax_Q_Private_Tac_trans [label="trans", URL=, fillcolor="#7FFFD4"] ; +Qminmax_Q_Private_Tac_interp_ord [label="interp_ord", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PNSubstL [label="PNSubstL", URL=, fillcolor="#F070D1"] ; +Ring_polynom_norm_aux [label="norm_aux", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Padd [label="Padd", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Pmul [label="Pmul", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Popp [label="Popp", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Psub [label="Psub", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mk_X [label="mk_X", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Ppow_N [label="Ppow_N", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Ppow_pos [label="Ppow_pos", URL=, fillcolor="#F070D1"] ; +Ring_polynom_P1 [label="P1", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkX [label="mkX", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkPinj_pred [label="mkPinj_pred", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkXi [label="mkXi", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkPX [label="mkPX", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PaddC [label="PaddC", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PsubC [label="PsubC", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PsubI [label="PsubI", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PsubX [label="PsubX", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkPinj [label="mkPinj", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PmulC [label="PmulC", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PmulI [label="PmulI", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PmulC_aux [label="PmulC_aux", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PaddI [label="PaddI", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PaddX [label="PaddX", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PSubstL [label="PSubstL", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PSubstL1 [label="PSubstL1", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PNSubst [label="PNSubst", URL=, fillcolor="#F070D1"] ; +Ring_polynom_POneSubst [label="POneSubst", URL=, fillcolor="#F070D1"] ; +Ring_polynom_PNSubst1 [label="PNSubst1", URL=, fillcolor="#F070D1"] ; +Ring_polynom_MFactor [label="MFactor", URL=, fillcolor="#F070D1"] ; +Ring_polynom_CFactor [label="CFactor", URL=, fillcolor="#F070D1"] ; +Z_lt_le_trans [label="lt_le_trans", URL=, fillcolor="#7FFFD4"] ; +Pos_le_1_l [label="le_1_l", URL=, fillcolor="#7FFFD4"] ; +Pos2Z_pos_le_pos [label="pos_le_pos", URL=, fillcolor="#7FFFD4"] ; +Pos2Z_inj_mul [label="inj_mul", URL=, fillcolor="#7FFFD4"] ; +Z_mul_le_mono_nonneg [label="mul_le_mono_nonneg", URL=, fillcolor="#7FFFD4"] ; +Z_mul_lt_mono_nonneg [label="mul_lt_mono_nonneg", URL=, fillcolor="#7FFFD4"] ; +Z_mul_le_mono_nonneg_l [label="mul_le_mono_nonneg_l", URL=, fillcolor="#7FFFD4"] ; +Z_mul_le_mono_nonneg_r [label="mul_le_mono_nonneg_r", URL=, fillcolor="#7FFFD4"] ; +Pos_le [label="le", URL=, fillcolor="#F070D1"] ; +SetoidTactics_DefaultRelation [label="DefaultRelation", URL=, fillcolor="#E2CDFA"] ; +SetoidTactics_Build_DefaultRelation [label="Build_DefaultRelation", URL=, fillcolor="#7FAAFF"] ; +SuccNat2Pos_inv [label="inv", URL=, fillcolor="#7FFFD4"] ; +Pos2Nat_is_succ [label="is_succ", URL=, fillcolor="#7FFFD4"] ; +Pos2Nat_inj_succ [label="inj_succ", URL=, fillcolor="#7FFFD4"] ; +Pos_iter_op [label="iter_op", URL=, fillcolor="#F070D1"] ; +Pos_iter_op_succ [label="iter_op_succ", URL=, fillcolor="#7FFFD4"] ; +Pos_of_succ_nat [label="of_succ_nat", URL=, fillcolor="#F070D1"] ; +Pos2Nat_inj [label="inj", URL=, fillcolor="#7FFFD4"] ; +SuccNat2Pos_id_succ [label="id_succ", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_neq_Symmetric [label="neq_Symmetric", URL=, fillcolor="#7FFFD4"] ; +Pos_of_nat_succ [label="of_nat_succ", URL=, fillcolor="#7FFFD4"] ; +Nat2Pos_id [label="id", URL=, fillcolor="#7FFFD4"] ; +_O_S [label="O_S", URL=<.html#O_S>, fillcolor="#7FFFD4"] ; +Pos2Nat_id [label="id", URL=, fillcolor="#7FFFD4"] ; +Morphisms_eq_rewrite_relation [label="eq_rewrite_relation", URL=, fillcolor="#7FFFD4"] ; +BinList_nth [label="nth", URL=, fillcolor="#F070D1"] ; +List_hd [label="hd", URL=, fillcolor="#F070D1"] ; +List_tl [label="tl", URL=, fillcolor="#F070D1"] ; +BinList_jump [label="jump", URL=, fillcolor="#F070D1"] ; +QOrderedType_Q_as_OT_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Q_Setoid [label="Q_Setoid", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qeq_trans [label="Qeq_trans", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qeq_sym [label="Qeq_sym", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qeq_refl [label="Qeq_refl", URL=, fillcolor="#7FFFD4"] ; +Z_mul_reg_r [label="mul_reg_r", URL=, fillcolor="#7FFFD4"] ; +Z_mul_cancel_r [label="mul_cancel_r", URL=, fillcolor="#7FFFD4"] ; +_proj1 [label="proj1", URL=<.html#proj1>, fillcolor="#7FFFD4"] ; +N_mul [label="mul", URL=, fillcolor="#F070D1"] ; +_nat_N_Z [label="nat_N_Z", URL=<.html#nat_N_Z>, fillcolor="#7FFFD4"] ; +N_of_nat [label="of_nat", URL=, fillcolor="#F070D1"] ; +N2Z_inj_mul [label="inj_mul", URL=, fillcolor="#7FFFD4"] ; +Nnat_Nat2N_inj_mul [label="inj_mul", URL=, fillcolor="#7FFFD4"] ; +Nnat_Nat2N_id [label="id", URL=, fillcolor="#7FFFD4"] ; +Nnat_N2Nat_inj_mul [label="inj_mul", URL=, fillcolor="#7FFFD4"] ; +Nnat_N2Nat_inj [label="inj", URL=, fillcolor="#7FFFD4"] ; +N_to_nat [label="to_nat", URL=, fillcolor="#F070D1"] ; +Nnat_N2Nat_id [label="id", URL=, fillcolor="#7FFFD4"] ; +BinNatDef_N_of_nat [label="of_nat", URL=, fillcolor="#F070D1"] ; +_N0 [label="N0", URL=<.html#N0>, fillcolor="#7FAAFF"] ; +_Npos [label="Npos", URL=<.html#Npos>, fillcolor="#7FAAFF"] ; +Pos2Nat_inj_mul [label="inj_mul", URL=, fillcolor="#7FFFD4"] ; +_mult_n_O [label="mult_n_O", URL=<.html#mult_n_O>, fillcolor="#7FFFD4"] ; +Pos_mul_succ_l [label="mul_succ_l", URL=, fillcolor="#7FFFD4"] ; +Pos2Nat_inj_add [label="inj_add", URL=, fillcolor="#7FFFD4"] ; +Pos_add_xO [label="add_xO", URL=, fillcolor="#7FFFD4"] ; +Pos_add_diag [label="add_diag", URL=, fillcolor="#7FFFD4"] ; +QOrderedType_Q_as_OT_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qlt_compat [label="Qlt_compat", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qcompare_comp [label="Qcompare_comp", URL=, fillcolor="#7FFFD4"] ; +_Zr_ring_lemma1 [label="Zr_ring_lemma1", URL=<.html#Zr_ring_lemma1>, fillcolor="#7FFFD4"] ; +Z_quotrem [label="quotrem", URL=, fillcolor="#F070D1"] ; +_Zcompare_mult_compat [label="Zcompare_mult_compat", URL=<.html#Zcompare_mult_compat>, fillcolor="#7FFFD4"] ; +Ring_polynom_PEmul [label="PEmul", URL=, fillcolor="#7FAAFF"] ; +NatDef_N_pos_div_eucl [label="pos_div_eucl", URL=, fillcolor="#F070D1"] ; +NatDef_N_leb [label="leb", URL=, fillcolor="#F070D1"] ; +NatDef_N_sub [label="sub", URL=, fillcolor="#F070D1"] ; +NatDef_N_double [label="double", URL=, fillcolor="#F070D1"] ; +NatDef_N_succ_double [label="succ_double", URL=, fillcolor="#F070D1"] ; +NatDef_N_compare [label="compare", URL=, fillcolor="#F070D1"] ; +_Ztriv_div_th [label="Ztriv_div_th", URL=<.html#Ztriv_div_th>, fillcolor="#7FFFD4"] ; +_Eq_ext [label="Eq_ext", URL=<.html#Eq_ext>, fillcolor="#7FFFD4"] ; +Z_pow [label="pow", URL=, fillcolor="#F070D1"] ; +_Zpower_theory [label="Zpower_theory", URL=<.html#Zpower_theory>, fillcolor="#7FFFD4"] ; +_IDmorph [label="IDmorph", URL=<.html#IDmorph>, fillcolor="#7FFFD4"] ; +ZArithRing_Private_proj1_eqb_eq [label="Private_proj1_eqb_eq", URL=, fillcolor="#7FFFD4"] ; +_Rth_ARth [label="Rth_ARth", URL=<.html#Rth_ARth>, fillcolor="#7FFFD4"] ; +Ring_polynom_interp_PElist [label="interp_PElist", URL=, fillcolor="#F070D1"] ; +_Zth [label="Zth", URL=<.html#Zth>, fillcolor="#7FFFD4"] ; +_Eqsth [label="Eqsth", URL=<.html#Eqsth>, fillcolor="#7FFFD4"] ; +Ring_polynom_ring_correct [label="ring_correct", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Pphi [label="Pphi", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Peq_ok [label="Peq_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_norm_subst_ok [label="norm_subst_ok", URL=, fillcolor="#7FFFD4"] ; +_div_theory [label="div_theory", URL=<.html#div_theory>, fillcolor="#E2CDFA"] ; +_ring_morph [label="ring_morph", URL=<.html#ring_morph>, fillcolor="#E2CDFA"] ; +_ring_eq_ext [label="ring_eq_ext", URL=<.html#ring_eq_ext>, fillcolor="#E2CDFA"] ; +_power_theory [label="power_theory", URL=<.html#power_theory>, fillcolor="#E2CDFA"] ; +_almost_ring_theory [label="almost_ring_theory", URL=<.html#almost_ring_theory>, fillcolor="#E2CDFA"] ; +_pow_N [label="pow_N", URL=<.html#pow_N>, fillcolor="#F070D1"] ; +Ring_polynom_interp_PElist_ok [label="interp_PElist_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_norm_subst_spec [label="norm_subst_spec", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PNSubstL_ok [label="PNSubstL_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_MPcond [label="MPcond", URL=, fillcolor="#F070D1"] ; +Ring_polynom_norm_aux_spec [label="norm_aux_spec", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Ppow_N_ok [label="Ppow_N_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Pmul_ok [label="Pmul_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Popp_ok [label="Popp_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Psub_ok [label="Psub_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_rsub_ext_Proper [label="rsub_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_ropp_ext_Proper [label="ropp_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_rmul_ext_Proper [label="rmul_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +_morph0 [label="morph0", URL=<.html#morph0>, fillcolor="#7FFFD4"] ; +_morph1 [label="morph1", URL=<.html#morph1>, fillcolor="#7FFFD4"] ; +_rpow_pow_N [label="rpow_pow_N", URL=<.html#rpow_pow_N>, fillcolor="#7FFFD4"] ; +_ARadd_comm [label="ARadd_comm", URL=<.html#ARadd_comm>, fillcolor="#7FFFD4"] ; +Ring_polynom_mkX_ok [label="mkX_ok", URL=, fillcolor="#7FFFD4"] ; +Setoid_Seq_refl [label="Seq_refl", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PExpr_ind [label="PExpr_ind", URL=, fillcolor="#7FFFD4"] ; +_ARsub_def [label="ARsub_def", URL=<.html#ARsub_def>, fillcolor="#7FFFD4"] ; +Ring_polynom_radd_ext_Proper [label="radd_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +_Radd_ext [label="Radd_ext", URL=<.html#Radd_ext>, fillcolor="#7FFFD4"] ; +Ring_polynom_get_PEopp [label="get_PEopp", URL=, fillcolor="#F070D1"] ; +Ring_polynom_norm_aux_PEadd [label="norm_aux_PEadd", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_norm_aux_PEopp [label="norm_aux_PEopp", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Padd_ok [label="Padd_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PEO [label="PEO", URL=, fillcolor="#7FAAFF"] ; +Ring_polynom_PEI [label="PEI", URL=, fillcolor="#7FAAFF"] ; +Ring_polynom_PEc [label="PEc", URL=, fillcolor="#7FAAFF"] ; +Ring_polynom_PEopp [label="PEopp", URL=, fillcolor="#7FAAFF"] ; +Ring_polynom_PEpow [label="PEpow", URL=, fillcolor="#7FAAFF"] ; +Ring_polynom_Pol_ind [label="Pol_ind", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mkPinj_ok [label="mkPinj_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_pow_pos_add [label="pow_pos_add", URL=, fillcolor="#7FFFD4"] ; +_ARadd_assoc [label="ARadd_assoc", URL=<.html#ARadd_assoc>, fillcolor="#7FFFD4"] ; +BinList_jump_pred_double [label="jump_pred_double", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mkPX_ok [label="mkPX_ok", URL=, fillcolor="#7FFFD4"] ; +Z_pos_sub_discr [label="pos_sub_discr", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_jump_add_ [label="jump_add'", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PaddC_ok [label="PaddC_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PaddX_ok [label="PaddX_ok", URL=, fillcolor="#7FFFD4"] ; +_ARmul_assoc [label="ARmul_assoc", URL=<.html#ARmul_assoc>, fillcolor="#7FFFD4"] ; +_ARadd_0_r [label="ARadd_0_r", URL=<.html#ARadd_0_r>, fillcolor="#7FFFD4"] ; +_ARadd_assoc1 [label="ARadd_assoc1", URL=<.html#ARadd_assoc1>, fillcolor="#7FFFD4"] ; +_ARadd_assoc2 [label="ARadd_assoc2", URL=<.html#ARadd_assoc2>, fillcolor="#7FFFD4"] ; +_ARdistr_l [label="ARdistr_l", URL=<.html#ARdistr_l>, fillcolor="#7FFFD4"] ; +_radd_ext2_Proper [label="radd_ext2_Proper", URL=<.html#radd_ext2_Proper>, fillcolor="#7FFFD4"] ; +_ARadd_0_l [label="ARadd_0_l", URL=<.html#ARadd_0_l>, fillcolor="#7FFFD4"] ; +_morph_add [label="morph_add", URL=<.html#morph_add>, fillcolor="#7FFFD4"] ; +BinList_jump_add [label="jump_add", URL=, fillcolor="#7FFFD4"] ; +BinList_jump_succ [label="jump_succ", URL=, fillcolor="#7FFFD4"] ; +BinList_jump_tl [label="jump_tl", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Pphi_ext [label="Pphi_ext", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Pphi0 [label="Pphi0", URL=, fillcolor="#7FFFD4"] ; +_ARmul_0_l [label="ARmul_0_l", URL=<.html#ARmul_0_l>, fillcolor="#7FFFD4"] ; +Ring_polynom_ceqb_spec [label="ceqb_spec", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Pequiv [label="Pequiv", URL=, fillcolor="#F070D1"] ; +Ring_polynom_Peq_spec [label="Peq_spec", URL=, fillcolor="#7FFFD4"] ; +_BoolSpec [label="BoolSpec", URL=<.html#BoolSpec>, fillcolor="#E2CDFA"] ; +_BoolSpecT [label="BoolSpecT", URL=<.html#BoolSpecT>, fillcolor="#7FAAFF"] ; +_BoolSpecF [label="BoolSpecF", URL=<.html#BoolSpecF>, fillcolor="#7FAAFF"] ; +_morph_eq [label="morph_eq", URL=<.html#morph_eq>, fillcolor="#7FFFD4"] ; +_Rmul_ext [label="Rmul_ext", URL=<.html#Rmul_ext>, fillcolor="#7FFFD4"] ; +_pow_pos_add [label="pow_pos_add", URL=<.html#pow_pos_add>, fillcolor="#7FFFD4"] ; +_pow_pos_succ [label="pow_pos_succ", URL=<.html#pow_pos_succ>, fillcolor="#7FFFD4"] ; +_pow_pos_swap [label="pow_pos_swap", URL=<.html#pow_pos_swap>, fillcolor="#7FFFD4"] ; +Setoid_Setoid_Theory [label="Setoid_Theory", URL=, fillcolor="#F070D1"] ; +_ARmul_1_l [label="ARmul_1_l", URL=<.html#ARmul_1_l>, fillcolor="#7FFFD4"] ; +BinList_nth_pred_double [label="nth_pred_double", URL=, fillcolor="#7FFFD4"] ; +BinList_nth_jump [label="nth_jump", URL=, fillcolor="#7FFFD4"] ; +_Ropp_ext [label="Ropp_ext", URL=<.html#Ropp_ext>, fillcolor="#7FFFD4"] ; +_ARsub_ext [label="ARsub_ext", URL=<.html#ARsub_ext>, fillcolor="#7FFFD4"] ; +_ropp_ext2_Proper [label="ropp_ext2_Proper", URL=<.html#ropp_ext2_Proper>, fillcolor="#7FFFD4"] ; +Ring_polynom_Psub_opp [label="Psub_opp", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PsubC_ok [label="PsubC_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PX_ext [label="PX_ext", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mkPinj_ext [label="mkPinj_ext", URL=, fillcolor="#7FFFD4"] ; +_morph_opp [label="morph_opp", URL=<.html#morph_opp>, fillcolor="#7FFFD4"] ; +Ring_polynom_mkPX_ext [label="mkPX_ext", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Pequiv_eq [label="Pequiv_eq", URL=, fillcolor="#7FFFD4"] ; +_morph_sub [label="morph_sub", URL=<.html#morph_sub>, fillcolor="#7FFFD4"] ; +_ARopp_mul_l [label="ARopp_mul_l", URL=<.html#ARopp_mul_l>, fillcolor="#7FFFD4"] ; +_ARopp_add [label="ARopp_add", URL=<.html#ARopp_add>, fillcolor="#7FFFD4"] ; +_ARmul_comm [label="ARmul_comm", URL=<.html#ARmul_comm>, fillcolor="#7FFFD4"] ; +_ARmul_assoc2 [label="ARmul_assoc2", URL=<.html#ARmul_assoc2>, fillcolor="#7FFFD4"] ; +Ring_polynom_PmulC_ok [label="PmulC_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PmulI_ok [label="PmulI_ok", URL=, fillcolor="#7FFFD4"] ; +_ARdistr_r [label="ARdistr_r", URL=<.html#ARdistr_r>, fillcolor="#7FFFD4"] ; +_ARmul_0_r [label="ARmul_0_r", URL=<.html#ARmul_0_r>, fillcolor="#7FFFD4"] ; +_ARmul_1_r [label="ARmul_1_r", URL=<.html#ARmul_1_r>, fillcolor="#7FFFD4"] ; +Ring_polynom_PmulC_aux_ok [label="PmulC_aux_ok", URL=, fillcolor="#7FFFD4"] ; +_morph_mul [label="morph_mul", URL=<.html#morph_mul>, fillcolor="#7FFFD4"] ; +_rmul_ext2_Proper [label="rmul_ext2_Proper", URL=<.html#rmul_ext2_Proper>, fillcolor="#7FFFD4"] ; +Ring_polynom_Pphi1 [label="Pphi1", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Ppow_pos_ok [label="Ppow_pos_ok", URL=, fillcolor="#7FFFD4"] ; +_ARmul_assoc1 [label="ARmul_assoc1", URL=<.html#ARmul_assoc1>, fillcolor="#7FFFD4"] ; +Ring_polynom_Mphi [label="Mphi", URL=, fillcolor="#F070D1"] ; +_fst [label="fst", URL=<.html#fst>, fillcolor="#F070D1"] ; +_snd [label="snd", URL=<.html#snd>, fillcolor="#F070D1"] ; +Ring_polynom_PSubstL_ok [label="PSubstL_ok", URL=, fillcolor="#7FFFD4"] ; +_list_ind [label="list_ind", URL=<.html#list_ind>, fillcolor="#7FFFD4"] ; +Ring_polynom_PSubstL1_ok [label="PSubstL1_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PNSubst_ok [label="PNSubst_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_PNSubst1_ok [label="PNSubst1_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_POneSubst_ok [label="POneSubst_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Mphi_ok [label="Mphi_ok", URL=, fillcolor="#7FFFD4"] ; +_div_eucl_th [label="div_eucl_th", URL=<.html#div_eucl_th>, fillcolor="#7FFFD4"] ; +Ring_polynom_mkZmon_ok [label="mkZmon_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_zmon_pred_ok [label="zmon_pred_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Mcphi_ok [label="Mcphi_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mon_of_pol_ok [label="mon_of_pol_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mkVmon_ok [label="mkVmon_ok", URL=, fillcolor="#7FFFD4"] ; +Z_mul_1_l [label="mul_1_l", URL=, fillcolor="#7FFFD4"] ; +Z_sub_diag [label="sub_diag", URL=, fillcolor="#7FFFD4"] ; +_ring_theory [label="ring_theory", URL=<.html#ring_theory>, fillcolor="#E2CDFA"] ; +_mk_rt [label="mk_rt", URL=<.html#mk_rt>, fillcolor="#7FAAFF"] ; +Z_sub_wd [label="sub_wd", URL=, fillcolor="#7FFFD4"] ; +Z_sub_0_r [label="sub_0_r", URL=, fillcolor="#7FFFD4"] ; +Z_sub_succ_l [label="sub_succ_l", URL=, fillcolor="#7FFFD4"] ; +Z_add_opp_r [label="add_opp_r", URL=, fillcolor="#7FFFD4"] ; +Z_pred_inj_wd [label="pred_inj_wd", URL=, fillcolor="#7FFFD4"] ; +Z_opp_wd [label="opp_wd", URL=, fillcolor="#7FFFD4"] ; +Z_add_pred_r [label="add_pred_r", URL=, fillcolor="#7FFFD4"] ; +Z_opp_succ [label="opp_succ", URL=, fillcolor="#7FFFD4"] ; +Z_opp_0 [label="opp_0", URL=, fillcolor="#7FFFD4"] ; +Z_add_pred_l [label="add_pred_l", URL=, fillcolor="#7FFFD4"] ; +Z_pred_inj [label="pred_inj", URL=, fillcolor="#7FFFD4"] ; +_Rmul_comm [label="Rmul_comm", URL=<.html#Rmul_comm>, fillcolor="#7FFFD4"] ; +_Ropp_mul_l [label="Ropp_mul_l", URL=<.html#Ropp_mul_l>, fillcolor="#7FFFD4"] ; +_Radd_assoc [label="Radd_assoc", URL=<.html#Radd_assoc>, fillcolor="#7FFFD4"] ; +_Rmul_0_l [label="Rmul_0_l", URL=<.html#Rmul_0_l>, fillcolor="#7FFFD4"] ; +_Rmul_1_l [label="Rmul_1_l", URL=<.html#Rmul_1_l>, fillcolor="#7FFFD4"] ; +_Radd_comm [label="Radd_comm", URL=<.html#Radd_comm>, fillcolor="#7FFFD4"] ; +_Ropp_add [label="Ropp_add", URL=<.html#Ropp_add>, fillcolor="#7FFFD4"] ; +_Rsub_def [label="Rsub_def", URL=<.html#Rsub_def>, fillcolor="#7FFFD4"] ; +_Rmul_assoc [label="Rmul_assoc", URL=<.html#Rmul_assoc>, fillcolor="#7FFFD4"] ; +_Radd_0_l [label="Radd_0_l", URL=<.html#Radd_0_l>, fillcolor="#7FFFD4"] ; +_Rdistr_l [label="Rdistr_l", URL=<.html#Rdistr_l>, fillcolor="#7FFFD4"] ; +_mk_art [label="mk_art", URL=<.html#mk_art>, fillcolor="#7FAAFF"] ; +_Ropp_def [label="Ropp_def", URL=<.html#Ropp_def>, fillcolor="#7FFFD4"] ; +Z_eqb_eq [label="eqb_eq", URL=, fillcolor="#7FFFD4"] ; +Pos_eqb_eq [label="eqb_eq", URL=, fillcolor="#7FFFD4"] ; +Pos_eqb [label="eqb", URL=, fillcolor="#F070D1"] ; +_mkmorph [label="mkmorph", URL=<.html#mkmorph>, fillcolor="#7FAAFF"] ; +PosDef_Pos_iter [label="iter", URL=, fillcolor="#F070D1"] ; +Z_pow_pos [label="pow_pos", URL=, fillcolor="#F070D1"] ; +_mkpow_th [label="mkpow_th", URL=<.html#mkpow_th>, fillcolor="#7FAAFF"] ; +_mk_reqe [label="mk_reqe", URL=<.html#mk_reqe>, fillcolor="#7FAAFF"] ; +Z_quotrem_eq [label="quotrem_eq", URL=, fillcolor="#7FFFD4"] ; +_mkdiv_th [label="mkdiv_th", URL=<.html#mkdiv_th>, fillcolor="#7FAAFF"] ; +N_add [label="add", URL=, fillcolor="#F070D1"] ; +N_pos_div_eucl [label="pos_div_eucl", URL=, fillcolor="#F070D1"] ; +N_pos_div_eucl_spec [label="pos_div_eucl_spec", URL=, fillcolor="#7FFFD4"] ; +N_le [label="le", URL=, fillcolor="#F070D1"] ; +N_lt [label="lt", URL=, fillcolor="#F070D1"] ; +N_add_assoc [label="add_assoc", URL=, fillcolor="#7FFFD4"] ; +N_leb [label="leb", URL=, fillcolor="#F070D1"] ; +N_sub [label="sub", URL=, fillcolor="#F070D1"] ; +N_double_add [label="double_add", URL=, fillcolor="#7FFFD4"] ; +N_double_mul [label="double_mul", URL=, fillcolor="#7FFFD4"] ; +N_sub_add [label="sub_add", URL=, fillcolor="#7FFFD4"] ; +N_add_comm [label="add_comm", URL=, fillcolor="#7FFFD4"] ; +N_double [label="double", URL=, fillcolor="#F070D1"] ; +N_succ_double [label="succ_double", URL=, fillcolor="#F070D1"] ; +N_leb_spec [label="leb_spec", URL=, fillcolor="#7FFFD4"] ; +N_succ_double_add [label="succ_double_add", URL=, fillcolor="#7FFFD4"] ; +N_succ_double_mul [label="succ_double_mul", URL=, fillcolor="#7FFFD4"] ; +N_leb_spec0 [label="leb_spec0", URL=, fillcolor="#F070D1"] ; +N_compare_nge_iff [label="compare_nge_iff", URL=, fillcolor="#7FFFD4"] ; +N_compare_lt_iff [label="compare_lt_iff", URL=, fillcolor="#7FFFD4"] ; +N_compare [label="compare", URL=, fillcolor="#F070D1"] ; +_reflect [label="reflect", URL=<.html#reflect>, fillcolor="#E2CDFA"] ; +N_compare_nle_iff [label="compare_nle_iff", URL=, fillcolor="#7FFFD4"] ; +N_compare_antisym [label="compare_antisym", URL=, fillcolor="#7FFFD4"] ; +N_compare_le_iff [label="compare_le_iff", URL=, fillcolor="#7FFFD4"] ; +Bool_iff_reflect [label="iff_reflect", URL=, fillcolor="#F070D1"] ; +N_leb_le [label="leb_le", URL=, fillcolor="#7FFFD4"] ; +_and_rec [label="and_rec", URL=<.html#and_rec>, fillcolor="#F070D1"] ; +Bool_diff_false_true [label="diff_false_true", URL=, fillcolor="#7FFFD4"] ; +_ReflectT [label="ReflectT", URL=<.html#ReflectT>, fillcolor="#7FAAFF"] ; +_ReflectF [label="ReflectF", URL=<.html#ReflectF>, fillcolor="#7FAAFF"] ; +N_bi_induction [label="bi_induction", URL=, fillcolor="#7FFFD4"] ; +N_succ [label="succ", URL=, fillcolor="#F070D1"] ; +N_add_wd [label="add_wd", URL=, fillcolor="#7FFFD4"] ; +N_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +N_succ_inj_wd [label="succ_inj_wd", URL=, fillcolor="#7FFFD4"] ; +N_add_succ_l [label="add_succ_l", URL=, fillcolor="#7FFFD4"] ; +N_add_succ_r [label="add_succ_r", URL=, fillcolor="#7FFFD4"] ; +N_add_0_l [label="add_0_l", URL=, fillcolor="#7FFFD4"] ; +N_add_0_r [label="add_0_r", URL=, fillcolor="#7FFFD4"] ; +N_succ_wd [label="succ_wd", URL=, fillcolor="#7FFFD4"] ; +N_eq [label="eq", URL=, fillcolor="#F070D1"] ; +N_succ_inj [label="succ_inj", URL=, fillcolor="#7FFFD4"] ; +N_pred_succ [label="pred_succ", URL=, fillcolor="#7FFFD4"] ; +N_pred_wd [label="pred_wd", URL=, fillcolor="#7FFFD4"] ; +N_pred [label="pred", URL=, fillcolor="#F070D1"] ; +PosDef_Pos_pred_N [label="pred_N", URL=, fillcolor="#F070D1"] ; +Pos_pred_N_succ [label="pred_N_succ", URL=, fillcolor="#7FFFD4"] ; +Pos_pred_double_succ [label="pred_double_succ", URL=, fillcolor="#7FFFD4"] ; +Pos_pred_N [label="pred_N", URL=, fillcolor="#F070D1"] ; +N_peano_rect [label="peano_rect", URL=, fillcolor="#F070D1"] ; +N_add_sub_assoc [label="add_sub_assoc", URL=, fillcolor="#7FFFD4"] ; +N_sub_wd [label="sub_wd", URL=, fillcolor="#7FFFD4"] ; +N_add_sub [label="add_sub", URL=, fillcolor="#7FFFD4"] ; +N_le_refl [label="le_refl", URL=, fillcolor="#7FFFD4"] ; +N_sub_diag [label="sub_diag", URL=, fillcolor="#7FFFD4"] ; +N_induction [label="induction", URL=, fillcolor="#7FFFD4"] ; +N_sub_succ [label="sub_succ", URL=, fillcolor="#7FFFD4"] ; +N_sub_0_r [label="sub_0_r", URL=, fillcolor="#7FFFD4"] ; +N_sub_succ_r [label="sub_succ_r", URL=, fillcolor="#7FFFD4"] ; +Pos_sub_mask_succ_r [label="sub_mask_succ_r", URL=, fillcolor="#7FFFD4"] ; +N_le_0_l [label="le_0_l", URL=, fillcolor="#7FFFD4"] ; +N_right_induction [label="right_induction", URL=, fillcolor="#7FFFD4"] ; +N_lt_succ_diag_r [label="lt_succ_diag_r", URL=, fillcolor="#7FFFD4"] ; +N_lt_eq_cases [label="lt_eq_cases", URL=, fillcolor="#7FFFD4"] ; +N_lt_wd [label="lt_wd", URL=, fillcolor="#7FFFD4"] ; +N_strong_right_induction [label="strong_right_induction", URL=, fillcolor="#7FFFD4"] ; +N_lt_exists_pred [label="lt_exists_pred", URL=, fillcolor="#7FFFD4"] ; +N_central_induction [label="central_induction", URL=, fillcolor="#7FFFD4"] ; +N_le_wd [label="le_wd", URL=, fillcolor="#7FFFD4"] ; +N_lt_succ_r [label="lt_succ_r", URL=, fillcolor="#7FFFD4"] ; +N_le_preorder [label="le_preorder", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_Tac_le_lt_trans [label="le_lt_trans", URL=, fillcolor="#7FFFD4"] ; +N_le_le_succ_r [label="le_le_succ_r", URL=, fillcolor="#7FFFD4"] ; +N_le_succ_r [label="le_succ_r", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_Tac_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_IsTotal_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +N_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +N_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +N_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +N_compare_refl [label="compare_refl", URL=, fillcolor="#7FFFD4"] ; +N_compare_eq_iff [label="compare_eq_iff", URL=, fillcolor="#7FFFD4"] ; +N_lt_asymm [label="lt_asymm", URL=, fillcolor="#7FFFD4"] ; +N_lt_le_incl [label="lt_le_incl", URL=, fillcolor="#7FFFD4"] ; +N_nlt_succ_diag_l [label="nlt_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +N_le_succ_l [label="le_succ_l", URL=, fillcolor="#7FFFD4"] ; +N_nle_succ_diag_l [label="nle_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +N_neq_succ_diag_l [label="neq_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_Tac_not_gt_le [label="not_gt_le", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_Tac_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_Tac_trans [label="trans", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_IsTotal_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_IsTotal_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_Tac_interp_ord [label="interp_ord", URL=, fillcolor="#F070D1"] ; +N_Private_OrderTac_IsTotal_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +N_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +N_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_IsTotal_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +N_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +N_lt_trichotomy [label="lt_trichotomy", URL=, fillcolor="#7FFFD4"] ; +N_le_gt_cases [label="le_gt_cases", URL=, fillcolor="#7FFFD4"] ; +N_le_trans [label="le_trans", URL=, fillcolor="#7FFFD4"] ; +Pos_lt_succ_r [label="lt_succ_r", URL=, fillcolor="#7FFFD4"] ; +N_lt_wf [label="lt_wf", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_Tac_not_ge_lt [label="not_ge_lt", URL=, fillcolor="#7FFFD4"] ; +N_lt_lt_succ_r [label="lt_lt_succ_r", URL=, fillcolor="#7FFFD4"] ; +N_Rlt_wd [label="Rlt_wd", URL=, fillcolor="#7FFFD4"] ; +N_neq_succ_0 [label="neq_succ_0", URL=, fillcolor="#7FFFD4"] ; +N_eq_le_incl [label="eq_le_incl", URL=, fillcolor="#7FFFD4"] ; +N_Private_OrderTac_Tac_lt_eq [label="lt_eq", URL=, fillcolor="#7FFFD4"] ; +N_pred_0 [label="pred_0", URL=, fillcolor="#7FFFD4"] ; +N_sub_gt [label="sub_gt", URL=, fillcolor="#7FFFD4"] ; +N_add_pred_r [label="add_pred_r", URL=, fillcolor="#7FFFD4"] ; +N_add_pred_l [label="add_pred_l", URL=, fillcolor="#7FFFD4"] ; +N_case_analysis [label="case_analysis", URL=, fillcolor="#7FFFD4"] ; +N_lt_ind_rel [label="lt_ind_rel", URL=, fillcolor="#7FFFD4"] ; +N_lt_ind [label="lt_ind", URL=, fillcolor="#7FFFD4"] ; +N_lt_succ_l [label="lt_succ_l", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qle_refl [label="Qle_refl", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qplus_le_l [label="Qplus_le_l", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qplus_le_r [label="Qplus_le_r", URL=, fillcolor="#7FFFD4"] ; +_False_rec [label="False_rec", URL=<.html#False_rec>, fillcolor="#F070D1"] ; +Nat2Z_inj_add [label="inj_add", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qplus_assoc [label="Qplus_assoc", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qinv_plus_distr [label="Qinv_plus_distr", URL=, fillcolor="#7FFFD4"] ; +N2Z_inj_add [label="inj_add", URL=, fillcolor="#7FFFD4"] ; +Nnat_Nat2N_inj_add [label="inj_add", URL=, fillcolor="#7FFFD4"] ; +Nnat_N2Nat_inj_add [label="inj_add", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qle_comp [label="Qle_comp", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qplus_comm [label="Qplus_comm", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qplus_le_compat [label="Qplus_le_compat", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qplus_0_r [label="Qplus_0_r", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qplus_opp_r [label="Qplus_opp_r", URL=, fillcolor="#7FFFD4"] ; +_Zr_ring_lemma2 [label="Zr_ring_lemma2", URL=<.html#Zr_ring_lemma2>, fillcolor="#7FFFD4"] ; +_get_signZ [label="get_signZ", URL=<.html#get_signZ>, fillcolor="#F070D1"] ; +Pos2Z_is_nonneg [label="is_nonneg", URL=, fillcolor="#7FFFD4"] ; +_get_signZ_th [label="get_signZ_th", URL=<.html#get_signZ_th>, fillcolor="#7FFFD4"] ; +Ring_polynom_ring_rw_pow_correct [label="ring_rw_pow_correct", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Pphi_pow_ok [label="Pphi_pow_ok", URL=, fillcolor="#7FFFD4"] ; +_sign_theory [label="sign_theory", URL=<.html#sign_theory>, fillcolor="#E2CDFA"] ; +Ring_polynom_Pphi_avoid_ok [label="Pphi_avoid_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_local_mkpow_ok [label="local_mkpow_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mult_dev_ok [label="mult_dev_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_Pphi_avoid [label="Pphi_avoid", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mult_dev [label="mult_dev", URL=, fillcolor="#F070D1"] ; +Ring_polynom_r_list_pow [label="r_list_pow", URL=, fillcolor="#F070D1"] ; +Ring_polynom_add_mult_dev [label="add_mult_dev", URL=, fillcolor="#F070D1"] ; +Ring_polynom_add_pow_list [label="add_pow_list", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkmult_c [label="mkmult_c", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkmult_rec [label="mkmult_rec", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkmult_c_pos [label="mkmult_c_pos", URL=, fillcolor="#F070D1"] ; +List_rev_ [label="rev'", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkmultm1 [label="mkmultm1", URL=, fillcolor="#F070D1"] ; +List_rev_append [label="rev_append", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkmult1 [label="mkmult1", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkadd_mult [label="mkadd_mult", URL=, fillcolor="#F070D1"] ; +Ring_polynom_mkmult_c_ok [label="mkmult_c_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_add_pow_list_ok [label="add_pow_list_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_add_mult_dev_ok [label="add_mult_dev_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mkadd_mult_ok [label="mkadd_mult_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mkmult_c_pos_ok [label="mkmult_c_pos_ok", URL=, fillcolor="#7FFFD4"] ; +_sign_spec [label="sign_spec", URL=<.html#sign_spec>, fillcolor="#7FFFD4"] ; +Ring_polynom_mkmult1_ok [label="mkmult1_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mkmult_rec_ok [label="mkmult_rec_ok", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_r_list_pow_rev [label="r_list_pow_rev", URL=, fillcolor="#7FFFD4"] ; +Ring_polynom_mkmultm1_ok [label="mkmultm1_ok", URL=, fillcolor="#7FFFD4"] ; +Pos_eqb_refl [label="eqb_refl", URL=, fillcolor="#7FFFD4"] ; +_mksign_th [label="mksign_th", URL=<.html#mksign_th>, fillcolor="#7FAAFF"] ; +ClassicalDedekindReals_sig_forall_dec [label="sig_forall_dec", URL=, fillcolor="#FACDEF"] ; +_sumor [label="sumor", URL=<.html#sumor>, fillcolor="#E2CDFA"] ; +_sumbool [label="sumbool", URL=<.html#sumbool>, fillcolor="#E2CDFA"] ; +_left [label="left", URL=<.html#left>, fillcolor="#7FAAFF"] ; +_right [label="right", URL=<.html#right>, fillcolor="#7FAAFF"] ; +QArith_base_Qplus_lt_le_compat [label="Qplus_lt_le_compat", URL=, fillcolor="#7FFFD4"] ; +Z_add_le_lt_mono [label="add_le_lt_mono", URL=, fillcolor="#7FFFD4"] ; +Setoid_Build_Setoid_Theory [label="Build_Setoid_Theory", URL=, fillcolor="#7FFFD4"] ; +Qfield_Qpower_theory [label="Qpower_theory", URL=, fillcolor="#7FFFD4"] ; +_get_sign_None_th [label="get_sign_None_th", URL=<.html#get_sign_None_th>, fillcolor="#7FFFD4"] ; +_triv_div_th [label="triv_div_th", URL=<.html#triv_div_th>, fillcolor="#7FFFD4"] ; +QArith_base_Qopp_comp [label="Qopp_comp", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qdiv [label="Qdiv", URL=, fillcolor="#F070D1"] ; +Qfield_Qsft [label="Qsft", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_comp [label="Qmult_comp", URL=, fillcolor="#7FFFD4"] ; +Morphisms_proper_prf [label="proper_prf", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qeq_bool_eq [label="Qeq_bool_eq", URL=, fillcolor="#7FFFD4"] ; +_F_R [label="F_R", URL=<.html#F_R>, fillcolor="#7FFFD4"] ; +_field_theory [label="field_theory", URL=<.html#field_theory>, fillcolor="#E2CDFA"] ; +QArith_base_Qeq_bool_iff [label="Qeq_bool_iff", URL=, fillcolor="#7FFFD4"] ; +Qfield_Qsrt [label="Qsrt", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_comm [label="Qmult_comm", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_inv_r [label="Qmult_inv_r", URL=, fillcolor="#7FFFD4"] ; +_mk_field [label="mk_field", URL=<.html#mk_field>, fillcolor="#7FAAFF"] ; +QArith_base_Qmult_1_l [label="Qmult_1_l", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qplus_0_l [label="Qplus_0_l", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_plus_distr_l [label="Qmult_plus_distr_l", URL=, fillcolor="#7FFFD4"] ; +QArith_base_Qmult_assoc [label="Qmult_assoc", URL=, fillcolor="#7FFFD4"] ; +Pos_mul_assoc [label="mul_assoc", URL=, fillcolor="#7FFFD4"] ; +_R_set1_Transitive [label="R_set1_Transitive", URL=<.html#R_set1_Transitive>, fillcolor="#7FFFD4"] ; +_R_set1 [label="R_set1", URL=<.html#R_set1>, fillcolor="#7FFFD4"] ; +_radd_ext_Proper [label="radd_ext_Proper", URL=<.html#radd_ext_Proper>, fillcolor="#7FFFD4"] ; +_R_set1_Reflexive [label="R_set1_Reflexive", URL=<.html#R_set1_Reflexive>, fillcolor="#7FFFD4"] ; +_rmul_ext_Proper [label="rmul_ext_Proper", URL=<.html#rmul_ext_Proper>, fillcolor="#7FFFD4"] ; +Nat_succ_pred [label="succ_pred", URL=, fillcolor="#7FFFD4"] ; +QExtra_Qbound_lt_ZExp2 [label="Qbound_lt_ZExp2", URL=, fillcolor="#F070D1"] ; +QExtra_Pos_log2floor_plus1 [label="Pos_log2floor_plus1", URL=, fillcolor="#F070D1"] ; +QMicromega_QTautoChecker [label="QTautoChecker", URL=, fillcolor="#F070D1"] ; +Qabs_Qabs_triangle_reverse [label="Qabs_triangle_reverse", URL=, fillcolor="#7FFFD4"] ; +Tauto_BFormula [label="BFormula", URL=, fillcolor="#F070D1"] ; +ConstructiveRcomplete_Qlt_trans_swap_hyp [label="Qlt_trans_swap_hyp", URL=, fillcolor="#7FFFD4"] ; +ClassicalDedekindReals_CReal_of_DReal_seq_bound [label="CReal_of_DReal_seq_bound", URL=, fillcolor="#7FFFD4"] ; +QExtra_Qbound_lt_ZExp2_spec [label="Qbound_lt_ZExp2_spec", URL=, fillcolor="#7FFFD4"] ; +VarMap_find [label="find", URL=, fillcolor="#F070D1"] ; +QMicromega_QWitness [label="QWitness", URL=, fillcolor="#F070D1"] ; +QMicromega_QTautoChecker_sound [label="QTautoChecker_sound", URL=, fillcolor="#7FFFD4"] ; +Tauto_eKind [label="eKind", URL=, fillcolor="#F070D1"] ; +VarMap_t [label="t", URL=, fillcolor="#E2CDFA"] ; +RingMicromega_Formula [label="Formula", URL=, fillcolor="#E2CDFA"] ; +EnvRing_PEc [label="PEc", URL=, fillcolor="#7FAAFF"] ; +EnvRing_PEX [label="PEX", URL=, fillcolor="#7FAAFF"] ; +EnvRing_PEadd [label="PEadd", URL=, fillcolor="#7FAAFF"] ; +EnvRing_PEsub [label="PEsub", URL=, fillcolor="#7FAAFF"] ; +EnvRing_PEmul [label="PEmul", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_OpEq [label="OpEq", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_OpLt [label="OpLt", URL=, fillcolor="#7FAAFF"] ; +VarMap_Empty [label="Empty", URL=, fillcolor="#7FAAFF"] ; +VarMap_Elt [label="Elt", URL=, fillcolor="#7FAAFF"] ; +VarMap_Branch [label="Branch", URL=, fillcolor="#7FAAFF"] ; +Tauto_A [label="A", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_Build_Formula [label="Build_Formula", URL=, fillcolor="#7FAAFF"] ; +Tauto_isProp [label="isProp", URL=, fillcolor="#7FAAFF"] ; +EnvRing_PExpr [label="PExpr", URL=, fillcolor="#E2CDFA"] ; +RingMicromega_Op2 [label="Op2", URL=, fillcolor="#E2CDFA"] ; +Tauto_kind [label="kind", URL=, fillcolor="#E2CDFA"] ; +Tauto_isBool [label="isBool", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_nformula_plus_nformula [label="nformula_plus_nformula", URL=, fillcolor="#F070D1"] ; +QMicromega_Qnegate [label="Qnegate", URL=, fillcolor="#F070D1"] ; +QArith_base_Qle_bool [label="Qle_bool", URL=, fillcolor="#F070D1"] ; +RingMicromega_eval_nformula [label="eval_nformula", URL=, fillcolor="#F070D1"] ; +QMicromega_Qeval_nformula [label="Qeval_nformula", URL=, fillcolor="#F070D1"] ; +RingMicromega_nformula_plus_nformula_correct [label="nformula_plus_nformula_correct", URL=, fillcolor="#7FFFD4"] ; +QMicromega_QSORaddon [label="QSORaddon", URL=, fillcolor="#7FFFD4"] ; +ListDef_map [label="map", URL=, fillcolor="#F070D1"] ; +RingMicromega_check_inconsistent_sound [label="check_inconsistent_sound", URL=, fillcolor="#7FFFD4"] ; +QMicromega_Qsor [label="Qsor", URL=, fillcolor="#7FFFD4"] ; +Refl_make_impl [label="make_impl", URL=, fillcolor="#F070D1"] ; +QMicromega_Qeval_nformula_dec [label="Qeval_nformula_dec", URL=, fillcolor="#7FFFD4"] ; +QMicromega_Qeval_formula [label="Qeval_formula", URL=, fillcolor="#F070D1"] ; +RingMicromega_eval_formula [label="eval_formula", URL=, fillcolor="#F070D1"] ; +Tauto_hold_eNOT [label="hold_eNOT", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_PolC [label="PolC", URL=, fillcolor="#F070D1"] ; +QMicromega_Qnormalise [label="Qnormalise", URL=, fillcolor="#F070D1"] ; +Tauto_eval_cnf [label="eval_cnf", URL=, fillcolor="#F070D1"] ; +QMicromega_qdeduce [label="qdeduce", URL=, fillcolor="#F070D1"] ; +Tauto_tauto_checker_sound [label="tauto_checker_sound", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_cnf_normalise [label="cnf_normalise", URL=, fillcolor="#F070D1"] ; +RingMicromega_PolEnv [label="PolEnv", URL=, fillcolor="#F070D1"] ; +QMicromega_qunsat [label="qunsat", URL=, fillcolor="#F070D1"] ; +QMicromega_QWeakChecker_sound [label="QWeakChecker_sound", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_NFormula [label="NFormula", URL=, fillcolor="#F070D1"] ; +QMicromega_QWeakChecker [label="QWeakChecker", URL=, fillcolor="#F070D1"] ; +RingMicromega_cnf_negate [label="cnf_negate", URL=, fillcolor="#F070D1"] ; +Tauto_eval_bf [label="eval_bf", URL=, fillcolor="#F070D1"] ; +Tauto_eval_tt [label="eval_tt", URL=, fillcolor="#F070D1"] ; +QMicromega_Qeval_formula_compat [label="Qeval_formula_compat", URL=, fillcolor="#7FFFD4"] ; +_prod_ind [label="prod_ind", URL=<.html#prod_ind>, fillcolor="#7FFFD4"] ; +RingMicromega_cnf_negate_correct [label="cnf_negate_correct", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_cnf_normalise_correct [label="cnf_normalise_correct", URL=, fillcolor="#7FFFD4"] ; +Refl_make_impl_map [label="make_impl_map", URL=, fillcolor="#7FFFD4"] ; +QMicromega_Qeval_formula_ [label="Qeval_formula'", URL=, fillcolor="#F070D1"] ; +Tauto_eNOT [label="eNOT", URL=, fillcolor="#F070D1"] ; +Tauto_hold [label="hold", URL=, fillcolor="#F070D1"] ; +RingMicromega_Op1 [label="Op1", URL=, fillcolor="#E2CDFA"] ; +_is_true [label="is_true", URL=<.html#is_true>, fillcolor="#F070D1"] ; +Tauto_rtyp [label="rtyp", URL=, fillcolor="#F070D1"] ; +_negb [label="negb", URL=<.html#negb>, fillcolor="#F070D1"] ; +RingMicromega_xnormalise [label="xnormalise", URL=, fillcolor="#F070D1"] ; +Tauto_cnf_ff [label="cnf_ff", URL=, fillcolor="#F070D1"] ; +Refl_make_conj [label="make_conj", URL=, fillcolor="#F070D1"] ; +RingMicromega_normalise_sound [label="normalise_sound", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_check_inconsistent [label="check_inconsistent", URL=, fillcolor="#F070D1"] ; +RingMicromega_xnormalise_correct [label="xnormalise_correct", URL=, fillcolor="#7FFFD4"] ; +Tauto_eval_cnf_ff [label="eval_cnf_ff", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_cnf_of_list_correct [label="cnf_of_list_correct", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_cnf_of_list [label="cnf_of_list", URL=, fillcolor="#F070D1"] ; +RingMicromega_eval_op1 [label="eval_op1", URL=, fillcolor="#F070D1"] ; +RingMicromega_eval_pol [label="eval_pol", URL=, fillcolor="#F070D1"] ; +RingMicromega_normalise [label="normalise", URL=, fillcolor="#F070D1"] ; +Tauto_cnf [label="cnf", URL=, fillcolor="#F070D1"] ; +RingMicromega_SORaddon [label="SORaddon", URL=, fillcolor="#E2CDFA"] ; +OrderedRing_SOR [label="SOR", URL=, fillcolor="#E2CDFA"] ; +Tauto_clause [label="clause", URL=, fillcolor="#F070D1"] ; +RingMicromega_norm [label="norm", URL=, fillcolor="#F070D1"] ; +RingMicromega_psub [label="psub", URL=, fillcolor="#F070D1"] ; +EnvRing_Pol [label="Pol", URL=, fillcolor="#E2CDFA"] ; +RingMicromega_Equal [label="Equal", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_NonEqual [label="NonEqual", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_Strict [label="Strict", URL=, fillcolor="#7FAAFF"] ; +RingMicromega_NonStrict [label="NonStrict", URL=, fillcolor="#7FAAFF"] ; +EnvRing_Psub [label="Psub", URL=, fillcolor="#F070D1"] ; +EnvRing_P0 [label="P0", URL=, fillcolor="#F070D1"] ; +EnvRing_Popp [label="Popp", URL=, fillcolor="#F070D1"] ; +EnvRing_mkPX [label="mkPX", URL=, fillcolor="#F070D1"] ; +EnvRing_PaddC [label="PaddC", URL=, fillcolor="#F070D1"] ; +EnvRing_PsubC [label="PsubC", URL=, fillcolor="#F070D1"] ; +EnvRing_PsubI [label="PsubI", URL=, fillcolor="#F070D1"] ; +EnvRing_PsubX [label="PsubX", URL=, fillcolor="#F070D1"] ; +EnvRing_Pinj [label="Pinj", URL=, fillcolor="#7FAAFF"] ; +EnvRing_PX [label="PX", URL=, fillcolor="#7FAAFF"] ; +EnvRing_mkPinj [label="mkPinj", URL=, fillcolor="#F070D1"] ; +EnvRing_Pc [label="Pc", URL=, fillcolor="#7FAAFF"] ; +EnvRing_Peq [label="Peq", URL=, fillcolor="#F070D1"] ; +EnvRing_norm_aux [label="norm_aux", URL=, fillcolor="#F070D1"] ; +EnvRing_Padd [label="Padd", URL=, fillcolor="#F070D1"] ; +EnvRing_Pmul [label="Pmul", URL=, fillcolor="#F070D1"] ; +EnvRing_mk_X [label="mk_X", URL=, fillcolor="#F070D1"] ; +EnvRing_Ppow_N [label="Ppow_N", URL=, fillcolor="#F070D1"] ; +EnvRing_P1 [label="P1", URL=, fillcolor="#F070D1"] ; +EnvRing_Ppow_pos [label="Ppow_pos", URL=, fillcolor="#F070D1"] ; +EnvRing_mkX [label="mkX", URL=, fillcolor="#F070D1"] ; +EnvRing_mkPinj_pred [label="mkPinj_pred", URL=, fillcolor="#F070D1"] ; +EnvRing_mkXi [label="mkXi", URL=, fillcolor="#F070D1"] ; +EnvRing_PmulC [label="PmulC", URL=, fillcolor="#F070D1"] ; +EnvRing_PmulI [label="PmulI", URL=, fillcolor="#F070D1"] ; +EnvRing_PmulC_aux [label="PmulC_aux", URL=, fillcolor="#F070D1"] ; +EnvRing_PaddI [label="PaddI", URL=, fillcolor="#F070D1"] ; +EnvRing_PaddX [label="PaddX", URL=, fillcolor="#F070D1"] ; +EnvRing_Pphi [label="Pphi", URL=, fillcolor="#F070D1"] ; +Env_hd [label="hd", URL=, fillcolor="#F070D1"] ; +Env_Env [label="Env", URL=, fillcolor="#F070D1"] ; +Env_jump [label="jump", URL=, fillcolor="#F070D1"] ; +Env_tail [label="tail", URL=, fillcolor="#F070D1"] ; +Env_nth [label="nth", URL=, fillcolor="#F070D1"] ; +Tauto_cnf_tt [label="cnf_tt", URL=, fillcolor="#F070D1"] ; +List_fold_right [label="fold_right", URL=, fillcolor="#F070D1"] ; +Tauto_eval_cnf_cons_iff [label="eval_cnf_cons_iff", URL=, fillcolor="#7FFFD4"] ; +Refl_make_conj_cons [label="make_conj_cons", URL=, fillcolor="#7FFFD4"] ; +Tauto_eval_clause [label="eval_clause", URL=, fillcolor="#F070D1"] ; +OrderedRing_Rle_ngt [label="Rle_ngt", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rlt_nge [label="Rlt_nge", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_eq0_cnf [label="eq0_cnf", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_SORRing_ring_lemma1 [label="SORRing_ring_lemma1", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rle_le_minus [label="Rle_le_minus", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_micomega_sor_setoid [label="micomega_sor_setoid", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_popp [label="popp", URL=, fillcolor="#F070D1"] ; +RingMicromega_rle_morph_Proper [label="rle_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rlt_lt_minus [label="Rlt_lt_minus", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_eval_pol_opp [label="eval_pol_opp", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_rlt_morph_Proper [label="rlt_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_micomega_sor_setoid_Reflexive [label="micomega_sor_setoid_Reflexive", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORsetoid [label="SORsetoid", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORlt_wd [label="SORlt_wd", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORrt [label="SORrt", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_Rops_wd [label="Rops_wd", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_SORrm [label="SORrm", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Popp_ok [label="Popp_ok", URL=, fillcolor="#7FFFD4"] ; +EnvRing_radd_ext_Proper [label="radd_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +EnvRing_Pol_ind [label="Pol_ind", URL=, fillcolor="#7FFFD4"] ; +EnvRing_rmul_ext_Proper [label="rmul_ext_Proper", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORtimes_wd [label="SORtimes_wd", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORopp_wd [label="SORopp_wd", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORplus_wd [label="SORplus_wd", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_sor_setoid_Reflexive [label="sor_setoid_Reflexive", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SOR_ring_lemma1 [label="SOR_ring_lemma1", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_rlt_morph_Proper [label="rlt_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_sor_setoid [label="sor_setoid", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_lt_mono_r [label="Rplus_lt_mono_r", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_comm [label="Rplus_comm", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_lt_mono_l [label="Rplus_lt_mono_l", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_le_mono_l [label="Rplus_le_mono_l", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rlt_le_neq [label="Rlt_le_neq", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_cancel_l [label="Rplus_cancel_l", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_rplus_morph_Proper [label="rplus_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_sor_setoid_Transitive [label="sor_setoid_Transitive", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORlt_le_neq [label="SORlt_le_neq", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORplus_le_mono_l [label="SORplus_le_mono_l", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_rle_morph_Proper [label="rle_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_SORle_wd [label="SORle_wd", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_ropp_morph_Proper [label="ropp_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +_pow_N_th [label="pow_N_th", URL=<.html#pow_N_th>, fillcolor="#7FFFD4"] ; +_gen_phiZ [label="gen_phiZ", URL=<.html#gen_phiZ>, fillcolor="#F070D1"] ; +_gen_phiZ_morph [label="gen_phiZ_morph", URL=<.html#gen_phiZ_morph>, fillcolor="#7FFFD4"] ; +OrderedRing_sor_setoid_Symmetric [label="sor_setoid_Symmetric", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_rtimes_morph_Proper [label="rtimes_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +_id_phi_N [label="id_phi_N", URL=<.html#id_phi_N>, fillcolor="#F070D1"] ; +_Smorph_morph [label="Smorph_morph", URL=<.html#Smorph_morph>, fillcolor="#7FFFD4"] ; +_gen_Zeqb_ok [label="gen_Zeqb_ok", URL=<.html#gen_Zeqb_ok>, fillcolor="#7FFFD4"] ; +_gen_phiZ_add [label="gen_phiZ_add", URL=<.html#gen_phiZ_add>, fillcolor="#7FFFD4"] ; +_gen_phiZ_ext [label="gen_phiZ_ext", URL=<.html#gen_phiZ_ext>, fillcolor="#7FFFD4"] ; +_gen_phiZ_mul [label="gen_phiZ_mul", URL=<.html#gen_phiZ_mul>, fillcolor="#7FFFD4"] ; +_semi_morph [label="semi_morph", URL=<.html#semi_morph>, fillcolor="#E2CDFA"] ; +_mkRmorph [label="mkRmorph", URL=<.html#mkRmorph>, fillcolor="#7FAAFF"] ; +_rmul_ext3_Proper [label="rmul_ext3_Proper", URL=<.html#rmul_ext3_Proper>, fillcolor="#7FFFD4"] ; +_R_setoid3_Symmetric [label="R_setoid3_Symmetric", URL=<.html#R_setoid3_Symmetric>, fillcolor="#7FFFD4"] ; +_ARopp_mul_r [label="ARopp_mul_r", URL=<.html#ARopp_mul_r>, fillcolor="#7FFFD4"] ; +_gen_phiZ1 [label="gen_phiZ1", URL=<.html#gen_phiZ1>, fillcolor="#F070D1"] ; +_gen_phiPOS1 [label="gen_phiPOS1", URL=<.html#gen_phiPOS1>, fillcolor="#F070D1"] ; +_R_setoid3 [label="R_setoid3", URL=<.html#R_setoid3>, fillcolor="#7FFFD4"] ; +_Ropp_opp [label="Ropp_opp", URL=<.html#Ropp_opp>, fillcolor="#7FFFD4"] ; +_R_setoid3_Reflexive [label="R_setoid3_Reflexive", URL=<.html#R_setoid3_Reflexive>, fillcolor="#7FFFD4"] ; +_same_genZ [label="same_genZ", URL=<.html#same_genZ>, fillcolor="#7FFFD4"] ; +_R_setoid3_Transitive [label="R_setoid3_Transitive", URL=<.html#R_setoid3_Transitive>, fillcolor="#7FFFD4"] ; +_ARgen_phiPOS_mult [label="ARgen_phiPOS_mult", URL=<.html#ARgen_phiPOS_mult>, fillcolor="#7FFFD4"] ; +_ropp_ext3_Proper [label="ropp_ext3_Proper", URL=<.html#ropp_ext3_Proper>, fillcolor="#7FFFD4"] ; +_ARgen_phiPOS_add [label="ARgen_phiPOS_add", URL=<.html#ARgen_phiPOS_add>, fillcolor="#7FFFD4"] ; +_radd_ext3_Proper [label="radd_ext3_Proper", URL=<.html#radd_ext3_Proper>, fillcolor="#7FFFD4"] ; +_ARgen_phiPOS_Psucc [label="ARgen_phiPOS_Psucc", URL=<.html#ARgen_phiPOS_Psucc>, fillcolor="#7FFFD4"] ; +_same_gen [label="same_gen", URL=<.html#same_gen>, fillcolor="#7FFFD4"] ; +_gen_phiPOS [label="gen_phiPOS", URL=<.html#gen_phiPOS>, fillcolor="#F070D1"] ; +_gen_phiZ1_pos_sub [label="gen_phiZ1_pos_sub", URL=<.html#gen_phiZ1_pos_sub>, fillcolor="#7FFFD4"] ; +_R_setoid3_relation [label="R_setoid3_relation", URL=<.html#R_setoid3_relation>, fillcolor="#7FFFD4"] ; +_Smorph_add [label="Smorph_add", URL=<.html#Smorph_add>, fillcolor="#7FFFD4"] ; +_Smorph_mul [label="Smorph_mul", URL=<.html#Smorph_mul>, fillcolor="#7FFFD4"] ; +_Smorph_opp [label="Smorph_opp", URL=<.html#Smorph_opp>, fillcolor="#7FFFD4"] ; +_Smorph_sub [label="Smorph_sub", URL=<.html#Smorph_sub>, fillcolor="#7FFFD4"] ; +_Smorph_eq [label="Smorph_eq", URL=<.html#Smorph_eq>, fillcolor="#7FFFD4"] ; +_Smorph0 [label="Smorph0", URL=<.html#Smorph0>, fillcolor="#7FFFD4"] ; +_Smorph1 [label="Smorph1", URL=<.html#Smorph1>, fillcolor="#7FFFD4"] ; +_phi_ext1_Proper [label="phi_ext1_Proper", URL=<.html#phi_ext1_Proper>, fillcolor="#7FFFD4"] ; +_pow_N_pow_N [label="pow_N_pow_N", URL=<.html#pow_N_pow_N>, fillcolor="#7FFFD4"] ; +OrderedRing_Rplus_le_mono_r [label="Rplus_le_mono_r", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_rtimes_morph_Proper [label="rtimes_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_ropp_morph_Proper [label="ropp_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_rplus_morph_Proper [label="rplus_morph_Proper", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_micomega_sor_setoid_Transitive [label="micomega_sor_setoid_Transitive", URL=, fillcolor="#7FFFD4"] ; +RingMicromega_micomega_sor_setoid_Symmetric [label="micomega_sor_setoid_Symmetric", URL=, fillcolor="#7FFFD4"] ; +_proj2 [label="proj2", URL=<.html#proj2>, fillcolor="#7FFFD4"] ; +OrderedRing_SORle_antisymm [label="SORle_antisymm", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rlt_neq [label="Rlt_neq", URL=, fillcolor="#7FFFD4"] ; +OrderedRing_Rlt_le_trans [label="Rlt_le_trans", URL=, fillcolor="#7FFFD4"] ; + OrderedRing_Rle_gt_cases -> OrderedRing_Rle_lt_eq [] ; + OrderedRing_Rlt_trichotomy -> OrderedRing_SORlt_trichotomy [] ; + OrderedRing_Rle_lt_eq -> Morphisms_reflexive_reflexive_proxy [] ; + OrderedRing_Rle_lt_eq -> Morphisms_iff_flip_impl_subrelation [] ; + OrderedRing_Rle_lt_eq -> Morphisms_reflexive_proper_proxy [] ; + OrderedRing_Rle_lt_eq -> Morphisms_Prop_or_iff_morphism [] ; + OrderedRing_Rle_lt_eq -> RelationClasses_iff_equivalence [] ; + OrderedRing_Rle_lt_eq -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + OrderedRing_Rle_lt_eq -> OrderedRing_rle_morph_Proper [] ; + OrderedRing_Rle_lt_eq -> OrderedRing_Req_em [] ; + OrderedRing_Rle_lt_eq -> OrderedRing_Rle_refl [] ; + OrderedRing_Req_em -> _or_introl [] ; + OrderedRing_Req_em -> _or_intror [] ; + OrderedRing_Req_em -> OrderedRing_Rlt_le_neq [] ; + OrderedRing_Req_em -> OrderedRing_Rlt_trichotomy [] ; + OrderedRing_Req_em -> OrderedRing_Rneq_symm [] ; + OrderedRing_Rle_refl -> OrderedRing_SORle_refl [] ; + OrderedRing_SORle_refl -> OrderedRing_SOR [] ; + OrderedRing_Rneq_symm -> Morphisms_subrelation_proper [] ; + OrderedRing_Rneq_symm -> Morphisms_subrelation_refl [] ; + OrderedRing_Rneq_symm -> RelationClasses_reflexivity [] ; + OrderedRing_Rneq_symm -> RelationClasses_Equivalence_PER [] ; + OrderedRing_Rneq_symm -> Morphisms_subrelation_respectful [] ; + OrderedRing_Rneq_symm -> _tt [] ; + OrderedRing_Rneq_symm -> Morphisms_iff_impl_subrelation [] ; + OrderedRing_Rneq_symm -> Morphisms_per_partial_app_morphism [] ; + OrderedRing_Rneq_symm -> Morphisms_Prop_not_iff_morphism [] ; + OrderedRing_Rneq_symm -> OrderedRing_sor_setoid_Reflexive [] ; + OrderedRing_Rneq_symm -> OrderedRing_sor_setoid [] ; + OrderedRing_SORlt_trichotomy -> OrderedRing_SOR [] ; + OrderedRing_Rlt_trans -> Morphisms_subrelation_proper [] ; + OrderedRing_Rlt_trans -> Morphisms_reflexive_reflexive_proxy [] ; + OrderedRing_Rlt_trans -> Morphisms_subrelation_refl [] ; + OrderedRing_Rlt_trans -> Morphisms_Reflexive_partial_app_morphism [] ; + OrderedRing_Rlt_trans -> RelationClasses_iff_Reflexive [] ; + OrderedRing_Rlt_trans -> Morphisms_iff_flip_impl_subrelation [] ; + OrderedRing_Rlt_trans -> Morphisms_reflexive_proper_proxy [] ; + OrderedRing_Rlt_trans -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + OrderedRing_Rlt_trans -> Morphisms_subrelation_respectful [] ; + OrderedRing_Rlt_trans -> _tt [] ; + OrderedRing_Rlt_trans -> Morphisms_iff_impl_subrelation [] ; + OrderedRing_Rlt_trans -> Morphisms_impl_pars [] ; + OrderedRing_Rlt_trans -> OrderedRing_sor_setoid_Reflexive [] ; + OrderedRing_Rlt_trans -> OrderedRing_Rlt_le_neq [] ; + OrderedRing_Rlt_trans -> OrderedRing_rle_morph_Proper [] ; + OrderedRing_Rlt_trans -> OrderedRing_Rle_antisymm [] ; + OrderedRing_Rlt_trans -> OrderedRing_Rle_trans [] ; + OrderedRing_Rle_antisymm -> OrderedRing_SORle_antisymm [] ; + OrderedRing_Rle_trans -> OrderedRing_SORle_trans [] ; + OrderedRing_SORle_trans -> OrderedRing_SOR [] ; + OrderedRing_Rle_lt_trans -> OrderedRing_rlt_morph_Proper [] ; + OrderedRing_Rle_lt_trans -> OrderedRing_Rle_lt_eq [] ; + OrderedRing_Rle_lt_trans -> OrderedRing_Rlt_trans [] ; + RingMicromega_cltb -> RingMicromega_cneqb [] ; + RingMicromega_cltb -> _andb [] ; + RingMicromega_cneqb -> _negb [] ; + _andb -> _bool [] ; + _andb -> _false [] ; + RingMicromega_rminus_morph_Proper -> OrderedRing_rminus_morph [] ; + RingMicromega_eval_pol_norm -> _Rth_ARth [] ; + RingMicromega_eval_pol_norm -> RingMicromega_eval_pol [] ; + RingMicromega_eval_pol_norm -> RingMicromega_norm [] ; + RingMicromega_eval_pol_norm -> OrderedRing_SORsetoid [] ; + RingMicromega_eval_pol_norm -> OrderedRing_SORrt [] ; + RingMicromega_eval_pol_norm -> RingMicromega_Rops_wd [] ; + RingMicromega_eval_pol_norm -> RingMicromega_SORrm [] ; + RingMicromega_eval_pol_norm -> RingMicromega_eval_pexpr [] ; + RingMicromega_eval_pol_norm -> RingMicromega_SORpower [] ; + RingMicromega_eval_pol_norm -> EnvRing_norm_aux_spec [] ; + OrderedRing_Rminus_eq_0 -> OrderedRing_Rplus_0_l [] ; + OrderedRing_Rminus_eq_0 -> OrderedRing_rminus_morph_Proper [] ; + RingMicromega_eval_pexpr -> RingMicromega_PolEnv [] ; + RingMicromega_eval_pexpr -> EnvRing_PEeval [] ; + RingMicromega_eval_pol_sub -> _Rth_ARth [] ; + RingMicromega_eval_pol_sub -> RingMicromega_eval_pol [] ; + RingMicromega_eval_pol_sub -> RingMicromega_psub [] ; + RingMicromega_eval_pol_sub -> OrderedRing_SORsetoid [] ; + RingMicromega_eval_pol_sub -> OrderedRing_SORrt [] ; + RingMicromega_eval_pol_sub -> RingMicromega_Rops_wd [] ; + RingMicromega_eval_pol_sub -> RingMicromega_SORrm [] ; + RingMicromega_eval_pol_sub -> EnvRing_Psub_ok [] ; + RingMicromega_eval_op2 -> _not [] ; + RingMicromega_eval_op2 -> RingMicromega_Op2 [] ; + EnvRing_Psub_ok -> _ARadd_assoc1 [] ; + EnvRing_Psub_ok -> EnvRing_PaddC_ok [] ; + EnvRing_Psub_ok -> EnvRing_PsubC_ok [] ; + EnvRing_Psub_ok -> EnvRing_PsubX_ok [] ; + EnvRing_pow_pos_add -> _ARmul_assoc [] ; + EnvRing_pow_pos_add -> _Rmul_ext [] ; + EnvRing_pow_pos_add -> _pow_pos_add [] ; + EnvRing_Pjump_add -> EnvRing_env_morph [] ; + EnvRing_Pjump_add -> Env_jump_add [] ; + EnvRing_mkPX_ok -> _ARadd_0_r [] ; + EnvRing_mkPX_ok -> _ARmul_0_l [] ; + EnvRing_mkPX_ok -> EnvRing_mkPX [] ; + EnvRing_mkPX_ok -> EnvRing_pow_pos_add [] ; + EnvRing_mkPX_ok -> EnvRing_mkPinj_ok [] ; + EnvRing_mkPX_ok -> EnvRing_Pphi0 [] ; + EnvRing_mkPX_ok -> EnvRing_ceqb_spec [] ; + EnvRing_mkPX_ok -> EnvRing_Peq_spec [] ; + EnvRing_PaddC_ok -> Morphisms_reflexive_reflexive_proxy [] ; + EnvRing_PaddC_ok -> Morphisms_Reflexive_partial_app_morphism [] ; + EnvRing_PaddC_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + EnvRing_PaddC_ok -> Morphisms_eq_proper_proxy [] ; + EnvRing_PaddC_ok -> Morphisms_reflexive_proper_proxy [] ; + EnvRing_PaddC_ok -> RelationClasses_Equivalence_Transitive [] ; + EnvRing_PaddC_ok -> Setoid_Seq_refl [] ; + EnvRing_PaddC_ok -> _ARadd_assoc [] ; + EnvRing_PaddC_ok -> _morph_add [] ; + EnvRing_PaddC_ok -> EnvRing_PaddC [] ; + EnvRing_PaddC_ok -> EnvRing_Pphi [] ; + EnvRing_PaddC_ok -> EnvRing_radd_ext_Proper [] ; + EnvRing_PaddC_ok -> EnvRing_Pol_ind [] ; + EnvRing_Pjump_xO_tail -> EnvRing_env_morph [] ; + EnvRing_Pjump_xO_tail -> Env_jump_simpl [] ; + EnvRing_Pjump_pred_double -> EnvRing_env_morph [] ; + EnvRing_Pjump_pred_double -> Env_jump_pred_double [] ; + EnvRing_Pjump_pred_double -> Env_jump_simpl [] ; + EnvRing_rsub_ext_Proper -> _ARsub_ext [] ; + EnvRing_ropp_ext_Proper -> _Ropp_ext [] ; + EnvRing_mkPinj_ok -> Setoid_Seq_refl [] ; + EnvRing_mkPinj_ok -> EnvRing_mkPinj [] ; + EnvRing_mkPinj_ok -> EnvRing_Pjump_add [] ; + EnvRing_PsubC_ok -> Morphisms_reflexive_reflexive_proxy [] ; + EnvRing_PsubC_ok -> Morphisms_Reflexive_partial_app_morphism [] ; + EnvRing_PsubC_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + EnvRing_PsubC_ok -> Morphisms_eq_proper_proxy [] ; + EnvRing_PsubC_ok -> RelationClasses_Equivalence_PER [] ; + EnvRing_PsubC_ok -> Morphisms_reflexive_proper_proxy [] ; + EnvRing_PsubC_ok -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + EnvRing_PsubC_ok -> Setoid_Seq_refl [] ; + EnvRing_PsubC_ok -> _ARsub_def [] ; + EnvRing_PsubC_ok -> _ARadd_assoc [] ; + EnvRing_PsubC_ok -> _morph_sub [] ; + EnvRing_PsubC_ok -> EnvRing_PsubC [] ; + EnvRing_PsubC_ok -> EnvRing_Pphi [] ; + EnvRing_PsubC_ok -> EnvRing_radd_ext_Proper [] ; + EnvRing_PsubC_ok -> EnvRing_Pol_ind [] ; + EnvRing_PsubX_ok -> Z_pos_sub_discr [] ; + EnvRing_PsubX_ok -> _ARadd_assoc2 [] ; + EnvRing_PsubX_ok -> _ARdistr_l [] ; + EnvRing_PsubX_ok -> EnvRing_Psub [] ; + EnvRing_PsubX_ok -> EnvRing_Popp_ok [] ; + EnvRing_PsubX_ok -> EnvRing_mkPX_ok [] ; + EnvRing_PsubX_ok -> EnvRing_Pjump_xO_tail [] ; + EnvRing_PsubX_ok -> EnvRing_Pjump_pred_double [] ; + EnvRing_PsubX_ok -> EnvRing_rsub_ext_Proper [] ; + EnvRing_PsubX_ok -> EnvRing_ropp_ext_Proper [] ; + EnvRing_env_morph -> _f_equal [] ; + EnvRing_env_morph -> _eq_trans [] ; + EnvRing_env_morph -> EnvRing_Pphi [] ; + EnvRing_env_morph -> EnvRing_Pol_ind [] ; + Env_jump_pred_double -> PosDef_Pos_add [] ; + Env_jump_pred_double -> Pos_succ_pred_double [] ; + Env_jump_pred_double -> Pos_add_diag [] ; + Env_jump_pred_double -> Env_tail [] ; + Env_jump_pred_double -> Env_jump_add [] ; + Env_jump_simpl -> PosDef_Pos_add [] ; + Env_jump_simpl -> Pos_add_diag [] ; + Env_jump_simpl -> Env_tail [] ; + Env_jump_simpl -> Env_jump_add [] ; + Env_jump_add -> Pos_add_assoc [] ; + Env_jump_add -> Env_jump [] ; + EnvRing_Pphi0 -> _morph0 [] ; + EnvRing_Pphi0 -> EnvRing_P0 [] ; + EnvRing_Pphi0 -> EnvRing_Pphi [] ; + EnvRing_ceqb_spec -> _True [] ; + EnvRing_ceqb_spec -> _eq_refl [] ; + EnvRing_ceqb_spec -> _I [] ; + EnvRing_ceqb_spec -> _BoolSpec [] ; + EnvRing_ceqb_spec -> _BoolSpecT [] ; + EnvRing_ceqb_spec -> _BoolSpecF [] ; + EnvRing_ceqb_spec -> _morph_eq [] ; + EnvRing_Peq_spec -> _BoolSpec [] ; + EnvRing_Peq_spec -> _BoolSpecT [] ; + EnvRing_Peq_spec -> _BoolSpecF [] ; + EnvRing_Peq_spec -> EnvRing_Peq_ok [] ; + EnvRing_Peq_ok -> Morphisms_reflexive_reflexive_proxy [] ; + EnvRing_Peq_ok -> Morphisms_Reflexive_partial_app_morphism [] ; + EnvRing_Peq_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + EnvRing_Peq_ok -> Morphisms_eq_proper_proxy [] ; + EnvRing_Peq_ok -> Morphisms_reflexive_proper_proxy [] ; + EnvRing_Peq_ok -> RelationClasses_Equivalence_Reflexive [] ; + EnvRing_Peq_ok -> Pos_compare_spec [] ; + EnvRing_Peq_ok -> _morph_eq [] ; + EnvRing_Peq_ok -> EnvRing_Peq [] ; + EnvRing_Peq_ok -> EnvRing_Pphi [] ; + EnvRing_Peq_ok -> EnvRing_radd_ext_Proper [] ; + EnvRing_Peq_ok -> EnvRing_Pol_ind [] ; + EnvRing_Peq_ok -> EnvRing_rmul_ext_Proper [] ; + EnvRing_PEeval -> EnvRing_PExpr [] ; + EnvRing_PEeval -> Env_nth [] ; + OrderedRing_Rplus_0_l -> _ring_subst_niter [] ; + OrderedRing_Rplus_0_l -> OrderedRing_SOR_ring_lemma1 [] ; + OrderedRing_rminus_morph_Proper -> Morphisms_reflexive_reflexive_proxy [] ; + OrderedRing_rminus_morph_Proper -> Morphisms_Reflexive_partial_app_morphism [] ; + OrderedRing_rminus_morph_Proper -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + OrderedRing_rminus_morph_Proper -> RelationClasses_reflexivity [] ; + OrderedRing_rminus_morph_Proper -> Morphisms_eq_proper_proxy [] ; + OrderedRing_rminus_morph_Proper -> RelationClasses_Equivalence_PER [] ; + OrderedRing_rminus_morph_Proper -> Morphisms_reflexive_proper_proxy [] ; + OrderedRing_rminus_morph_Proper -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + OrderedRing_rminus_morph_Proper -> _Rsub_def [] ; + OrderedRing_rminus_morph_Proper -> OrderedRing_SORrt [] ; + OrderedRing_rminus_morph_Proper -> OrderedRing_sor_setoid_Reflexive [] ; + OrderedRing_rminus_morph_Proper -> OrderedRing_sor_setoid [] ; + OrderedRing_rminus_morph_Proper -> OrderedRing_rplus_morph_Proper [] ; + OrderedRing_rminus_morph_Proper -> OrderedRing_sor_setoid_Transitive [] ; + OrderedRing_rminus_morph_Proper -> OrderedRing_ropp_morph_Proper [] ; + RingMicromega_SORpower -> RingMicromega_SORaddon [] ; + EnvRing_norm_aux_spec -> _rpow_pow_N [] ; + EnvRing_norm_aux_spec -> EnvRing_Psub_ok [] ; + EnvRing_norm_aux_spec -> EnvRing_PEeval [] ; + EnvRing_norm_aux_spec -> EnvRing_mkX_ok [] ; + EnvRing_norm_aux_spec -> EnvRing_PExpr_ind [] ; + EnvRing_norm_aux_spec -> EnvRing_norm_aux_PEadd [] ; + EnvRing_norm_aux_spec -> EnvRing_norm_aux_PEopp [] ; + EnvRing_norm_aux_spec -> EnvRing_Ppow_N_ok [] ; + EnvRing_mkX_ok -> Morphisms_reflexive_reflexive_proxy [] ; + EnvRing_mkX_ok -> RelationClasses_Equivalence_PER [] ; + EnvRing_mkX_ok -> Morphisms_reflexive_proper_proxy [] ; + EnvRing_mkX_ok -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + EnvRing_mkX_ok -> _morph0 [] ; + EnvRing_mkX_ok -> _morph1 [] ; + EnvRing_mkX_ok -> Setoid_Seq_refl [] ; + EnvRing_mkX_ok -> _ARadd_0_r [] ; + EnvRing_mkX_ok -> _ARmul_1_l [] ; + EnvRing_mkX_ok -> EnvRing_mk_X [] ; + EnvRing_mkX_ok -> EnvRing_Pphi [] ; + EnvRing_mkX_ok -> EnvRing_radd_ext_Proper [] ; + EnvRing_mkX_ok -> EnvRing_rmul_ext_Proper [] ; + EnvRing_mkX_ok -> Env_nth_pred_double [] ; + EnvRing_mkX_ok -> Env_nth_jump [] ; + EnvRing_mkX_ok -> Env_nth_spec [] ; + EnvRing_PExpr_ind -> EnvRing_PEc [] ; + EnvRing_PExpr_ind -> EnvRing_PEX [] ; + EnvRing_PExpr_ind -> EnvRing_PEadd [] ; + EnvRing_PExpr_ind -> EnvRing_PEsub [] ; + EnvRing_PExpr_ind -> EnvRing_PEmul [] ; + EnvRing_PExpr_ind -> EnvRing_PExpr [] ; + EnvRing_PExpr_ind -> EnvRing_PEopp [] ; + EnvRing_PExpr_ind -> EnvRing_PEpow [] ; + EnvRing_get_PEopp -> _option [] ; + EnvRing_get_PEopp -> _Some [] ; + EnvRing_get_PEopp -> _None [] ; + EnvRing_get_PEopp -> EnvRing_PExpr [] ; + EnvRing_norm_aux_PEadd -> _eq [] ; + EnvRing_norm_aux_PEadd -> _eq_refl [] ; + EnvRing_norm_aux_PEadd -> EnvRing_PEc [] ; + EnvRing_norm_aux_PEadd -> EnvRing_PEX [] ; + EnvRing_norm_aux_PEadd -> EnvRing_PEadd [] ; + EnvRing_norm_aux_PEadd -> EnvRing_PEsub [] ; + EnvRing_norm_aux_PEadd -> EnvRing_PEmul [] ; + EnvRing_norm_aux_PEadd -> EnvRing_norm_aux [] ; + EnvRing_norm_aux_PEadd -> EnvRing_get_PEopp [] ; + EnvRing_norm_aux_PEadd -> EnvRing_PEopp [] ; + EnvRing_norm_aux_PEadd -> EnvRing_PEpow [] ; + EnvRing_norm_aux_PEopp -> _eq [] ; + EnvRing_norm_aux_PEopp -> _True [] ; + EnvRing_norm_aux_PEopp -> _eq_refl [] ; + EnvRing_norm_aux_PEopp -> _I [] ; + EnvRing_norm_aux_PEopp -> EnvRing_norm_aux [] ; + EnvRing_norm_aux_PEopp -> EnvRing_get_PEopp [] ; + EnvRing_Padd_ok -> _ARadd_assoc1 [] ; + EnvRing_Padd_ok -> EnvRing_PaddC_ok [] ; + EnvRing_Padd_ok -> EnvRing_PaddX_ok [] ; + EnvRing_Ppow_N_ok -> _N0 [] ; + EnvRing_Ppow_N_ok -> _Npos [] ; + EnvRing_Ppow_N_ok -> _pow_N [] ; + EnvRing_Ppow_N_ok -> EnvRing_Ppow_N [] ; + EnvRing_Ppow_N_ok -> EnvRing_Pphi1 [] ; + EnvRing_Ppow_N_ok -> EnvRing_Ppow_pos_ok [] ; + EnvRing_Pmul_ok -> _ARdistr_r [] ; + EnvRing_Pmul_ok -> EnvRing_Padd_ok [] ; + EnvRing_Pmul_ok -> EnvRing_PmulI_ok [] ; + EnvRing_PEopp -> _N [] ; + EnvRing_PEpow -> _N [] ; + EnvRing_PmulC_ok -> Morphisms_subrelation_proper [] ; + EnvRing_PmulC_ok -> Morphisms_subrelation_refl [] ; + EnvRing_PmulC_ok -> Morphisms_PER_morphism [] ; + EnvRing_PmulC_ok -> Morphisms_iff_flip_impl_subrelation [] ; + EnvRing_PmulC_ok -> Morphisms_subrelation_respectful [] ; + EnvRing_PmulC_ok -> _tt [] ; + EnvRing_PmulC_ok -> _morph1 [] ; + EnvRing_PmulC_ok -> _ARmul_0_r [] ; + EnvRing_PmulC_ok -> _ARmul_1_r [] ; + EnvRing_PmulC_ok -> EnvRing_PmulC [] ; + EnvRing_PmulC_ok -> EnvRing_PmulC_aux_ok [] ; + EnvRing_PmulI_ok -> Z_pos_sub_discr [] ; + EnvRing_PmulI_ok -> EnvRing_Pmul [] ; + EnvRing_PmulI_ok -> EnvRing_Pjump_xO_tail [] ; + EnvRing_PmulI_ok -> EnvRing_Pjump_pred_double [] ; + EnvRing_PmulI_ok -> EnvRing_PmulC_ok [] ; + EnvRing_PmulC_aux_ok -> _ARdistr_l [] ; + EnvRing_PmulC_aux_ok -> _ARmul_assoc2 [] ; + EnvRing_PmulC_aux_ok -> _morph_mul [] ; + EnvRing_PmulC_aux_ok -> EnvRing_PmulC_aux [] ; + EnvRing_PmulC_aux_ok -> EnvRing_mkPX_ok [] ; + EnvRing_Pphi1 -> _morph1 [] ; + EnvRing_Pphi1 -> EnvRing_P1 [] ; + EnvRing_Pphi1 -> EnvRing_Pphi [] ; + EnvRing_Ppow_pos_ok -> _ARmul_assoc1 [] ; + EnvRing_Ppow_pos_ok -> EnvRing_Ppow_pos [] ; + EnvRing_Ppow_pos_ok -> EnvRing_Pmul_ok [] ; + EnvRing_PaddX_ok -> Z_pos_sub_discr [] ; + EnvRing_PaddX_ok -> _ARadd_assoc2 [] ; + EnvRing_PaddX_ok -> _ARdistr_l [] ; + EnvRing_PaddX_ok -> EnvRing_Padd [] ; + EnvRing_PaddX_ok -> EnvRing_mkPX_ok [] ; + EnvRing_PaddX_ok -> EnvRing_Pjump_xO_tail [] ; + EnvRing_PaddX_ok -> EnvRing_Pjump_pred_double [] ; + Env_nth_pred_double -> PosDef_Pos_add [] ; + Env_nth_pred_double -> Pos_succ_pred_double [] ; + Env_nth_pred_double -> Pos_add_1_r [] ; + Env_nth_pred_double -> Pos_add_diag [] ; + Env_nth_pred_double -> Env_tail [] ; + Env_nth_pred_double -> Env_nth [] ; + Env_nth_jump -> PosDef_Pos_add [] ; + Env_nth_jump -> Pos_add_comm [] ; + Env_nth_jump -> Env_hd [] ; + Env_nth_jump -> Env_tail [] ; + Env_nth_spec -> PosDef_Pos_add [] ; + Env_nth_spec -> Pos_add_diag [] ; + Env_nth_spec -> Env_hd [] ; + Env_nth_spec -> Env_tail [] ; + OrderedRing_rminus_morph -> Morphisms_proper_prf [] ; + OrderedRing_rminus_morph -> OrderedRing_rminus_morph_Proper [] ; + RingMicromega_xnegate_correct -> RingMicromega_eval_nformula [] ; + RingMicromega_xnegate_correct -> Refl_make_conj [] ; + RingMicromega_xnegate_correct -> RingMicromega_NonEqual [] ; + RingMicromega_xnegate_correct -> RingMicromega_eq0_cnf [] ; + RingMicromega_xnegate_correct -> RingMicromega_eval_pol_opp [] ; + RingMicromega_xnegate_correct -> RingMicromega_xnegate [] ; + RingMicromega_xnegate_correct -> OrderedRing_Req_dne [] ; + Tauto_eval_cnf_tt -> _I [] ; + Tauto_eval_cnf_tt -> _iff [] ; + Tauto_eval_cnf_tt -> _conj [] ; + Tauto_eval_cnf_tt -> Tauto_eval_cnf [] ; + Tauto_eval_cnf_tt -> Tauto_cnf_tt [] ; + RingMicromega_xnegate -> _list [] ; + RingMicromega_xnegate -> _nil [] ; + RingMicromega_xnegate -> _cons [] ; + RingMicromega_xnegate -> _pair [] ; + RingMicromega_xnegate -> RingMicromega_NFormula [] ; + RingMicromega_xnegate -> RingMicromega_Equal [] ; + RingMicromega_xnegate -> RingMicromega_Strict [] ; + RingMicromega_xnegate -> RingMicromega_NonStrict [] ; + RingMicromega_xnegate -> RingMicromega_popp [] ; + OrderedRing_Req_dne -> OrderedRing_Req_em [] ; + QMicromega_Qeval_expr -> QArith_base_Qpower [] ; + QMicromega_Qeval_expr -> QArith_base_Qminus [] ; + QMicromega_Qeval_expr -> Z_of_N [] ; + QMicromega_Qeval_expr -> EnvRing_PExpr [] ; + QMicromega_Qeval_expr -> RingMicromega_PolEnv [] ; + QMicromega_Qeval_pop2 -> QArith_base_Qlt [] ; + QMicromega_Qeval_pop2 -> QArith_base_Qle [] ; + QMicromega_Qeval_pop2 -> QArith_base_Qeq [] ; + QMicromega_Qeval_pop2 -> RingMicromega_Op2 [] ; + QMicromega_Qeval_op2_hold -> Tauto_isBool [] ; + QMicromega_Qeval_op2_hold -> Tauto_hold [] ; + QMicromega_Qeval_op2_hold -> QMicromega_Qeval_op2 [] ; + QMicromega_Qeval_op2_hold -> QMicromega_pop2_bop2 [] ; + QMicromega_Qeval_expr_ -> QArith_base_Qmult [] ; + QMicromega_Qeval_expr_ -> QArith_base_Qminus [] ; + QMicromega_Qeval_expr_ -> _pow_N [] ; + QMicromega_Qeval_expr_ -> RingMicromega_eval_pexpr [] ; + QMicromega_Qeval_expr_compat -> _eq_ind_r [] ; + QMicromega_Qeval_expr_compat -> _f_equal [] ; + QMicromega_Qeval_expr_compat -> _eq_trans [] ; + QMicromega_Qeval_expr_compat -> EnvRing_PExpr_ind [] ; + QMicromega_Qeval_expr_compat -> QMicromega_Qeval_expr [] ; + QMicromega_Qeval_expr_compat -> QMicromega_Qeval_expr_ [] ; + QMicromega_Qeval_expr_compat -> QMicromega_QNpower [] ; + QMicromega_Qeval_op2 -> Tauto_rtyp [] ; + QMicromega_Qeval_op2 -> QMicromega_Qeval_pop2 [] ; + QMicromega_Qeval_op2 -> QMicromega_Qeval_bop2 [] ; + QMicromega_Qeval_bop2 -> QArith_base_Qeq_bool [] ; + QMicromega_Qeval_bop2 -> RingMicromega_Op2 [] ; + QMicromega_Qeval_bop2 -> QArith_base_Qle_bool [] ; + QMicromega_Qeval_bop2 -> _negb [] ; + QMicromega_Qeval_bop2 -> QMicromega_Qlt_bool [] ; + QMicromega_Qlt_bool -> Z_mul [] ; + QMicromega_Qlt_bool -> QArith_base_Qden [] ; + QMicromega_Qlt_bool -> QArith_base_Qnum [] ; + QMicromega_Qlt_bool -> Z_ltb [] ; + Z_ltb -> _bool [] ; + Z_ltb -> _true [] ; + Z_ltb -> Z_compare [] ; + Z_ltb -> _false [] ; + QMicromega_QNpower -> _eq [] ; + QMicromega_QNpower -> QArith_base_Qpower [] ; + QMicromega_QNpower -> _eq_refl [] ; + QMicromega_QNpower -> Z_of_N [] ; + QMicromega_QNpower -> _N0 [] ; + QMicromega_QNpower -> _Npos [] ; + QMicromega_QNpower -> _pow_N [] ; + QMicromega_pop2_bop2 -> RelationClasses_Equivalence_PER [] ; + QMicromega_pop2_bop2 -> RelationClasses_iff_equivalence [] ; + QMicromega_pop2_bop2 -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + QMicromega_pop2_bop2 -> Morphisms_Prop_not_iff_morphism [] ; + QMicromega_pop2_bop2 -> QArith_base_Qeq_bool_iff [] ; + QMicromega_pop2_bop2 -> RingMicromega_OpEq [] ; + QMicromega_pop2_bop2 -> RingMicromega_OpLt [] ; + QMicromega_pop2_bop2 -> _is_true [] ; + QMicromega_pop2_bop2 -> RingMicromega_OpNEq [] ; + QMicromega_pop2_bop2 -> RingMicromega_OpLe [] ; + QMicromega_pop2_bop2 -> RingMicromega_OpGe [] ; + QMicromega_pop2_bop2 -> RingMicromega_OpGt [] ; + QMicromega_pop2_bop2 -> QMicromega_Qeval_pop2 [] ; + QMicromega_pop2_bop2 -> QMicromega_Qeval_bop2 [] ; + QMicromega_pop2_bop2 -> Bool_negb_true_iff [] ; + QMicromega_pop2_bop2 -> QMicromega_Qlt_bool_iff [] ; + QMicromega_pop2_bop2 -> QArith_base_Qle_bool_iff [] ; + Bool_negb_true_iff -> _iff [] ; + Bool_negb_true_iff -> _conj [] ; + Bool_negb_true_iff -> _eq_sym [] ; + Bool_negb_true_iff -> _negb [] ; + QMicromega_Qlt_bool_iff -> QArith_base_Qlt [] ; + QMicromega_Qlt_bool_iff -> QMicromega_Qlt_bool [] ; + QMicromega_Qlt_bool_iff -> Z_ltb_lt [] ; + QArith_base_Qle_bool_iff -> QArith_base_Qle [] ; + QArith_base_Qle_bool_iff -> QArith_base_Qle_bool [] ; + QArith_base_Qle_bool_iff -> Z_leb_le [] ; + Z_leb_le -> Z_le [] ; + Z_leb_le -> Z_leb [] ; + Z_leb_le -> _False_ind [] ; + Z_leb_le -> _eq_ind [] ; + Z_leb_le -> _True [] ; + Z_leb_le -> _eq_refl [] ; + Z_leb_le -> _I [] ; + Z_leb_le -> _iff [] ; + Z_leb_le -> _conj [] ; + Z_ltb_lt -> Z_lt [] ; + Z_ltb_lt -> _False_ind [] ; + Z_ltb_lt -> _eq_ind [] ; + Z_ltb_lt -> _True [] ; + Z_ltb_lt -> _eq_refl [] ; + Z_ltb_lt -> _I [] ; + Z_ltb_lt -> _iff [] ; + Z_ltb_lt -> _conj [] ; + Z_ltb_lt -> Z_ltb [] ; + Tauto_e_rtyp -> Tauto_rtyp [] ; + Tauto_eval_f -> _eq [] ; + Tauto_eval_f -> Tauto_eNOT [] ; + Tauto_eval_f -> Tauto_eFF [] ; + Tauto_eval_f -> Tauto_eOR [] ; + Tauto_eval_f -> Tauto_eTT [] ; + Tauto_eval_f -> Tauto_eAND [] ; + Tauto_eval_f -> Tauto_eIFF [] ; + Tauto_eval_f -> Tauto_eIMPL [] ; + Tauto_eval_f -> Tauto_GFormula [] ; + Tauto_eFF -> _false [] ; + Tauto_eFF -> _False [] ; + Tauto_eFF -> Tauto_rtyp [] ; + Tauto_eOR -> _or [] ; + Tauto_eOR -> Tauto_rtyp [] ; + Tauto_eOR -> _orb [] ; + Tauto_eTT -> _true [] ; + Tauto_eTT -> _True [] ; + Tauto_eTT -> Tauto_rtyp [] ; + Tauto_eAND -> _and [] ; + Tauto_eAND -> Tauto_rtyp [] ; + Tauto_eAND -> _andb [] ; + Tauto_eIFF -> _iff [] ; + Tauto_eIFF -> Tauto_rtyp [] ; + Tauto_eIFF -> Bool_eqb [] ; + Tauto_eIMPL -> Tauto_isProp [] ; + Tauto_eIMPL -> Tauto_rtyp [] ; + Tauto_eIMPL -> _implb [] ; + Tauto_GFormula -> _option [] ; + Tauto_GFormula -> Tauto_isProp [] ; + Tauto_GFormula -> Tauto_kind [] ; + Tauto_GFormula -> Tauto_isBool [] ; + _implb -> _bool [] ; + _implb -> _true [] ; + Bool_eqb -> _bool [] ; + Bool_eqb -> _true [] ; + Bool_eqb -> _false [] ; + _orb -> _bool [] ; + _orb -> _true [] ; + RingMicromega_check_normalised_formulas -> RingMicromega_check_inconsistent [] ; + RingMicromega_check_normalised_formulas -> RingMicromega_eval_Psatz [] ; + RingMicromega_Psatz -> _nat [] ; + RingMicromega_Psatz -> RingMicromega_PolC [] ; + RingMicromega_eval_Psatz -> _cons [] ; + RingMicromega_eval_Psatz -> RingMicromega_nformula_plus_nformula [] ; + RingMicromega_eval_Psatz -> RingMicromega_cltb [] ; + RingMicromega_eval_Psatz -> RingMicromega_Psatz [] ; + RingMicromega_eval_Psatz -> RingMicromega_pexpr_times_nformula [] ; + RingMicromega_eval_Psatz -> RingMicromega_map_option2 [] ; + RingMicromega_eval_Psatz -> ListDef_nth [] ; + RingMicromega_eval_Psatz -> RingMicromega_nformula_times_nformula [] ; + RingMicromega_eval_Psatz -> EnvRing_Psquare [] ; + RingMicromega_pexpr_times_nformula -> _option [] ; + RingMicromega_pexpr_times_nformula -> _pair [] ; + RingMicromega_pexpr_times_nformula -> _Some [] ; + RingMicromega_pexpr_times_nformula -> _None [] ; + RingMicromega_pexpr_times_nformula -> RingMicromega_NFormula [] ; + RingMicromega_pexpr_times_nformula -> RingMicromega_Equal [] ; + RingMicromega_pexpr_times_nformula -> EnvRing_Pmul [] ; + RingMicromega_map_option2 -> _option [] ; + RingMicromega_map_option2 -> _None [] ; + ListDef_nth -> _nat [] ; + ListDef_nth -> _list [] ; + RingMicromega_nformula_times_nformula -> _pair [] ; + RingMicromega_nformula_times_nformula -> RingMicromega_NFormula [] ; + RingMicromega_nformula_times_nformula -> EnvRing_Pmul [] ; + RingMicromega_nformula_times_nformula -> RingMicromega_map_option [] ; + RingMicromega_nformula_times_nformula -> RingMicromega_OpMult [] ; + RingMicromega_map_option -> _option [] ; + RingMicromega_map_option -> _None [] ; + EnvRing_Psquare -> EnvRing_Pmul [] ; + RingMicromega_OpMult -> _option [] ; + RingMicromega_OpMult -> _Some [] ; + RingMicromega_OpMult -> _None [] ; + RingMicromega_OpMult -> RingMicromega_Op1 [] ; + RingMicromega_OpMult -> RingMicromega_Equal [] ; + RingMicromega_OpMult -> RingMicromega_NonEqual [] ; + RingMicromega_OpMult -> RingMicromega_NonStrict [] ; + RingMicromega_checker_nf_sound -> RingMicromega_check_inconsistent_sound [] ; + RingMicromega_checker_nf_sound -> RingMicromega_check_normalised_formulas [] ; + RingMicromega_checker_nf_sound -> RingMicromega_eval_Psatz_Sound [] ; + RingMicromega_checker_nf_sound -> Refl_make_conj_impl [] ; + RingMicromega_checker_nf_sound -> Refl_make_conj_in [] ; + RingMicromega_eval_Psatz_Sound -> RingMicromega_nformula_plus_nformula_correct [] ; + RingMicromega_eval_Psatz_Sound -> RingMicromega_micomega_sor_setoid_Symmetric [] ; + RingMicromega_eval_Psatz_Sound -> RingMicromega_eval_Psatz [] ; + RingMicromega_eval_Psatz_Sound -> RingMicromega_nformula_times_nformula_correct [] ; + RingMicromega_eval_Psatz_Sound -> RingMicromega_pexpr_times_nformula_correct [] ; + RingMicromega_eval_Psatz_Sound -> EnvRing_Psquare_ok [] ; + RingMicromega_eval_Psatz_Sound -> OrderedRing_Rtimes_square_nonneg [] ; + RingMicromega_eval_Psatz_Sound -> List_nth_in_or_default [] ; + RingMicromega_eval_Psatz_Sound -> RingMicromega_cltb_sound [] ; + RingMicromega_eval_Psatz_Sound -> _eq_rect [] ; + RingMicromega_eval_Psatz_Sound -> RingMicromega_Psatz_ind [] ; + List_In -> _eq [] ; + List_In -> _or [] ; + List_In -> _False [] ; + List_In -> _list [] ; + Refl_make_conj_impl -> _I [] ; + Refl_make_conj_impl -> _iff [] ; + Refl_make_conj_impl -> _and_ind [] ; + Refl_make_conj_impl -> _conj [] ; + Refl_make_conj_impl -> _list_ind [] ; + Refl_make_conj_impl -> Refl_make_impl [] ; + Refl_make_conj_impl -> Refl_make_conj [] ; + Refl_make_conj_in -> _False_ind [] ; + Refl_make_conj_in -> _eq_ind_r [] ; + Refl_make_conj_in -> _list_ind [] ; + Refl_make_conj_in -> Refl_make_conj [] ; + Refl_make_conj_in -> List_In [] ; + RingMicromega_nformula_times_nformula_correct -> RingMicromega_eval_nformula [] ; + RingMicromega_nformula_times_nformula_correct -> RingMicromega_micomega_sor_setoid [] ; + RingMicromega_nformula_times_nformula_correct -> RingMicromega_rle_morph_Proper [] ; + RingMicromega_nformula_times_nformula_correct -> RingMicromega_rlt_morph_Proper [] ; + RingMicromega_nformula_times_nformula_correct -> RingMicromega_Rops_wd [] ; + RingMicromega_nformula_times_nformula_correct -> RingMicromega_SORrm [] ; + RingMicromega_nformula_times_nformula_correct -> EnvRing_Pmul_ok [] ; + RingMicromega_nformula_times_nformula_correct -> RingMicromega_nformula_times_nformula [] ; + RingMicromega_nformula_times_nformula_correct -> RingMicromega_OpMult_sound [] ; + RingMicromega_pexpr_times_nformula_correct -> RingMicromega_eval_nformula [] ; + RingMicromega_pexpr_times_nformula_correct -> RingMicromega_NonEqual [] ; + RingMicromega_pexpr_times_nformula_correct -> RingMicromega_Strict [] ; + RingMicromega_pexpr_times_nformula_correct -> RingMicromega_NonStrict [] ; + RingMicromega_pexpr_times_nformula_correct -> RingMicromega_micomega_sor_setoid_Reflexive [] ; + RingMicromega_pexpr_times_nformula_correct -> RingMicromega_Rops_wd [] ; + RingMicromega_pexpr_times_nformula_correct -> RingMicromega_SORrm [] ; + RingMicromega_pexpr_times_nformula_correct -> RingMicromega_rtimes_morph_Proper [] ; + RingMicromega_pexpr_times_nformula_correct -> RingMicromega_micomega_sor_setoid_Transitive [] ; + RingMicromega_pexpr_times_nformula_correct -> EnvRing_Pmul_ok [] ; + RingMicromega_pexpr_times_nformula_correct -> RingMicromega_pexpr_times_nformula [] ; + RingMicromega_pexpr_times_nformula_correct -> OrderedRing_Rtimes_0_r [] ; + EnvRing_Psquare_ok -> _ARmul_assoc1 [] ; + EnvRing_Psquare_ok -> EnvRing_Pmul_ok [] ; + EnvRing_Psquare_ok -> EnvRing_Psquare [] ; + OrderedRing_Rtimes_square_nonneg -> OrderedRing_Rle_lt_eq [] ; + OrderedRing_Rtimes_square_nonneg -> OrderedRing_Rtimes_neg_neg [] ; + OrderedRing_Rtimes_square_nonneg -> OrderedRing_Rtimes_0_l [] ; + List_nth_in_or_default -> _O [] ; + List_nth_in_or_default -> _S [] ; + List_nth_in_or_default -> _eq_refl [] ; + List_nth_in_or_default -> _or_introl [] ; + List_nth_in_or_default -> _or_intror [] ; + List_nth_in_or_default -> _sumbool [] ; + List_nth_in_or_default -> _left [] ; + List_nth_in_or_default -> _right [] ; + List_nth_in_or_default -> ListDef_nth [] ; + List_nth_in_or_default -> List_In [] ; + List_nth_in_or_default -> _list_rec [] ; + RingMicromega_cltb_sound -> OrderedRing_Rlt_le_neq [] ; + RingMicromega_cltb_sound -> RingMicromega_cltb [] ; + RingMicromega_cltb_sound -> RingMicromega_cleb_sound [] ; + RingMicromega_cltb_sound -> RingMicromega_cneqb_sound [] ; + RingMicromega_cltb_sound -> _andb_prop [] ; + _eq_rect -> _eq [] ; + RingMicromega_Psatz_ind -> RingMicromega_Psatz [] ; + RingMicromega_Psatz_ind -> RingMicromega_PsatzLet [] ; + RingMicromega_Psatz_ind -> RingMicromega_PsatzIn [] ; + RingMicromega_Psatz_ind -> RingMicromega_PsatzSquare [] ; + RingMicromega_Psatz_ind -> RingMicromega_PsatzMulC [] ; + RingMicromega_Psatz_ind -> RingMicromega_PsatzMulE [] ; + RingMicromega_Psatz_ind -> RingMicromega_PsatzAdd [] ; + RingMicromega_Psatz_ind -> RingMicromega_PsatzC [] ; + RingMicromega_Psatz_ind -> RingMicromega_PsatzZ [] ; + RingMicromega_PsatzLet -> _nat [] ; + RingMicromega_PsatzLet -> RingMicromega_PolC [] ; + RingMicromega_PsatzIn -> _nat [] ; + RingMicromega_PsatzIn -> RingMicromega_PolC [] ; + RingMicromega_PsatzSquare -> _nat [] ; + RingMicromega_PsatzSquare -> RingMicromega_PolC [] ; + RingMicromega_PsatzMulC -> _nat [] ; + RingMicromega_PsatzMulC -> RingMicromega_PolC [] ; + RingMicromega_PsatzMulE -> _nat [] ; + RingMicromega_PsatzMulE -> RingMicromega_PolC [] ; + RingMicromega_PsatzAdd -> _nat [] ; + RingMicromega_PsatzAdd -> RingMicromega_PolC [] ; + RingMicromega_PsatzC -> _nat [] ; + RingMicromega_PsatzC -> RingMicromega_PolC [] ; + RingMicromega_PsatzZ -> _nat [] ; + RingMicromega_PsatzZ -> RingMicromega_PolC [] ; + RingMicromega_cleb_sound -> RingMicromega_SORcleb_morph [] ; + RingMicromega_cneqb_sound -> _False_ind [] ; + RingMicromega_cneqb_sound -> _eq_ind [] ; + RingMicromega_cneqb_sound -> _True [] ; + RingMicromega_cneqb_sound -> _eq_refl [] ; + RingMicromega_cneqb_sound -> _I [] ; + RingMicromega_cneqb_sound -> RingMicromega_cneqb [] ; + RingMicromega_cneqb_sound -> RingMicromega_SORcneqb_morph [] ; + _andb_prop -> _and [] ; + _andb_prop -> _eq [] ; + _andb_prop -> _true [] ; + _andb_prop -> _eq_refl [] ; + _andb_prop -> _conj [] ; + _andb_prop -> _andb [] ; + RingMicromega_SORcneqb_morph -> RingMicromega_SORaddon [] ; + RingMicromega_SORcleb_morph -> RingMicromega_SORaddon [] ; + _list_rec -> _list [] ; + _list_rec -> _nil [] ; + _list_rec -> _cons [] ; + OrderedRing_Rtimes_neg_neg -> OrderedRing_Rtimes_pos_pos [] ; + OrderedRing_Rtimes_neg_neg -> OrderedRing_Ropp_pos_neg [] ; + OrderedRing_Rtimes_0_l -> _ring_subst_niter [] ; + OrderedRing_Rtimes_0_l -> OrderedRing_SOR_ring_lemma1 [] ; + OrderedRing_Rtimes_pos_pos -> OrderedRing_SORtimes_pos_pos [] ; + OrderedRing_SORtimes_pos_pos -> OrderedRing_SOR [] ; + OrderedRing_Ropp_pos_neg -> OrderedRing_Ropp_lt_mono [] ; + OrderedRing_Ropp_lt_mono -> OrderedRing_rlt_morph_Proper [] ; + OrderedRing_Ropp_lt_mono -> OrderedRing_Rplus_lt_mono_l [] ; + OrderedRing_Rtimes_0_r -> _ring_subst_niter [] ; + OrderedRing_Rtimes_0_r -> OrderedRing_SOR_ring_lemma1 [] ; + RingMicromega_OpMult_sound -> RingMicromega_eval_op1 [] ; + RingMicromega_OpMult_sound -> RingMicromega_Strict [] ; + RingMicromega_OpMult_sound -> RingMicromega_micomega_sor_setoid_Reflexive [] ; + RingMicromega_OpMult_sound -> RingMicromega_rtimes_morph_Proper [] ; + RingMicromega_OpMult_sound -> RingMicromega_micomega_sor_setoid_Transitive [] ; + RingMicromega_OpMult_sound -> RingMicromega_OpMult [] ; + RingMicromega_OpMult_sound -> OrderedRing_Rtimes_neq_0 [] ; + RingMicromega_OpMult_sound -> OrderedRing_Rtimes_nonneg_nonneg [] ; + OrderedRing_Rtimes_neq_0 -> OrderedRing_Rlt_neq [] ; + OrderedRing_Rtimes_neq_0 -> OrderedRing_Rlt_trichotomy [] ; + OrderedRing_Rtimes_neq_0 -> OrderedRing_Rneq_symm [] ; + OrderedRing_Rtimes_neq_0 -> OrderedRing_Rtimes_neg_neg [] ; + OrderedRing_Rtimes_neq_0 -> OrderedRing_Rtimes_comm [] ; + OrderedRing_Rtimes_neq_0 -> OrderedRing_Rtimes_pos_neg [] ; + OrderedRing_Rtimes_nonneg_nonneg -> OrderedRing_Rle_lt_eq [] ; + OrderedRing_Rtimes_nonneg_nonneg -> OrderedRing_Rtimes_0_l [] ; + OrderedRing_Rtimes_nonneg_nonneg -> OrderedRing_Rtimes_pos_pos [] ; + OrderedRing_Rtimes_nonneg_nonneg -> OrderedRing_Rtimes_0_r [] ; + OrderedRing_Rtimes_comm -> _ring_subst_niter [] ; + OrderedRing_Rtimes_comm -> OrderedRing_SOR_ring_lemma1 [] ; + OrderedRing_Rtimes_pos_neg -> OrderedRing_Rtimes_pos_pos [] ; + OrderedRing_Rtimes_pos_neg -> OrderedRing_Ropp_pos_neg [] ; + Tauto_cnf_checker_sound -> _False_ind [] ; + Tauto_cnf_checker_sound -> _eq_ind [] ; + Tauto_cnf_checker_sound -> _eq_refl [] ; + Tauto_cnf_checker_sound -> Morphisms_iff_impl_subrelation [] ; + Tauto_cnf_checker_sound -> RelationClasses_iff_Symmetric [] ; + Tauto_cnf_checker_sound -> RelationClasses_symmetry [] ; + Tauto_cnf_checker_sound -> Tauto_eval_cnf [] ; + Tauto_cnf_checker_sound -> Refl_make_conj_impl [] ; + Tauto_cnf_checker_sound -> Tauto_cnf_checker [] ; + Tauto_tauto_checker -> _unit [] ; + Tauto_tauto_checker -> Tauto_rtyp [] ; + Tauto_tauto_checker -> Tauto_cnf_checker [] ; + Tauto_tauto_checker -> Tauto_xcnf [] ; + Tauto_xcnf_correct -> _eq_trans [] ; + Tauto_xcnf_correct -> Tauto_GFormula_ind [] ; + Tauto_xcnf_correct -> Tauto_xcnf_iff [] ; + Tauto_xcnf_correct -> Tauto_xcnf_impl [] ; + Tauto_xcnf_correct -> Tauto_hold_eEQ [] ; + Tauto_xcnf_correct -> Tauto_hold_eFF [] ; + Tauto_xcnf_correct -> Tauto_hold_eOR [] ; + Tauto_xcnf_correct -> Tauto_hold_eTT [] ; + Tauto_cnf_checker -> _bool [] ; + Tauto_cnf_checker -> _true [] ; + Tauto_cnf_checker -> _false [] ; + Tauto_cnf_checker -> Tauto_cnf [] ; + Tauto_xcnf -> Tauto_mk_impl [] ; + Tauto_xcnf -> Tauto_mk_and [] ; + Tauto_xcnf -> Tauto_mk_iff [] ; + Tauto_xcnf -> Tauto_is_bool [] ; + Tauto_xcnf -> Tauto_mk_or [] ; + Tauto_mk_impl -> _negb [] ; + Tauto_mk_impl -> Tauto_TFormula [] ; + Tauto_mk_impl -> Tauto_or_cnf_opt [] ; + Tauto_mk_impl -> Tauto_and_cnf_opt [] ; + Tauto_mk_and -> Tauto_TFormula [] ; + Tauto_mk_and -> Tauto_or_cnf_opt [] ; + Tauto_mk_and -> Tauto_and_cnf_opt [] ; + Tauto_mk_iff -> _negb [] ; + Tauto_mk_iff -> Tauto_TFormula [] ; + Tauto_mk_iff -> Tauto_or_cnf_opt [] ; + Tauto_mk_iff -> Tauto_and_cnf_opt [] ; + Tauto_TFormula -> Tauto_GFormula [] ; + Tauto_is_bool -> _bool [] ; + Tauto_is_bool -> _true [] ; + Tauto_is_bool -> _false [] ; + Tauto_is_bool -> _Some [] ; + Tauto_is_bool -> _None [] ; + Tauto_is_bool -> Tauto_TFormula [] ; + Tauto_mk_or -> Tauto_TFormula [] ; + Tauto_mk_or -> Tauto_or_cnf_opt [] ; + Tauto_mk_or -> Tauto_and_cnf_opt [] ; + Tauto_or_cnf_opt -> _orb [] ; + Tauto_or_cnf_opt -> Tauto_is_cnf_ff [] ; + Tauto_or_cnf_opt -> Tauto_is_cnf_tt [] ; + Tauto_or_cnf_opt -> Tauto_or_cnf [] ; + Tauto_and_cnf_opt -> Tauto_cnf_ff [] ; + Tauto_and_cnf_opt -> _orb [] ; + Tauto_and_cnf_opt -> Tauto_and_cnf [] ; + Tauto_and_cnf_opt -> Tauto_is_cnf_ff [] ; + Tauto_and_cnf_opt -> Tauto_is_cnf_tt [] ; + Tauto_and_cnf -> List_rev_append [] ; + Tauto_and_cnf -> Tauto_cnf [] ; + Tauto_is_cnf_ff -> _bool [] ; + Tauto_is_cnf_ff -> _true [] ; + Tauto_is_cnf_ff -> _false [] ; + Tauto_is_cnf_ff -> Tauto_cnf [] ; + Tauto_is_cnf_tt -> _bool [] ; + Tauto_is_cnf_tt -> _true [] ; + Tauto_is_cnf_tt -> _false [] ; + Tauto_is_cnf_tt -> Tauto_cnf [] ; + Tauto_or_cnf -> List_rev_append [] ; + Tauto_or_cnf -> Tauto_cnf_tt [] ; + Tauto_or_cnf -> Tauto_or_clause_cnf [] ; + Tauto_or_clause_cnf -> Tauto_xor_clause_cnf [] ; + Tauto_xor_clause_cnf -> Tauto_cnf [] ; + Tauto_xor_clause_cnf -> List_fold_left [] ; + Tauto_xor_clause_cnf -> Tauto_or_clause [] ; + List_fold_left -> _list [] ; + Tauto_or_clause -> Tauto_add_term [] ; + Tauto_add_term -> _bool [] ; + Tauto_add_term -> _nil [] ; + Tauto_add_term -> _cons [] ; + Tauto_add_term -> _option [] ; + Tauto_add_term -> _Some [] ; + Tauto_add_term -> _None [] ; + Tauto_add_term -> _fst [] ; + Tauto_add_term -> Tauto_clause [] ; + Tauto_or_cnf_opt_correct -> _eq_ind_r [] ; + Tauto_or_cnf_opt_correct -> Tauto_eval_cnf_ff [] ; + Tauto_or_cnf_opt_correct -> Tauto_eval_cnf_tt [] ; + Tauto_or_cnf_opt_correct -> Tauto_or_cnf_opt [] ; + Tauto_or_cnf_opt_correct -> Tauto_or_cnf_correct [] ; + Tauto_or_cnf_opt_correct -> Tauto_is_cnf_ff_inv [] ; + Tauto_or_cnf_opt_correct -> Tauto_is_cnf_tt_inv [] ; + Tauto_GFormula_ind -> Tauto_A [] ; + Tauto_GFormula_ind -> Tauto_GFormula [] ; + Tauto_GFormula_ind -> Tauto_TT [] ; + Tauto_GFormula_ind -> Tauto_FF [] ; + Tauto_GFormula_ind -> Tauto_X [] ; + Tauto_GFormula_ind -> Tauto_AND [] ; + Tauto_GFormula_ind -> Tauto_OR [] ; + Tauto_GFormula_ind -> Tauto_NOT [] ; + Tauto_GFormula_ind -> Tauto_IMPL [] ; + Tauto_GFormula_ind -> Tauto_IFF [] ; + Tauto_GFormula_ind -> Tauto_EQ [] ; + Tauto_hold_eAND -> _iff_refl [] ; + Tauto_hold_eAND -> Tauto_isBool [] ; + Tauto_hold_eAND -> Tauto_hold [] ; + Tauto_hold_eAND -> Tauto_eAND [] ; + Tauto_hold_eAND -> Bool_andb_true_iff [] ; + Tauto_xcnf_iff -> Morphisms_iff_impl_subrelation [] ; + Tauto_xcnf_iff -> Tauto_hold_eNOT [] ; + Tauto_xcnf_iff -> Tauto_e_rtyp [] ; + Tauto_xcnf_iff -> Tauto_eval_f [] ; + Tauto_xcnf_iff -> Tauto_or_cnf_opt_correct [] ; + Tauto_xcnf_iff -> Tauto_eval_cnf_and_opt [] ; + Tauto_xcnf_iff -> Tauto_mk_iff_is_bool [] ; + Tauto_xcnf_iff -> Tauto_hold_eIFF_IMPL [] ; + Tauto_xcnf_impl -> Morphisms_iff_impl_subrelation [] ; + Tauto_xcnf_impl -> Tauto_hold_eNOT [] ; + Tauto_xcnf_impl -> Tauto_e_rtyp [] ; + Tauto_xcnf_impl -> Tauto_eval_f [] ; + Tauto_xcnf_impl -> Tauto_xcnf [] ; + Tauto_xcnf_impl -> Tauto_or_cnf_opt_correct [] ; + Tauto_xcnf_impl -> Tauto_eval_cnf_and_opt [] ; + Tauto_xcnf_impl -> Tauto_NOT [] ; + Tauto_xcnf_impl -> Tauto_IMPL [] ; + Tauto_xcnf_impl -> Tauto_hold_eIMPL [] ; + Tauto_or_cnf_correct -> Tauto_eval_cnf_cons_iff [] ; + Tauto_or_cnf_correct -> Tauto_or_cnf [] ; + Tauto_or_cnf_correct -> Tauto_eval_cnf_app [] ; + Tauto_or_cnf_correct -> Tauto_or_clause_cnf_correct [] ; + Tauto_hold_eEQ -> _False_ind [] ; + Tauto_hold_eEQ -> _eq_ind [] ; + Tauto_hold_eEQ -> _True [] ; + Tauto_hold_eEQ -> _eq_refl [] ; + Tauto_hold_eEQ -> _I [] ; + Tauto_hold_eEQ -> _conj [] ; + Tauto_hold_eEQ -> Tauto_isBool [] ; + Tauto_hold_eEQ -> Tauto_hold [] ; + Tauto_hold_eEQ -> Tauto_eIFF [] ; + Tauto_hold_eFF -> _eq_refl [] ; + Tauto_hold_eFF -> Tauto_isBool [] ; + Tauto_hold_eFF -> Tauto_eNOT [] ; + Tauto_hold_eFF -> Tauto_hold [] ; + Tauto_hold_eFF -> Tauto_eFF [] ; + Tauto_hold_eOR -> _iff_refl [] ; + Tauto_hold_eOR -> Tauto_isBool [] ; + Tauto_hold_eOR -> Tauto_hold [] ; + Tauto_hold_eOR -> Tauto_eOR [] ; + Tauto_hold_eOR -> Bool_orb_true_iff [] ; + Tauto_hold_eTT -> _eq_refl [] ; + Tauto_hold_eTT -> _I [] ; + Tauto_hold_eTT -> Tauto_isBool [] ; + Tauto_hold_eTT -> Tauto_hold [] ; + Tauto_hold_eTT -> Tauto_eTT [] ; + Tauto_eval_cnf_app -> Tauto_eval_cnf [] ; + Tauto_eval_cnf_app -> Refl_make_conj_rapp [] ; + Tauto_is_bool_inv -> _False_ind [] ; + Tauto_is_bool_inv -> _eq_ind [] ; + Tauto_is_bool_inv -> _True [] ; + Tauto_is_bool_inv -> _I [] ; + Tauto_is_bool_inv -> _f_equal [] ; + Tauto_is_bool_inv -> Tauto_A [] ; + Tauto_is_bool_inv -> Tauto_is_bool [] ; + Tauto_is_bool_inv -> Tauto_TT [] ; + Tauto_is_bool_inv -> Tauto_FF [] ; + Tauto_is_bool_inv -> Tauto_X [] ; + Tauto_is_bool_inv -> Tauto_AND [] ; + Tauto_is_bool_inv -> Tauto_OR [] ; + Tauto_is_bool_inv -> Tauto_NOT [] ; + Tauto_is_bool_inv -> Tauto_IMPL [] ; + Tauto_is_bool_inv -> Tauto_IFF [] ; + Tauto_is_bool_inv -> Tauto_EQ [] ; + Tauto_eval_cnf_and_opt -> Morphisms_subrelation_proper [] ; + Tauto_eval_cnf_and_opt -> Morphisms_subrelation_refl [] ; + Tauto_eval_cnf_and_opt -> Morphisms_PER_morphism [] ; + Tauto_eval_cnf_and_opt -> Morphisms_iff_flip_impl_subrelation [] ; + Tauto_eval_cnf_and_opt -> Morphisms_subrelation_respectful [] ; + Tauto_eval_cnf_and_opt -> _tt [] ; + Tauto_eval_cnf_and_opt -> _eq_ind_r [] ; + Tauto_eval_cnf_and_opt -> Tauto_eval_cnf_ff [] ; + Tauto_eval_cnf_and_opt -> Tauto_eval_cnf_tt [] ; + Tauto_eval_cnf_and_opt -> Tauto_and_cnf_opt [] ; + Tauto_eval_cnf_and_opt -> Tauto_eval_cnf_app [] ; + Tauto_eval_cnf_and_opt -> Tauto_is_cnf_ff_inv [] ; + Tauto_eval_cnf_and_opt -> Tauto_is_cnf_tt_inv [] ; + Tauto_mk_iff_is_bool -> Tauto_xcnf [] ; + Tauto_mk_iff_is_bool -> Tauto_is_bool_inv [] ; + Tauto_mk_iff_is_bool -> Tauto_and_cnf_opt_cnf_tt [] ; + Tauto_mk_iff_is_bool -> Tauto_or_cnf_opt_cnf_ff_r [] ; + Tauto_mk_iff_is_bool -> Tauto_and_cnf_opt_cnf_ff_r [] ; + Tauto_mk_iff_is_bool -> Tauto_or_cnf_opt_cnf_ff [] ; + Tauto_TT -> _option [] ; + Tauto_TT -> Tauto_isProp [] ; + Tauto_TT -> Tauto_kind [] ; + Tauto_TT -> Tauto_isBool [] ; + Tauto_FF -> _option [] ; + Tauto_FF -> Tauto_isProp [] ; + Tauto_FF -> Tauto_kind [] ; + Tauto_FF -> Tauto_isBool [] ; + Tauto_X -> _option [] ; + Tauto_X -> Tauto_isProp [] ; + Tauto_X -> Tauto_kind [] ; + Tauto_X -> Tauto_isBool [] ; + Tauto_AND -> _option [] ; + Tauto_AND -> Tauto_isProp [] ; + Tauto_AND -> Tauto_kind [] ; + Tauto_AND -> Tauto_isBool [] ; + Tauto_OR -> _option [] ; + Tauto_OR -> Tauto_isProp [] ; + Tauto_OR -> Tauto_kind [] ; + Tauto_OR -> Tauto_isBool [] ; + Tauto_NOT -> _option [] ; + Tauto_NOT -> Tauto_isProp [] ; + Tauto_NOT -> Tauto_kind [] ; + Tauto_NOT -> Tauto_isBool [] ; + Tauto_IMPL -> _option [] ; + Tauto_IMPL -> Tauto_isProp [] ; + Tauto_IMPL -> Tauto_kind [] ; + Tauto_IMPL -> Tauto_isBool [] ; + Tauto_IFF -> _option [] ; + Tauto_IFF -> Tauto_isProp [] ; + Tauto_IFF -> Tauto_kind [] ; + Tauto_IFF -> Tauto_isBool [] ; + Tauto_EQ -> _option [] ; + Tauto_EQ -> Tauto_isProp [] ; + Tauto_EQ -> Tauto_kind [] ; + Tauto_EQ -> Tauto_isBool [] ; + Tauto_and_cnf_opt_cnf_tt -> _eq_ind_r [] ; + Tauto_and_cnf_opt_cnf_tt -> Tauto_cnf_tt [] ; + Tauto_and_cnf_opt_cnf_tt -> Tauto_and_cnf_opt [] ; + Tauto_and_cnf_opt_cnf_tt -> Tauto_is_cnf_ff_inv [] ; + Tauto_and_cnf_opt_cnf_tt -> Bool_orb_comm [] ; + Tauto_or_cnf_opt_cnf_ff_r -> _eq_ind_r [] ; + Tauto_or_cnf_opt_cnf_ff_r -> Tauto_or_cnf_opt [] ; + Tauto_or_cnf_opt_cnf_ff_r -> Tauto_is_cnf_tt_cnf_ff [] ; + Tauto_or_cnf_opt_cnf_ff_r -> Bool_orb_comm [] ; + Tauto_or_cnf_opt_cnf_ff_r -> Tauto_if_cnf_tt [] ; + Tauto_and_cnf_opt_cnf_ff_r -> _eq_ind_r [] ; + Tauto_and_cnf_opt_cnf_ff_r -> Tauto_and_cnf_opt [] ; + Tauto_and_cnf_opt_cnf_ff_r -> Bool_orb_comm [] ; + Tauto_and_cnf_opt_cnf_ff_r -> Tauto_is_cnf_ff_cnf_ff [] ; + Tauto_or_cnf_opt_cnf_ff -> _eq_ind_r [] ; + Tauto_or_cnf_opt_cnf_ff -> Tauto_or_cnf_opt [] ; + Tauto_or_cnf_opt_cnf_ff -> Tauto_is_cnf_ff_inv [] ; + Tauto_or_cnf_opt_cnf_ff -> Tauto_is_cnf_tt_cnf_ff [] ; + Tauto_or_cnf_opt_cnf_ff -> Tauto_is_cnf_tt_inv [] ; + Tauto_is_cnf_ff_inv -> _False_ind [] ; + Tauto_is_cnf_ff_inv -> _eq_ind [] ; + Tauto_is_cnf_ff_inv -> _True [] ; + Tauto_is_cnf_ff_inv -> _eq_refl [] ; + Tauto_is_cnf_ff_inv -> _I [] ; + Tauto_is_cnf_ff_inv -> Tauto_cnf_ff [] ; + Tauto_is_cnf_ff_inv -> Tauto_is_cnf_ff [] ; + Tauto_is_cnf_tt_cnf_ff -> _eq [] ; + Tauto_is_cnf_tt_cnf_ff -> _eq_refl [] ; + Tauto_is_cnf_tt_cnf_ff -> Tauto_cnf_ff [] ; + Tauto_is_cnf_tt_cnf_ff -> Tauto_is_cnf_tt [] ; + Tauto_is_cnf_tt_inv -> _False_ind [] ; + Tauto_is_cnf_tt_inv -> _eq_ind [] ; + Tauto_is_cnf_tt_inv -> _True [] ; + Tauto_is_cnf_tt_inv -> _eq_refl [] ; + Tauto_is_cnf_tt_inv -> _I [] ; + Tauto_is_cnf_tt_inv -> _cons [] ; + Tauto_is_cnf_tt_inv -> Tauto_cnf_tt [] ; + Tauto_is_cnf_tt_inv -> Tauto_is_cnf_tt [] ; + Bool_orb_comm -> _eq [] ; + Bool_orb_comm -> _false [] ; + Bool_orb_comm -> _eq_refl [] ; + Bool_orb_comm -> _orb [] ; + Tauto_is_cnf_ff_cnf_ff -> _eq [] ; + Tauto_is_cnf_ff_cnf_ff -> _eq_refl [] ; + Tauto_is_cnf_ff_cnf_ff -> Tauto_cnf_ff [] ; + Tauto_is_cnf_ff_cnf_ff -> Tauto_is_cnf_ff [] ; + Tauto_if_cnf_tt -> _eq_sym [] ; + Tauto_if_cnf_tt -> Tauto_is_cnf_tt_inv [] ; + _app -> _list [] ; + _app -> _cons [] ; + Refl_make_conj_rapp -> List_rev_append [] ; + Refl_make_conj_rapp -> Refl_make_conj_app [] ; + Refl_make_conj_app -> Morphisms_reflexive_reflexive_proxy [] ; + Refl_make_conj_app -> Morphisms_Reflexive_partial_app_morphism [] ; + Refl_make_conj_app -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Refl_make_conj_app -> Morphisms_eq_proper_proxy [] ; + Refl_make_conj_app -> RelationClasses_Equivalence_PER [] ; + Refl_make_conj_app -> Morphisms_reflexive_proper_proxy [] ; + Refl_make_conj_app -> RelationClasses_iff_equivalence [] ; + Refl_make_conj_app -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Refl_make_conj_app -> Morphisms_Prop_and_iff_morphism [] ; + Refl_make_conj_app -> _list_ind [] ; + Refl_make_conj_app -> Refl_make_conj_cons [] ; + Refl_make_conj_app -> _app [] ; + Bool_orb_true_iff -> _eq [] ; + Bool_orb_true_iff -> _false [] ; + Bool_orb_true_iff -> _eq_refl [] ; + Bool_orb_true_iff -> _iff [] ; + Bool_orb_true_iff -> _conj [] ; + Bool_orb_true_iff -> _or_ind [] ; + Bool_orb_true_iff -> _or_introl [] ; + Bool_orb_true_iff -> _or_intror [] ; + Bool_orb_true_iff -> _orb [] ; + Tauto_or_clause_cnf_correct -> Morphisms_PER_morphism [] ; + Tauto_or_clause_cnf_correct -> Tauto_eval_cnf [] ; + Tauto_or_clause_cnf_correct -> Tauto_or_clause_cnf [] ; + Tauto_or_clause_cnf_correct -> Tauto_or_clause_correct [] ; + Tauto_or_clause_correct -> Morphisms_Prop_or_iff_morphism [] ; + Tauto_or_clause_correct -> Tauto_or_clause [] ; + Tauto_or_clause_correct -> Tauto_add_term_correct [] ; + Tauto_eval_opt_clause -> _option [] ; + Tauto_eval_opt_clause -> Tauto_eval_clause [] ; + Tauto_add_term_correct -> _true [] ; + Tauto_add_term_correct -> _false [] ; + Tauto_add_term_correct -> Morphisms_subrelation_proper [] ; + Tauto_add_term_correct -> Morphisms_reflexive_reflexive_proxy [] ; + Tauto_add_term_correct -> Morphisms_subrelation_refl [] ; + Tauto_add_term_correct -> Morphisms_Reflexive_partial_app_morphism [] ; + Tauto_add_term_correct -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Tauto_add_term_correct -> Morphisms_eq_proper_proxy [] ; + Tauto_add_term_correct -> RelationClasses_Equivalence_PER [] ; + Tauto_add_term_correct -> Morphisms_iff_flip_impl_subrelation [] ; + Tauto_add_term_correct -> Morphisms_reflexive_proper_proxy [] ; + Tauto_add_term_correct -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + Tauto_add_term_correct -> Morphisms_subrelation_respectful [] ; + Tauto_add_term_correct -> _tt [] ; + Tauto_add_term_correct -> RelationClasses_iff_equivalence [] ; + Tauto_add_term_correct -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Tauto_add_term_correct -> Morphisms_per_partial_app_morphism [] ; + Tauto_add_term_correct -> Morphisms_trans_co_impl_morphism [] ; + Tauto_add_term_correct -> Morphisms_Prop_not_iff_morphism [] ; + Tauto_add_term_correct -> Morphisms_impl_pars [] ; + Tauto_add_term_correct -> Morphisms_Prop_and_iff_morphism [] ; + Tauto_add_term_correct -> _list_ind [] ; + Tauto_add_term_correct -> Refl_make_conj_cons [] ; + Tauto_add_term_correct -> Tauto_add_term [] ; + Tauto_add_term_correct -> Tauto_eval_opt_clause [] ; + Tauto_hold_eIMPL -> _false [] ; + Tauto_hold_eIMPL -> _eq_refl [] ; + Tauto_hold_eIMPL -> _iff_refl [] ; + Tauto_hold_eIMPL -> Tauto_isBool [] ; + Tauto_hold_eIMPL -> Tauto_hold [] ; + Tauto_hold_eIMPL -> Tauto_eIMPL [] ; + Tauto_hold_eIFF_IMPL -> Morphisms_reflexive_reflexive_proxy [] ; + Tauto_hold_eIFF_IMPL -> Morphisms_Reflexive_partial_app_morphism [] ; + Tauto_hold_eIFF_IMPL -> RelationClasses_Equivalence_PER [] ; + Tauto_hold_eIFF_IMPL -> Morphisms_reflexive_proper_proxy [] ; + Tauto_hold_eIFF_IMPL -> RelationClasses_iff_equivalence [] ; + Tauto_hold_eIFF_IMPL -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Tauto_hold_eIFF_IMPL -> Morphisms_Prop_and_iff_morphism [] ; + Tauto_hold_eIFF_IMPL -> Tauto_hold_eAND [] ; + Tauto_hold_eIFF_IMPL -> Tauto_hold_eIMPL [] ; + Tauto_hold_eIFF_IMPL -> Tauto_hold_eIFF [] ; + Tauto_hold_eIFF -> _False_ind [] ; + Tauto_hold_eIFF -> _eq_ind [] ; + Tauto_hold_eIFF -> _True [] ; + Tauto_hold_eIFF -> _I [] ; + Tauto_hold_eIFF -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Tauto_hold_eIFF -> Morphisms_eq_proper_proxy [] ; + Tauto_hold_eIFF -> RelationClasses_iff_Transitive [] ; + Tauto_hold_eIFF -> _and_ind [] ; + Tauto_hold_eIFF -> _iff_refl [] ; + Tauto_hold_eIFF -> Tauto_isBool [] ; + Tauto_hold_eIFF -> Tauto_hold [] ; + Tauto_hold_eIFF -> Tauto_eIFF [] ; + Tauto_hold_eIFF -> Bool_eqb_true_iff [] ; + Bool_eqb_true_iff -> _iff [] ; + Bool_eqb_true_iff -> _conj [] ; + Bool_eqb_true_iff -> _eq_sym [] ; + Bool_eqb_true_iff -> Bool_eqb [] ; + Bool_andb_true_iff -> _eq [] ; + Bool_andb_true_iff -> _true [] ; + Bool_andb_true_iff -> _eq_refl [] ; + Bool_andb_true_iff -> _iff [] ; + Bool_andb_true_iff -> _and_ind [] ; + Bool_andb_true_iff -> _conj [] ; + Bool_andb_true_iff -> _andb [] ; + RingMicromega_eval_nformula_dec -> _pair [] ; + RingMicromega_eval_nformula_dec -> RingMicromega_eval_nformula [] ; + RingMicromega_eval_nformula_dec -> RingMicromega_Equal [] ; + RingMicromega_eval_nformula_dec -> RingMicromega_NonEqual [] ; + RingMicromega_eval_nformula_dec -> RingMicromega_Strict [] ; + RingMicromega_eval_nformula_dec -> RingMicromega_NonStrict [] ; + RingMicromega_eval_nformula_dec -> OrderedRing_Rle_ngt [] ; + RingMicromega_eval_nformula_dec -> OrderedRing_Rlt_nge [] ; + QArith_base_Qmult_0_l -> QArith_base_Qmult [] ; + QArith_base_Qmult_0_l -> _eq_refl [] ; + QArith_base_Qmult_0_l -> QArith_base_Qeq [] ; + QArith_base_Qmult_lt_compat_r -> QArith_base_Qlt [] ; + QArith_base_Qmult_lt_compat_r -> QArith_base_Qmult [] ; + QArith_base_Qmult_lt_compat_r -> Z_mul_1_r [] ; + QArith_base_Qmult_lt_compat_r -> Pos2Z_inj_mul [] ; + QArith_base_Qmult_lt_compat_r -> Z_mul_shuffle1 [] ; + QArith_base_Qmult_lt_compat_r -> Z_mul_pos_pos [] ; + QArith_base_Qle_trans -> QArith_base_Qmake [] ; + QArith_base_Qle_trans -> QArith_base_Qle [] ; + QArith_base_Qle_trans -> Z_mul_le_mono_pos_r [] ; + QArith_base_Qle_trans -> Z_mul_shuffle0 [] ; + QArith_base_Qlt_not_eq -> QArith_base_Qlt [] ; + QArith_base_Qlt_not_eq -> QArith_base_Qeq [] ; + QArith_base_Qlt_not_eq -> Z_lt_neq [] ; + QArith_base_Q_dec -> QArith_base_Qlt [] ; + QArith_base_Q_dec -> QArith_base_Qeq [] ; + QArith_base_Q_dec -> _Z_dec_ [] ; + QArith_base_Qle_antisym -> QArith_base_Qle [] ; + QArith_base_Qle_antisym -> QArith_base_Qeq [] ; + QArith_base_Qle_antisym -> Z_le_antisymm [] ; + QArith_base_Qnot_le_lt -> QArith_base_Qlt [] ; + QArith_base_Qnot_le_lt -> QArith_base_Qle [] ; + QArith_base_Qnot_le_lt -> Z_nle_gt [] ; + OrderedRing_mk_SOR_theory -> _not [] ; + OrderedRing_mk_SOR_theory -> _or [] ; + OrderedRing_mk_SOR_theory -> _iff [] ; + OrderedRing_mk_SOR_theory -> Setoid_Setoid_Theory [] ; + OrderedRing_mk_SOR_theory -> _ring_theory [] ; + Z_nle_gt -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_nle_gt -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_nle_gt -> Z_Private_OrderTac_Tac_not_ge_lt [] ; + Z_le_antisymm -> Z_Private_OrderTac_Tac_not_neq_eq [] ; + Z_le_antisymm -> Z_Private_OrderTac_Tac_le_antisym [] ; + Z_le_antisymm -> Z_Private_OrderTac_Tac_eq_neq [] ; + Z_le_antisymm -> Z_Private_OrderTac_Tac_eq_refl [] ; + Z_Private_OrderTac_Tac_le_antisym -> RelationClasses_StrictOrder_Irreflexive [] ; + Z_Private_OrderTac_Tac_le_antisym -> RelationClasses_StrictOrder_Transitive [] ; + Z_Private_OrderTac_Tac_le_antisym -> Z_Private_OrderTac_IsTotal_le_lteq [] ; + Z_Private_OrderTac_Tac_le_antisym -> Z_Private_OrderTac_IsTotal_eq_equiv [] ; + Z_Private_OrderTac_Tac_le_antisym -> Z_Private_OrderTac_IsTotal_lt_strorder [] ; + Z_Private_OrderTac_Tac_eq_neq -> Z_Private_OrderTac_Tac_eq_sym [] ; + Z_Private_OrderTac_Tac_eq_neq -> Z_Private_OrderTac_Tac_eq_trans [] ; + Z_Private_OrderTac_Tac_eq_refl -> RelationClasses_reflexivity [] ; + Z_Private_OrderTac_Tac_eq_refl -> RelationClasses_Equivalence_Reflexive [] ; + Z_Private_OrderTac_Tac_eq_refl -> Z_Private_OrderTac_IsTotal_eq_equiv [] ; + _Z_dec_ -> _sumor [] ; + _Z_dec_ -> Z_eq_dec [] ; + _Z_dec_ -> _not_Zeq_inf [] ; + _Z_dec_ -> _inleft [] ; + _Z_dec_ -> _inright [] ; + Z_eq_dec -> Pos_eq_dec [] ; + Z_eq_dec -> _Z_rec [] ; + _not_Zeq_inf -> _Z_le_lt_eq_dec [] ; + _not_Zeq_inf -> _Z_lt_ge_dec [] ; + _not_Zeq_inf -> Z_ge_le [] ; + _Z_le_lt_eq_dec -> Z_le [] ; + _Z_le_lt_eq_dec -> Z_lt [] ; + _Z_le_lt_eq_dec -> _and_ind [] ; + _Z_le_lt_eq_dec -> Z_compare_eq_iff [] ; + _Z_le_lt_eq_dec -> _False_rec [] ; + _Z_le_lt_eq_dec -> _sumbool [] ; + _Z_le_lt_eq_dec -> _left [] ; + _Z_le_lt_eq_dec -> _right [] ; + _Z_le_lt_eq_dec -> _Zcompare_rec [] ; + Z_ge -> _eq [] ; + Z_ge -> Z_compare [] ; + Z_ge -> _not [] ; + _Z_lt_ge_dec -> Z_ge [] ; + _Z_lt_ge_dec -> _Z_lt_dec [] ; + Z_ge_le -> Z_ge_le_iff [] ; + Z_ge_le_iff -> Z_le [] ; + Z_ge_le_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Z_ge_le_iff -> RelationClasses_reflexivity [] ; + Z_ge_le_iff -> Morphisms_eq_proper_proxy [] ; + Z_ge_le_iff -> RelationClasses_iff_Transitive [] ; + Z_ge_le_iff -> RelationClasses_iff_Reflexive [] ; + Z_ge_le_iff -> Morphisms_Prop_not_iff_morphism [] ; + Z_ge_le_iff -> _CompOpp_iff [] ; + Z_ge_le_iff -> Z_compare_antisym [] ; + Z_ge_le_iff -> Z_ge [] ; + _Z_lt_dec -> Z_lt [] ; + _Z_lt_dec -> _not [] ; + _Z_lt_dec -> _False_ind [] ; + _Z_lt_dec -> _eq_ind [] ; + _Z_lt_dec -> _True [] ; + _Z_lt_dec -> _eq_refl [] ; + _Z_lt_dec -> _I [] ; + _Z_lt_dec -> _sumbool [] ; + _Z_lt_dec -> _left [] ; + _Z_lt_dec -> _right [] ; + _Zcompare_rec -> _Zcompare_rect [] ; + _Zcompare_rect -> _eq [] ; + _Zcompare_rect -> Z_compare [] ; + _Zcompare_rect -> _eq_refl [] ; + Pos_eq_dec -> _not [] ; + Pos_eq_dec -> _False_ind [] ; + Pos_eq_dec -> _True [] ; + Pos_eq_dec -> _I [] ; + Pos_eq_dec -> _eq_ind_r [] ; + Pos_eq_dec -> _f_equal [] ; + Pos_eq_dec -> _sumbool_rec [] ; + Pos_eq_dec -> _positive_rec [] ; + _Z_rec -> _Z [] ; + _Z_rec -> _Z0 [] ; + _Z_rec -> _Zpos [] ; + _Z_rec -> _Zneg [] ; + _sumbool_rec -> _sumbool [] ; + _sumbool_rec -> _left [] ; + _sumbool_rec -> _right [] ; + _positive_rec -> _positive [] ; + _positive_rec -> _xO [] ; + _positive_rec -> _xH [] ; + _positive_rec -> _xI [] ; + Z_lt_neq -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_lt_neq -> Z_Private_OrderTac_Tac_eq_lt [] ; + Z_lt_neq -> Z_Private_OrderTac_Tac_eq_sym [] ; + Z_mul_shuffle1 -> Z_mul_shuffle0 [] ; + Z_mul_pos_pos -> Z_mul_lt_mono_pos_r [] ; + QArith_base_Qeq_bool_neq -> Morphisms_subrelation_proper [] ; + QArith_base_Qeq_bool_neq -> Morphisms_reflexive_reflexive_proxy [] ; + QArith_base_Qeq_bool_neq -> Morphisms_subrelation_refl [] ; + QArith_base_Qeq_bool_neq -> Morphisms_Reflexive_partial_app_morphism [] ; + QArith_base_Qeq_bool_neq -> RelationClasses_iff_Reflexive [] ; + QArith_base_Qeq_bool_neq -> Morphisms_iff_flip_impl_subrelation [] ; + QArith_base_Qeq_bool_neq -> Morphisms_reflexive_proper_proxy [] ; + QArith_base_Qeq_bool_neq -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + QArith_base_Qeq_bool_neq -> Morphisms_subrelation_respectful [] ; + QArith_base_Qeq_bool_neq -> _tt [] ; + QArith_base_Qeq_bool_neq -> _eq_ind_r [] ; + QArith_base_Qeq_bool_neq -> RelationClasses_iff_Symmetric [] ; + QArith_base_Qeq_bool_neq -> RelationClasses_symmetry [] ; + QArith_base_Qeq_bool_neq -> Morphisms_Prop_not_iff_morphism [] ; + QArith_base_Qeq_bool_neq -> Morphisms_impl_pars [] ; + QArith_base_Qeq_bool_neq -> QArith_base_Qeq_bool_iff [] ; + QArith_base_Qle_bool_imp_le -> QArith_base_Qle_bool_iff [] ; + RingMicromega_mk_SOR_addon -> _false [] ; + RingMicromega_mk_SOR_addon -> _not [] ; + RingMicromega_mk_SOR_addon -> _ring_morph [] ; + RingMicromega_mk_SOR_addon -> _power_theory [] ; + RingMicromega_OpAdd_sound -> RingMicromega_eval_op1 [] ; + RingMicromega_OpAdd_sound -> RingMicromega_Equal [] ; + RingMicromega_OpAdd_sound -> RingMicromega_micomega_sor_setoid [] ; + RingMicromega_OpAdd_sound -> RingMicromega_rle_morph_Proper [] ; + RingMicromega_OpAdd_sound -> RingMicromega_rlt_morph_Proper [] ; + RingMicromega_OpAdd_sound -> RingMicromega_micomega_sor_setoid_Reflexive [] ; + RingMicromega_OpAdd_sound -> RingMicromega_rplus_morph_Proper [] ; + RingMicromega_OpAdd_sound -> RingMicromega_micomega_sor_setoid_Transitive [] ; + RingMicromega_OpAdd_sound -> RingMicromega_OpAdd [] ; + RingMicromega_OpAdd_sound -> OrderedRing_Rplus_pos_pos [] ; + RingMicromega_OpAdd_sound -> OrderedRing_Rplus_nonneg_pos [] ; + RingMicromega_OpAdd_sound -> OrderedRing_Rplus_0_r [] ; + RingMicromega_OpAdd_sound -> OrderedRing_Rplus_nonneg_nonneg [] ; + RingMicromega_OpAdd_sound -> OrderedRing_Rplus_pos_nonneg [] ; + RingMicromega_OpAdd -> _option [] ; + RingMicromega_OpAdd -> _Some [] ; + RingMicromega_OpAdd -> _None [] ; + RingMicromega_OpAdd -> RingMicromega_Op1 [] ; + RingMicromega_OpAdd -> RingMicromega_NonEqual [] ; + RingMicromega_OpAdd -> RingMicromega_Strict [] ; + RingMicromega_OpAdd -> RingMicromega_NonStrict [] ; + OrderedRing_Rplus_pos_pos -> OrderedRing_Rplus_0_l [] ; + OrderedRing_Rplus_pos_pos -> OrderedRing_Rplus_lt_mono [] ; + OrderedRing_Rplus_nonneg_pos -> OrderedRing_Rplus_0_l [] ; + OrderedRing_Rplus_nonneg_pos -> OrderedRing_Rplus_le_lt_mono [] ; + OrderedRing_Rplus_0_r -> _ring_subst_niter [] ; + OrderedRing_Rplus_0_r -> OrderedRing_SOR_ring_lemma1 [] ; + OrderedRing_Rplus_nonneg_nonneg -> OrderedRing_Rplus_0_l [] ; + OrderedRing_Rplus_nonneg_nonneg -> OrderedRing_Rplus_le_mono [] ; + OrderedRing_Rplus_pos_nonneg -> OrderedRing_Rplus_0_l [] ; + OrderedRing_Rplus_pos_nonneg -> OrderedRing_Rplus_lt_le_mono [] ; + OrderedRing_Rplus_lt_le_mono -> OrderedRing_Rplus_lt_mono_r [] ; + OrderedRing_Rplus_lt_le_mono -> OrderedRing_Rlt_le_trans [] ; + OrderedRing_Rplus_le_mono -> OrderedRing_Rplus_le_mono_r [] ; + OrderedRing_Rplus_le_mono -> OrderedRing_Rle_trans [] ; + OrderedRing_Rplus_le_lt_mono -> OrderedRing_Rplus_lt_mono_l [] ; + OrderedRing_Rplus_le_lt_mono -> OrderedRing_Rplus_le_mono_r [] ; + OrderedRing_Rplus_le_lt_mono -> OrderedRing_Rle_lt_trans [] ; + OrderedRing_Rplus_lt_mono -> OrderedRing_Rplus_lt_mono_r [] ; + OrderedRing_Rplus_lt_mono -> OrderedRing_Rlt_trans [] ; + ZifyInst_Inj_pos_Z -> Pos2Z_pos_is_pos [] ; + ZifyInst_Inj_pos_Z -> ZifyClasses_InjTyp [] ; + ZifyInst_Inj_pos_Z -> ZifyClasses_mkinj [] ; + ZifyClasses_rew_iff -> _iff [] ; + ZifyClasses_rew_iff -> _proj1 [] ; + _Zmult_lt_compat2 -> Z_mul_le_mono_pos_r [] ; + _Zmult_lt_compat2 -> Z_le_lt_trans [] ; + ZifyClasses_mkapp2 -> _eq_ind [] ; + Z_pow_add_r -> Z_mul_assoc [] ; + Z_pow_add_r -> Z_mul_1_l [] ; + Z_pow_add_r -> Z_add_nonneg_nonneg [] ; + Z_pow_add_r -> Z_le_ind [] ; + Z_pow_add_r -> Z_pow_wd [] ; + Z_pow_add_r -> Z_pow_succ_r [] ; + Z_pow_add_r -> Z_pow_0_r [] ; + Qpower_Qpower_minus -> Qpower_Qpower_not_0 [] ; + Qpower_Qpower_minus -> Qpower_Qpower_opp [] ; + Qpower_Qpower_minus -> Qpower_Qpower_plus [] ; + Z_add_1_r -> Z_add_0_r [] ; + Z_add_1_r -> Z_add_succ_r [] ; + Z_add_1_r -> Z_one_succ [] ; + ZifyClasses_and_morph -> _iff [] ; + ZifyClasses_and_morph -> _and_ind [] ; + ZifyClasses_and_morph -> _conj [] ; + QExtra_Pos_log2floor_plus1_spec -> QExtra_Pos_log2floor_plus1 [] ; + QExtra_Pos_log2floor_plus1_spec -> VarMap_find [] ; + QExtra_Pos_log2floor_plus1_spec -> VarMap_Empty [] ; + QExtra_Pos_log2floor_plus1_spec -> VarMap_Elt [] ; + QExtra_Pos_log2floor_plus1_spec -> VarMap_Branch [] ; + QExtra_Pos_log2floor_plus1_spec -> ZifyInst_Inj_pos_Z [] ; + QExtra_Pos_log2floor_plus1_spec -> ZifyClasses_rew_iff [] ; + QExtra_Pos_log2floor_plus1_spec -> ZifyClasses_mkapp2 [] ; + QExtra_Pos_log2floor_plus1_spec -> Pos2Z_inj_pow [] ; + QExtra_Pos_log2floor_plus1_spec -> ZifyClasses_inj [] ; + QExtra_Pos_log2floor_plus1_spec -> ZifyClasses_mkrel [] ; + QExtra_Pos_log2floor_plus1_spec -> Z_pow_pos_nonneg [] ; + QExtra_Pos_log2floor_plus1_spec -> Z_pow_nonneg [] ; + QExtra_Pos_log2floor_plus1_spec -> ZMicromega_ZTautoChecker_sound [] ; + QExtra_Pos_log2floor_plus1_spec -> Pos_pow_succ_r [] ; + QExtra_Pos_log2floor_plus1_spec -> ZifyClasses_rew_iff_rev [] ; + QExtra_Pos_log2floor_plus1_spec -> ZifyClasses_mkapp [] ; + Pos2Z_inj_succ -> _eq_ind_r [] ; + Pos2Z_inj_succ -> Z_succ [] ; + Pos2Z_inj_succ -> Pos_add_1_r [] ; + Qpower_Qpower_decomp_pos -> QArith_base_Qpower [] ; + Qpower_Qpower_decomp_pos -> QArith_base_Q_Setoid [] ; + Qpower_Qpower_decomp_pos -> Qpower_Qpower_decomp_positive [] ; + Z_to_N -> _Z [] ; + Z_to_N -> _N [] ; + Z_to_N -> _N0 [] ; + Z_to_N -> _Npos [] ; + _Zmult_lt_reg_r -> Z_mul_lt_mono_pos_r [] ; + PosExtra_Pos_pow_1_r -> Pos_pow [] ; + PosExtra_Pos_pow_1_r -> Datatypes_id [] ; + PosExtra_Pos_pow_1_r -> Pos_iter_invariant [] ; + Pos_pow -> Pos_mul [] ; + Pos_pow -> Pos_iter [] ; + Pos2Z_pos_is_pos -> _Z0 [] ; + Pos2Z_pos_is_pos -> _Zpos [] ; + Pos2Z_pos_is_pos -> Z_lt [] ; + Pos2Z_pos_is_pos -> _eq_refl [] ; + Pos2Z_inj_pow -> Z_pow [] ; + Pos2Z_inj_pow -> Pos2Z_inj_pow_pos [] ; + ZMicromega_ZTautoChecker -> Tauto_BFormula [] ; + ZMicromega_ZTautoChecker -> ListDef_map [] ; + ZMicromega_ZTautoChecker -> Tauto_tauto_checker [] ; + ZMicromega_ZTautoChecker -> ZMicromega_normalise [] ; + ZMicromega_ZTautoChecker -> ZMicromega_ZChecker [] ; + ZMicromega_ZTautoChecker -> ZMicromega_Zdeduce [] ; + ZMicromega_ZTautoChecker -> ZMicromega_negate [] ; + QArith_base_Qlt_shift_div_l -> QArith_base_Qle_comp [] ; + QArith_base_Qlt_shift_div_l -> QArith_base_Qlt_not_eq [] ; + QArith_base_Qlt_shift_div_l -> QArith_base_Qnot_le_lt [] ; + QArith_base_Qlt_shift_div_l -> QArith_base_Qnot_eq_sym [] ; + QArith_base_Qlt_shift_div_l -> QArith_base_Qinv_lt_0_compat [] ; + QArith_base_Qlt_shift_div_l -> QArith_base_Qmult_lt_0_le_reg_r [] ; + QArith_base_Qlt_shift_div_l -> QArith_base_Qlt_not_le [] ; + QArith_base_Qlt_shift_div_l -> QArith_base_Qdiv_mult_l [] ; + ZifyClasses_inj -> ZifyClasses_InjTyp [] ; + ZifyClasses_mkrel -> _eq_ind [] ; + ZifyClasses_mkrel -> _iff [] ; + Z_pow_pos_nonneg -> Z_mul_pos_pos [] ; + Z_pow_pos_nonneg -> Z_lt_0_1 [] ; + Z_pow_pos_nonneg -> Z_lt_1_2 [] ; + Z_pow_pos_nonneg -> Z_le_ind [] ; + Z_pow_pos_nonneg -> Z_pow_wd [] ; + Z_pow_pos_nonneg -> Z_pow_succ_r [] ; + Z_pow_pos_nonneg -> Z_pow_0_r [] ; + Z_pow_nonneg -> Z_mul_nonneg_nonneg [] ; + Z_pow_nonneg -> Z_lt_ge_cases [] ; + Z_pow_nonneg -> Z_lt_0_1 [] ; + Z_pow_nonneg -> Z_lt_1_2 [] ; + Z_pow_nonneg -> Z_le_ind [] ; + Z_pow_nonneg -> Z_pow_wd [] ; + Z_pow_nonneg -> Z_pow_neg_r [] ; + Z_pow_nonneg -> Z_pow_succ_r [] ; + Z_pow_nonneg -> Z_pow_0_r [] ; + ZMicromega_ZTautoChecker_sound -> Tauto_tauto_checker_sound [] ; + ZMicromega_ZTautoChecker_sound -> Tauto_eval_bf [] ; + ZMicromega_ZTautoChecker_sound -> Refl_make_impl_map [] ; + ZMicromega_ZTautoChecker_sound -> ZMicromega_ZTautoChecker [] ; + ZMicromega_ZTautoChecker_sound -> ZMicromega_normalise_correct [] ; + ZMicromega_ZTautoChecker_sound -> ZMicromega_Zeval_nformula_dec [] ; + ZMicromega_ZTautoChecker_sound -> ZMicromega_Zeval_formula_compat [] ; + ZMicromega_ZTautoChecker_sound -> ZMicromega_ZChecker_sound [] ; + ZMicromega_ZTautoChecker_sound -> ZMicromega_negate_correct [] ; + Qpower_Qpower_0_lt -> QArith_base_Qlt_le_weak [] ; + Qpower_Qpower_0_lt -> QArith_base_Qlt_not_eq [] ; + Qpower_Qpower_0_lt -> QArith_base_Qlt_leneq [] ; + Qpower_Qpower_0_lt -> Qpower_Qpower_not_0 [] ; + Qpower_Qpower_0_lt -> QArith_base_Qnot_eq_sym [] ; + Qpower_Qpower_0_lt -> Qpower_Qpower_0_le [] ; + ZMicromega_ZArithProof -> _list [] ; + ZMicromega_ZArithProof -> ZMicromega_ZWitness [] ; + ZMicromega_DoneProof -> _list [] ; + ZMicromega_DoneProof -> ZMicromega_ZWitness [] ; + ZMicromega_RatProof -> _list [] ; + ZMicromega_RatProof -> ZMicromega_ZWitness [] ; + ZMicromega_CutProof -> _list [] ; + ZMicromega_CutProof -> ZMicromega_ZWitness [] ; + ZMicromega_ZWitness -> _Z [] ; + ZMicromega_ZWitness -> RingMicromega_Psatz [] ; + QArith_base_Qlt_leneq -> Morphisms_subrelation_proper [] ; + QArith_base_Qlt_leneq -> Morphisms_reflexive_reflexive_proxy [] ; + QArith_base_Qlt_leneq -> Morphisms_subrelation_refl [] ; + QArith_base_Qlt_leneq -> Morphisms_Reflexive_partial_app_morphism [] ; + QArith_base_Qlt_leneq -> Morphisms_iff_flip_impl_subrelation [] ; + QArith_base_Qlt_leneq -> Morphisms_reflexive_proper_proxy [] ; + QArith_base_Qlt_leneq -> Morphisms_subrelation_respectful [] ; + QArith_base_Qlt_leneq -> _tt [] ; + QArith_base_Qlt_leneq -> Morphisms_iff_impl_subrelation [] ; + QArith_base_Qlt_leneq -> Morphisms_Prop_not_iff_morphism [] ; + QArith_base_Qlt_leneq -> Morphisms_Prop_and_iff_morphism [] ; + QArith_base_Qlt_leneq -> QArith_base_Qeq_alt [] ; + QArith_base_Qlt_leneq -> QArith_base_Qle_alt [] ; + QArith_base_Qlt_leneq -> QArith_base_Qlt_alt [] ; + Qpower_Qpower_not_0 -> QArith_base_Qpower [] ; + Qpower_Qpower_not_0 -> QArith_base_Q_Setoid [] ; + Qpower_Qpower_not_0 -> QArith_base_Qmult_comp [] ; + Qpower_Qpower_not_0 -> QArith_base_Qmult_inv_r [] ; + Qpower_Qpower_not_0 -> QArith_base_Qmult_0_r [] ; + Qpower_Qpower_not_0 -> Qpower_Qpower_not_0_positive [] ; + QArith_base_Qnot_eq_sym -> _not [] ; + QArith_base_Qnot_eq_sym -> QArith_base_Qeq_sym [] ; + Qpower_Qpower_0_le -> QArith_base_Qpower [] ; + Qpower_Qpower_0_le -> QArith_base_Qinv_le_0_compat [] ; + Qpower_Qpower_0_le -> Qpower_Qpower_pos_positive [] ; + QArith_base_Qinv_le_0_compat -> QArith_base_Qinv [] ; + QArith_base_Qinv_le_0_compat -> QArith_base_Qle [] ; + Qpower_Qpower_pos_positive -> QArith_base_Qpower_positive [] ; + Qpower_Qpower_pos_positive -> QArith_base_Qmult_le_0_compat [] ; + QArith_base_Qmult_le_0_compat -> QArith_base_Qmult [] ; + QArith_base_Qmult_le_0_compat -> QArith_base_Qle [] ; + QArith_base_Qmult_le_0_compat -> Z_mul_1_r [] ; + QArith_base_Qmult_le_0_compat -> Z_mul_nonneg_nonneg [] ; + Z_mul_nonneg_nonneg -> Z_mul_le_mono_nonneg [] ; + Z_mul_nonneg_nonneg -> Z_Private_OrderTac_Tac_le_refl [] ; + Z_Private_OrderTac_Tac_le_refl -> Morphisms_iff_flip_impl_subrelation [] ; + Z_Private_OrderTac_Tac_le_refl -> RelationClasses_Equivalence_Reflexive [] ; + Z_Private_OrderTac_Tac_le_refl -> Z_Private_OrderTac_IsTotal_le_lteq [] ; + Z_Private_OrderTac_Tac_le_refl -> Z_Private_OrderTac_IsTotal_eq_equiv [] ; + QArith_base_Qmult_0_r -> QArith_base_Qmult [] ; + QArith_base_Qmult_0_r -> _ring_subst_niter [] ; + QArith_base_Qmult_0_r -> QArith_base_Qeq [] ; + QArith_base_Qmult_0_r -> _Zr_ring_lemma1 [] ; + Qpower_Qpower_not_0_positive -> QArith_base_Qpower_positive [] ; + Qpower_Qpower_not_0_positive -> QArith_base_Qmult_integral [] ; + QArith_base_Qmult_integral -> QArith_base_Qmult [] ; + QArith_base_Qmult_integral -> QArith_base_Qeq [] ; + QArith_base_Qmult_integral -> Z_mul_1_r [] ; + QArith_base_Qmult_integral -> Z_eq_mul_0 [] ; + Z_eq_mul_0 -> Z_lt_neq [] ; + Z_eq_mul_0 -> Z_mul_pos_pos [] ; + Z_eq_mul_0 -> Z_mul_neg_neg [] ; + Z_eq_mul_0 -> Z_mul_neg_pos [] ; + Z_mul_neg_neg -> Z_mul_lt_mono_neg_r [] ; + Z_mul_neg_pos -> Z_mul_pos_neg [] ; + Z_mul_pos_neg -> Z_mul_lt_mono_neg_r [] ; + Z_mul_lt_mono_neg_r -> Z_mul_comm [] ; + Z_mul_lt_mono_neg_r -> Z_mul_lt_mono_neg_l [] ; + ZMicromega_ZSORaddon -> Z_mul [] ; + ZMicromega_ZSORaddon -> Morphisms_subrelation_proper [] ; + ZMicromega_ZSORaddon -> Morphisms_reflexive_reflexive_proxy [] ; + ZMicromega_ZSORaddon -> Morphisms_subrelation_refl [] ; + ZMicromega_ZSORaddon -> Morphisms_Reflexive_partial_app_morphism [] ; + ZMicromega_ZSORaddon -> RelationClasses_iff_Reflexive [] ; + ZMicromega_ZSORaddon -> Morphisms_iff_flip_impl_subrelation [] ; + ZMicromega_ZSORaddon -> Morphisms_reflexive_proper_proxy [] ; + ZMicromega_ZSORaddon -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + ZMicromega_ZSORaddon -> Morphisms_subrelation_respectful [] ; + ZMicromega_ZSORaddon -> _tt [] ; + ZMicromega_ZSORaddon -> RelationClasses_iff_Symmetric [] ; + ZMicromega_ZSORaddon -> RelationClasses_symmetry [] ; + ZMicromega_ZSORaddon -> Morphisms_Prop_not_iff_morphism [] ; + ZMicromega_ZSORaddon -> Morphisms_impl_pars [] ; + ZMicromega_ZSORaddon -> Z_sub [] ; + ZMicromega_ZSORaddon -> Z_eqb_eq [] ; + ZMicromega_ZSORaddon -> _mkmorph [] ; + ZMicromega_ZSORaddon -> _mkpow_th [] ; + ZMicromega_ZSORaddon -> RingMicromega_SORaddon [] ; + ZMicromega_ZSORaddon -> Z_leb_le [] ; + ZMicromega_ZSORaddon -> RingMicromega_mk_SOR_addon [] ; + ZMicromega_normalise_correct -> Tauto_eval_cnf_ff [] ; + ZMicromega_normalise_correct -> ZMicromega_normalise [] ; + ZMicromega_normalise_correct -> ZMicromega_cnf_of_list_correct [] ; + ZMicromega_normalise_correct -> ZMicromega_xnnormalise_correct [] ; + ZMicromega_normalise_correct -> ZMicromega_xnormalise_correct [] ; + ZMicromega_Zeval_formula -> RingMicromega_Formula [] ; + ZMicromega_Zeval_formula -> ZMicromega_Zeval_expr [] ; + ZMicromega_Zeval_formula -> ZMicromega_Zeval_op2 [] ; + ZMicromega_normalise -> Tauto_cnf_ff [] ; + ZMicromega_normalise -> ZMicromega_cnf_of_list [] ; + ZMicromega_normalise -> ZMicromega_xnnormalise [] ; + ZMicromega_normalise -> ZMicromega_xnormalise [] ; + ZMicromega_eval_nformula -> Z_le [] ; + ZMicromega_eval_nformula -> Z_mul [] ; + ZMicromega_eval_nformula -> Z_lt [] ; + ZMicromega_eval_nformula -> Z_add [] ; + ZMicromega_eval_nformula -> RingMicromega_eval_nformula [] ; + ZMicromega_Zeval_nformula_dec -> RingMicromega_eval_nformula_dec [] ; + ZMicromega_Zeval_nformula_dec -> ZMicromega_eval_nformula [] ; + ZMicromega_Zeval_nformula_dec -> ZMicromega_Zsor [] ; + ZMicromega_Zeval_formula_compat -> RingMicromega_Build_Formula [] ; + ZMicromega_Zeval_formula_compat -> ZMicromega_Zeval_formula [] ; + ZMicromega_Zeval_formula_compat -> ZMicromega_Zeval_op2_hold [] ; + ZMicromega_Zsor -> Z_add_le_mono_l [] ; + ZMicromega_Zsor -> _Zth [] ; + ZMicromega_Zsor -> OrderedRing_SOR [] ; + ZMicromega_Zsor -> OrderedRing_mk_SOR_theory [] ; + ZMicromega_Zsor -> Z_le_antisymm [] ; + ZMicromega_Zsor -> Z_mul_pos_pos [] ; + ZMicromega_Zsor -> Z_le_neq [] ; + ZMicromega_Zsor -> _Zsth [] ; + ZMicromega_ZChecker -> ZMicromega_ZArithProof [] ; + ZMicromega_ZChecker -> ZMicromega_Zunsat [] ; + ZMicromega_ZChecker -> ZMicromega_xnnormalise [] ; + ZMicromega_ZChecker -> ZMicromega_eval_Psatz [] ; + ZMicromega_ZChecker -> Pos_leb [] ; + ZMicromega_ZChecker -> ZMicromega_max_var_nformulae [] ; + ZMicromega_ZChecker -> ZMicromega_mk_eq_pos [] ; + ZMicromega_ZChecker -> ZMicromega_nformula_of_cutting_plane [] ; + ZMicromega_ZChecker -> ZMicromega_bound_var [] ; + ZMicromega_ZChecker -> ZMicromega_genCuttingPlane [] ; + ZMicromega_ZChecker -> ZMicromega_popp [] ; + ZMicromega_Zdeduce -> Z_add [] ; + ZMicromega_Zdeduce -> Z_eqb [] ; + ZMicromega_Zdeduce -> RingMicromega_nformula_plus_nformula [] ; + ZMicromega_Zunsat -> _Z0 [] ; + ZMicromega_Zunsat -> Z_leb [] ; + ZMicromega_Zunsat -> Z_eqb [] ; + ZMicromega_Zunsat -> RingMicromega_check_inconsistent [] ; + ZMicromega_ZChecker_sound -> Pos_eqb_refl [] ; + ZMicromega_ZChecker_sound -> _proj2 [] ; + ZMicromega_ZChecker_sound -> Refl_make_conj_impl [] ; + ZMicromega_ZChecker_sound -> ZMicromega_ZChecker [] ; + ZMicromega_ZChecker_sound -> ZMicromega_Zunsat_sound [] ; + ZMicromega_ZChecker_sound -> ZMicromega_Private_Pos_neq_le_lt [] ; + ZMicromega_ZChecker_sound -> ZMicromega_eval_nformula_mk_eq_pos [] ; + ZMicromega_ZChecker_sound -> ZMicromega_cutting_plane_sound [] ; + ZMicromega_ZChecker_sound -> Pos_leb_spec [] ; + ZMicromega_ZChecker_sound -> ZMicromega_agree_env_eval_nformulae [] ; + ZMicromega_ZChecker_sound -> Pos_eqb_neq [] ; + ZMicromega_ZChecker_sound -> ZMicromega_eval_nformula_bound_var [] ; + ZMicromega_ZChecker_sound -> ZMicromega_eval_Psatz_sound [] ; + ZMicromega_ZChecker_sound -> ZMicromega_eval_nformula_split [] ; + ZMicromega_ZChecker_sound -> ZMicromega_genCuttingPlaneNone [] ; + ZMicromega_ZChecker_sound -> ZMicromega_ZArithProof_ind [] ; + ZMicromega_negate -> ZMicromega_cnf_of_list [] ; + ZMicromega_negate -> ZMicromega_xnnormalise [] ; + ZMicromega_negate -> ZMicromega_xnegate [] ; + ZMicromega_negate_correct -> Tauto_eval_cnf_tt [] ; + ZMicromega_negate_correct -> ZMicromega_negate [] ; + ZMicromega_negate_correct -> ZMicromega_cnf_of_list_correct [] ; + ZMicromega_negate_correct -> ZMicromega_xnegate_correct [] ; + ZMicromega_negate_correct -> ZMicromega_xnnormalise_correct [] ; + ZMicromega_cnf_of_list_correct -> _list_ind [] ; + ZMicromega_cnf_of_list_correct -> Tauto_eval_cnf_cons_iff [] ; + ZMicromega_cnf_of_list_correct -> ZMicromega_cnf_of_list [] ; + ZMicromega_cnf_of_list_correct -> ZMicromega_Zunsat_sound [] ; + ZMicromega_cnf_of_list -> _cons [] ; + ZMicromega_cnf_of_list -> _pair [] ; + ZMicromega_cnf_of_list -> Tauto_cnf_tt [] ; + ZMicromega_cnf_of_list -> List_fold_right [] ; + ZMicromega_cnf_of_list -> ZMicromega_Zunsat [] ; + ZMicromega_xnnormalise -> _pair [] ; + ZMicromega_xnnormalise -> RingMicromega_Formula [] ; + ZMicromega_xnnormalise -> RingMicromega_NFormula [] ; + ZMicromega_xnnormalise -> RingMicromega_Equal [] ; + ZMicromega_xnnormalise -> RingMicromega_NonEqual [] ; + ZMicromega_xnnormalise -> RingMicromega_Strict [] ; + ZMicromega_xnnormalise -> RingMicromega_NonStrict [] ; + ZMicromega_xnnormalise -> ZMicromega_psub [] ; + ZMicromega_xnnormalise -> ZMicromega_normZ [] ; + ZMicromega_xnegate -> _list [] ; + ZMicromega_xnegate -> _nil [] ; + ZMicromega_xnegate -> _cons [] ; + ZMicromega_xnegate -> _pair [] ; + ZMicromega_xnegate -> RingMicromega_NFormula [] ; + ZMicromega_xnegate -> RingMicromega_Equal [] ; + ZMicromega_xnegate -> RingMicromega_NonStrict [] ; + ZMicromega_xnegate -> ZMicromega_psub [] ; + ZMicromega_Zunsat_sound -> RingMicromega_check_inconsistent_sound [] ; + ZMicromega_Zunsat_sound -> ZMicromega_ZSORaddon [] ; + ZMicromega_Zunsat_sound -> ZMicromega_eval_nformula [] ; + ZMicromega_Zunsat_sound -> ZMicromega_Zsor [] ; + ZMicromega_Zunsat_sound -> ZMicromega_Zunsat [] ; + ZMicromega_xnegate_correct -> Refl_make_conj [] ; + ZMicromega_xnegate_correct -> RingMicromega_NonEqual [] ; + ZMicromega_xnegate_correct -> RingMicromega_Strict [] ; + ZMicromega_xnegate_correct -> ZMicromega_eval_nformula [] ; + ZMicromega_xnegate_correct -> ZMicromega_xnegate [] ; + ZMicromega_xnegate_correct -> ZMicromega_eval_pol_sub [] ; + ZMicromega_xnegate_correct -> Z_eq_decidable [] ; + ZMicromega_xnegate_correct -> ZMicromega_eval_pol_Pc [] ; + ZMicromega_xnegate_correct -> ZMicromega_eq_cnf [] ; + ZMicromega_xnnormalise_correct -> ZMicromega_eval_nformula [] ; + ZMicromega_xnnormalise_correct -> ZMicromega_xnnormalise [] ; + ZMicromega_xnnormalise_correct -> Z_lt_0_sub [] ; + ZMicromega_xnnormalise_correct -> ZMicromega_eval_pol_sub [] ; + ZMicromega_xnnormalise_correct -> ZMicromega_le_0_iff [] ; + ZMicromega_xnnormalise_correct -> ZMicromega_eval_pol_norm [] ; + ZMicromega_xnnormalise_correct -> ZMicromega_Zeval_formula_compat_ [] ; + ZMicromega_xnnormalise_correct -> Z_add_sub_assoc [] ; + Z_lt_0_sub -> Z_add_lt_mono_r [] ; + Z_lt_0_sub -> Z_sub_simpl_r [] ; + ZMicromega_eval_pol_sub -> RingMicromega_eval_pol_sub [] ; + ZMicromega_eval_pol_sub -> ZMicromega_ZSORaddon [] ; + ZMicromega_eval_pol_sub -> ZMicromega_Zsor [] ; + ZMicromega_eval_pol_sub -> ZMicromega_eval_pol [] ; + ZMicromega_eval_pol_sub -> ZMicromega_psub [] ; + ZMicromega_eval_pol -> Z_mul [] ; + ZMicromega_eval_pol -> Z_add [] ; + ZMicromega_eval_pol -> RingMicromega_eval_pol [] ; + ZMicromega_le_0_iff -> Z_le_0_sub [] ; + ZMicromega_eval_pol_norm -> RingMicromega_eval_pol_norm [] ; + ZMicromega_eval_pol_norm -> ZMicromega_ZSORaddon [] ; + ZMicromega_eval_pol_norm -> ZMicromega_Zsor [] ; + ZMicromega_eval_pol_norm -> ZMicromega_eval_pol [] ; + ZMicromega_eval_pol_norm -> ZMicromega_normZ [] ; + ZMicromega_eval_pol_norm -> ZMicromega_eval_expr [] ; + ZMicromega_Zeval_formula_compat_ -> RingMicromega_OpEq [] ; + ZMicromega_Zeval_formula_compat_ -> RingMicromega_OpLt [] ; + ZMicromega_Zeval_formula_compat_ -> RingMicromega_Build_Formula [] ; + ZMicromega_Zeval_formula_compat_ -> Tauto_isProp [] ; + ZMicromega_Zeval_formula_compat_ -> RingMicromega_OpNEq [] ; + ZMicromega_Zeval_formula_compat_ -> RingMicromega_OpLe [] ; + ZMicromega_Zeval_formula_compat_ -> RingMicromega_OpGe [] ; + ZMicromega_Zeval_formula_compat_ -> RingMicromega_OpGt [] ; + ZMicromega_Zeval_formula_compat_ -> Z_ge_le [] ; + ZMicromega_Zeval_formula_compat_ -> ZMicromega_Zeval_formula [] ; + ZMicromega_Zeval_formula_compat_ -> ZMicromega_Zeval_formula_ [] ; + ZMicromega_Zeval_formula_compat_ -> ZMicromega_Zeval_expr_compat [] ; + ZMicromega_Zeval_formula_compat_ -> Z_gt_lt [] ; + ZMicromega_Zeval_formula_compat_ -> Z_le_ge [] ; + ZMicromega_Zeval_formula_compat_ -> Z_lt_gt [] ; + ZMicromega_psub -> Z_eqb [] ; + ZMicromega_psub -> Z_sub [] ; + ZMicromega_psub -> RingMicromega_psub [] ; + ZMicromega_normZ -> Z_mul [] ; + ZMicromega_normZ -> Z_eqb [] ; + ZMicromega_normZ -> Z_sub [] ; + ZMicromega_normZ -> RingMicromega_norm [] ; + ZMicromega_Zeval_formula_ -> Z_le [] ; + ZMicromega_Zeval_formula_ -> Z_mul [] ; + ZMicromega_Zeval_formula_ -> Z_lt [] ; + ZMicromega_Zeval_formula_ -> Z_sub [] ; + ZMicromega_Zeval_formula_ -> _pow_N [] ; + ZMicromega_Zeval_formula_ -> RingMicromega_eval_formula [] ; + Z_add_sub_assoc -> Z_add_assoc [] ; + Z_add_sub_assoc -> Z_add_opp_r [] ; + ZMicromega_eval_expr -> Z_mul [] ; + ZMicromega_eval_expr -> Z_sub [] ; + ZMicromega_eval_expr -> _pow_N [] ; + ZMicromega_eval_expr -> RingMicromega_eval_pexpr [] ; + ZMicromega_Zeval_expr_compat -> EnvRing_PExpr_ind [] ; + ZMicromega_Zeval_expr_compat -> ZMicromega_eval_expr [] ; + ZMicromega_Zeval_expr_compat -> ZMicromega_Zeval_expr [] ; + ZMicromega_Zeval_expr_compat -> IntDef_Z_mul [] ; + ZMicromega_Zeval_expr_compat -> IntDef_Z_sub [] ; + ZMicromega_Zeval_expr_compat -> ZMicromega_ZNpower [] ; + Z_gt -> _eq [] ; + Z_gt -> Z_compare [] ; + ZMicromega_Zeval_expr -> Z_of_N [] ; + ZMicromega_Zeval_expr -> Z_sub [] ; + ZMicromega_Zeval_expr -> Z_pow [] ; + ZMicromega_Zeval_expr -> EnvRing_PExpr [] ; + ZMicromega_Zeval_expr -> RingMicromega_PolEnv [] ; + ZMicromega_Zeval_pop2 -> Z_le [] ; + ZMicromega_Zeval_pop2 -> Z_lt [] ; + ZMicromega_Zeval_pop2 -> RingMicromega_Op2 [] ; + ZMicromega_Zeval_pop2 -> Z_ge [] ; + ZMicromega_Zeval_pop2 -> Z_gt [] ; + ZMicromega_Zeval_op2 -> Tauto_rtyp [] ; + ZMicromega_Zeval_op2 -> ZMicromega_Zeval_pop2 [] ; + ZMicromega_Zeval_op2 -> ZMicromega_Zeval_bop2 [] ; + Z_gt_lt -> Z_gt_lt_iff [] ; + Z_le_ge -> Z_ge_le_iff [] ; + Z_lt_gt -> Z_gt_lt_iff [] ; + Z_gt_lt_iff -> Z_lt [] ; + Z_gt_lt_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Z_gt_lt_iff -> RelationClasses_reflexivity [] ; + Z_gt_lt_iff -> Morphisms_eq_proper_proxy [] ; + Z_gt_lt_iff -> RelationClasses_iff_Transitive [] ; + Z_gt_lt_iff -> RelationClasses_iff_Reflexive [] ; + Z_gt_lt_iff -> _CompOpp_iff [] ; + Z_gt_lt_iff -> Z_compare_antisym [] ; + Z_gt_lt_iff -> Z_gt [] ; + ZMicromega_Zeval_bop2 -> Z_leb [] ; + ZMicromega_Zeval_bop2 -> Z_eqb [] ; + ZMicromega_Zeval_bop2 -> RingMicromega_Op2 [] ; + ZMicromega_Zeval_bop2 -> _negb [] ; + ZMicromega_Zeval_bop2 -> Z_ltb [] ; + ZMicromega_Zeval_bop2 -> Z_geb [] ; + ZMicromega_Zeval_bop2 -> Z_gtb [] ; + Z_geb -> _bool [] ; + Z_geb -> _true [] ; + Z_geb -> Z_compare [] ; + Z_geb -> _false [] ; + Z_gtb -> _bool [] ; + Z_gtb -> _true [] ; + Z_gtb -> Z_compare [] ; + Z_gtb -> _false [] ; + IntDef_Z_add -> PosDef_Pos_add [] ; + IntDef_Z_add -> IntDef_Z_pos_sub [] ; + IntDef_Z_mul -> _Z [] ; + IntDef_Z_mul -> _Z0 [] ; + IntDef_Z_mul -> _Zpos [] ; + IntDef_Z_mul -> PosDef_Pos_mul [] ; + IntDef_Z_mul -> _Zneg [] ; + IntDef_Z_opp -> _Z [] ; + IntDef_Z_opp -> _Z0 [] ; + IntDef_Z_opp -> _Zpos [] ; + IntDef_Z_opp -> _Zneg [] ; + IntDef_Z_sub -> IntDef_Z_add [] ; + IntDef_Z_sub -> IntDef_Z_opp [] ; + ZMicromega_ZNpower -> Z_of_N [] ; + ZMicromega_ZNpower -> Z_mul_comm [] ; + ZMicromega_ZNpower -> Z_mul_assoc [] ; + ZMicromega_ZNpower -> _N0 [] ; + ZMicromega_ZNpower -> _Npos [] ; + ZMicromega_ZNpower -> Z_pow [] ; + ZMicromega_ZNpower -> _pow_N [] ; + ZMicromega_ZNpower -> Z_mul_1_l [] ; + ZMicromega_ZNpower -> _f_equal2 [] ; + _f_equal2 -> _eq [] ; + _f_equal2 -> _eq_refl [] ; + IntDef_Z_pos_sub -> IntDef_Z_pred_double [] ; + IntDef_Z_pos_sub -> IntDef_Z_double [] ; + IntDef_Z_pos_sub -> IntDef_Z_succ_double [] ; + IntDef_Z_pred_double -> _Z [] ; + IntDef_Z_pred_double -> _Zpos [] ; + IntDef_Z_pred_double -> _Zneg [] ; + IntDef_Z_pred_double -> PosDef_Pos_pred_double [] ; + IntDef_Z_double -> _Z [] ; + IntDef_Z_double -> _Z0 [] ; + IntDef_Z_double -> _Zpos [] ; + IntDef_Z_double -> _xO [] ; + IntDef_Z_double -> _Zneg [] ; + IntDef_Z_succ_double -> _Z [] ; + IntDef_Z_succ_double -> _Zpos [] ; + IntDef_Z_succ_double -> _Zneg [] ; + IntDef_Z_succ_double -> PosDef_Pos_pred_double [] ; + Z_le_0_sub -> Z_add_le_mono_r [] ; + Z_le_0_sub -> Z_sub_simpl_r [] ; + Z_sub_simpl_r -> Z_sub_diag [] ; + Z_sub_simpl_r -> Z_sub_sub_distr [] ; + Z_sub_sub_distr -> Z_add_assoc [] ; + Z_sub_sub_distr -> Z_opp_sub_distr [] ; + Z_opp_sub_distr -> Z_add_opp_r [] ; + Z_opp_sub_distr -> Z_opp_add_distr [] ; + Z_opp_sub_distr -> Z_opp_involutive [] ; + Z_opp_add_distr -> Morphisms_per_partial_app_morphism [] ; + Z_opp_add_distr -> Z_bi_induction [] ; + Z_opp_add_distr -> Z_add_0_l [] ; + Z_opp_add_distr -> Z_pred_inj_wd [] ; + Z_opp_add_distr -> Z_opp_wd [] ; + Z_opp_add_distr -> Z_opp_succ [] ; + Z_opp_add_distr -> Z_opp_0 [] ; + Z_opp_add_distr -> Z_add_pred_l [] ; + Z_opp_involutive -> Z_bi_induction [] ; + Z_opp_involutive -> Z_succ_inj_wd [] ; + Z_opp_involutive -> Z_opp_0 [] ; + Z_opp_involutive -> Z_opp_pred [] ; + Z_opp_pred -> Z_eq_equiv [] ; + Z_opp_pred -> Z_succ_wd [] ; + Z_opp_pred -> Z_succ_pred [] ; + Z_opp_pred -> Z_opp_wd [] ; + Z_opp_pred -> Z_opp_succ [] ; + Z_eq_decidable -> Z_Private_OrderTac_Tac_eq_lt [] ; + Z_eq_decidable -> Z_Private_OrderTac_Tac_lt_eq [] ; + Z_eq_decidable -> Z_Private_OrderTac_Tac_not_neq_eq [] ; + Z_eq_decidable -> Z_Private_OrderTac_Tac_eq_neq [] ; + Z_eq_decidable -> Z_Private_OrderTac_Tac_eq_refl [] ; + Z_eq_decidable -> Decidable_decidable [] ; + ZMicromega_eval_pol_Pc -> _eq [] ; + ZMicromega_eval_pol_Pc -> _eq_refl [] ; + ZMicromega_eval_pol_Pc -> EnvRing_Pc [] ; + ZMicromega_eval_pol_Pc -> ZMicromega_eval_pol [] ; + ZMicromega_eq_cnf -> Morphisms_Prop_and_iff_morphism [] ; + ZMicromega_eq_cnf -> RelationClasses_PreOrder_Reflexive [] ; + ZMicromega_eq_cnf -> Z_le_preorder [] ; + ZMicromega_eq_cnf -> Z_nlt_ge [] ; + ZMicromega_eq_cnf -> Z_le_antisymm [] ; + ZMicromega_eq_cnf -> ZMicromega_lt_le_iff [] ; + ZMicromega_eq_cnf -> Z_opp_pos_neg [] ; + ZMicromega_eq_cnf -> Z_sub_opp_l [] ; + ZMicromega_lt_le_iff -> Z_succ_pred [] ; + ZMicromega_lt_le_iff -> Z_lt_succ_r [] ; + ZMicromega_lt_le_iff -> Z_sub_1_r [] ; + Z_sub_1_r -> RelationClasses_Equivalence_Reflexive [] ; + Z_sub_1_r -> Z_eq_equiv [] ; + Z_sub_1_r -> Z_pred_wd [] ; + Z_sub_1_r -> Z_one_succ [] ; + Z_sub_1_r -> Z_sub_succ_r [] ; + Z_sub_1_r -> Z_sub_wd [] ; + Z_sub_1_r -> Z_sub_0_r [] ; + Z_opp_pos_neg -> Z_opp_lt_mono [] ; + Z_sub_opp_l -> Z_add_opp_r [] ; + Z_opp_lt_mono -> Z_lt_0_sub [] ; + Z_opp_lt_mono -> Z_sub_opp_r [] ; + Z_opp_lt_mono -> Z_add_opp_l [] ; + Z_sub_opp_r -> Z_add_opp_r [] ; + Z_sub_opp_r -> Z_opp_involutive [] ; + Z_add_opp_l -> Z_add_opp_r [] ; + Decidable_decidable -> _not [] ; + Decidable_decidable -> _or [] ; + ZMicromega_eval_Psatz -> Z_leb [] ; + ZMicromega_eval_Psatz -> Z_mul [] ; + ZMicromega_eval_Psatz -> Z_add [] ; + ZMicromega_eval_Psatz -> Z_eqb [] ; + ZMicromega_eval_Psatz -> RingMicromega_eval_Psatz [] ; + ZMicromega_eval_Psatz -> ZMicromega_ZWitness [] ; + ZMicromega_Private_Pos_neq_le_lt -> ZMicromega_Private_Pos_neq_lt [] ; + ZMicromega_Private_Pos_neq_le_lt -> Pos_le_lt_trans [] ; + Pos_leb -> _bool [] ; + Pos_leb -> _true [] ; + Pos_leb -> _false [] ; + Pos_leb -> Pos_compare [] ; + ZMicromega_max_var_nformulae -> _fst [] ; + ZMicromega_max_var_nformulae -> RingMicromega_NFormula [] ; + ZMicromega_max_var_nformulae -> List_fold_left [] ; + ZMicromega_max_var_nformulae -> ZMicromega_max_var [] ; + ZMicromega_mk_eq_pos -> _Z [] ; + ZMicromega_mk_eq_pos -> RingMicromega_Formula [] ; + ZMicromega_mk_eq_pos -> EnvRing_PEX [] ; + ZMicromega_mk_eq_pos -> EnvRing_PEsub [] ; + ZMicromega_mk_eq_pos -> RingMicromega_OpEq [] ; + ZMicromega_mk_eq_pos -> RingMicromega_Build_Formula [] ; + Z_leb_spec -> Morphisms_iff_flip_impl_subrelation [] ; + Z_leb_spec -> Z_compare_lt_iff [] ; + Z_leb_spec -> _BoolSpec [] ; + Z_leb_spec -> _BoolSpecT [] ; + Z_leb_spec -> _BoolSpecF [] ; + Z_leb_spec -> Z_leb_spec0 [] ; + Z_leb_spec -> Z_compare_nge_iff [] ; + ZMicromega_eval_nformula_mk_eq_pos -> ZMicromega_xnnormalise_correct [] ; + ZMicromega_eval_nformula_mk_eq_pos -> ZMicromega_mk_eq_pos [] ; + ZMicromega_nformula_of_cutting_plane -> _pair [] ; + ZMicromega_nformula_of_cutting_plane -> RingMicromega_NFormula [] ; + ZMicromega_nformula_of_cutting_plane -> ZMicromega_padd [] ; + Z_opp_nonneg_nonpos -> Z_opp_le_mono [] ; + ZMicromega_cutting_plane_sound -> RingMicromega_NonEqual [] ; + ZMicromega_cutting_plane_sound -> RingMicromega_Strict [] ; + ZMicromega_cutting_plane_sound -> Z_eq_mul_0 [] ; + ZMicromega_cutting_plane_sound -> ZMicromega_genCuttingPlane [] ; + ZMicromega_cutting_plane_sound -> Z_gtb_lt [] ; + ZMicromega_cutting_plane_sound -> Z_divide_opp_r [] ; + ZMicromega_cutting_plane_sound -> ZMicromega_eval_pol_add [] ; + ZMicromega_cutting_plane_sound -> Bool_negb_false_iff [] ; + ZMicromega_cutting_plane_sound -> ZMicromega_Zdivide_ceiling [] ; + ZMicromega_cutting_plane_sound -> Z_lt_le_pred [] ; + ZMicromega_cutting_plane_sound -> ZMicromega_makeCuttingPlane_ns_sound [] ; + ZMicromega_cutting_plane_sound -> Z_div_unique_exact [] ; + ZMicromega_cutting_plane_sound -> Bool_andb_false_iff [] ; + ZMicromega_cutting_plane_sound -> Z_sub_move_0_r [] ; + Pos_leb_spec -> Morphisms_iff_flip_impl_subrelation [] ; + Pos_leb_spec -> Pos_compare_lt_iff [] ; + Pos_leb_spec -> _BoolSpec [] ; + Pos_leb_spec -> _BoolSpecT [] ; + Pos_leb_spec -> _BoolSpecF [] ; + Pos_leb_spec -> Pos_leb_spec0 [] ; + Pos_leb_spec -> Pos_compare_nge_iff [] ; + ZMicromega_bound_var -> _Z [] ; + ZMicromega_bound_var -> _Z0 [] ; + ZMicromega_bound_var -> RingMicromega_Formula [] ; + ZMicromega_bound_var -> EnvRing_PEc [] ; + ZMicromega_bound_var -> EnvRing_PEX [] ; + ZMicromega_bound_var -> RingMicromega_Build_Formula [] ; + ZMicromega_bound_var -> RingMicromega_OpGe [] ; + ZMicromega_agree_env_eval_nformulae -> Morphisms_Prop_and_iff_morphism [] ; + ZMicromega_agree_env_eval_nformulae -> Refl_make_conj_cons [] ; + ZMicromega_agree_env_eval_nformulae -> ZMicromega_max_var_nformulae [] ; + ZMicromega_agree_env_eval_nformulae -> Pos_max_1_l [] ; + ZMicromega_agree_env_eval_nformulae -> ZMicromega_max_var_nformulae_mono_aux_ [] ; + ZMicromega_agree_env_eval_nformulae -> ZMicromega_max_var_nformulae_mono_aux [] ; + ZMicromega_agree_env_eval_nformulae -> _and_iff_compat_l [] ; + ZMicromega_agree_env_eval_nformulae -> ZMicromega_agree_env_eval_nformula [] ; + ZMicromega_genCuttingPlane -> _option [] ; + ZMicromega_genCuttingPlane -> _Some [] ; + ZMicromega_genCuttingPlane -> _None [] ; + ZMicromega_genCuttingPlane -> Z_eqb [] ; + ZMicromega_genCuttingPlane -> RingMicromega_NFormula [] ; + ZMicromega_genCuttingPlane -> _negb [] ; + ZMicromega_genCuttingPlane -> RingMicromega_Equal [] ; + ZMicromega_genCuttingPlane -> RingMicromega_NonStrict [] ; + ZMicromega_genCuttingPlane -> _andb [] ; + ZMicromega_genCuttingPlane -> ZMicromega_makeCuttingPlane [] ; + Pos_eqb_neq -> RelationClasses_reflexivity [] ; + Pos_eqb_neq -> RelationClasses_iff_Reflexive [] ; + Pos_eqb_neq -> RelationClasses_iff_Symmetric [] ; + Pos_eqb_neq -> RelationClasses_symmetry [] ; + Pos_eqb_neq -> Morphisms_Prop_not_iff_morphism [] ; + Pos_eqb_neq -> Pos_eqb_eq [] ; + Pos_eqb_neq -> Bool_not_true_iff_false [] ; + ZMicromega_popp -> Z_opp [] ; + ZMicromega_popp -> RingMicromega_popp [] ; + ZMicromega_eval_nformula_bound_var -> ZMicromega_xnnormalise_correct [] ; + ZMicromega_eval_nformula_bound_var -> ZMicromega_bound_var [] ; + ZMicromega_eval_Psatz_sound -> RingMicromega_eval_Psatz_Sound [] ; + ZMicromega_eval_Psatz_sound -> Refl_make_conj_in [] ; + ZMicromega_eval_Psatz_sound -> ZMicromega_ZSORaddon [] ; + ZMicromega_eval_Psatz_sound -> ZMicromega_eval_nformula [] ; + ZMicromega_eval_Psatz_sound -> ZMicromega_Zsor [] ; + ZMicromega_eval_Psatz_sound -> ZMicromega_eval_Psatz [] ; + ZMicromega_Private_Pos_neq_lt -> Pos_lt_irrefl [] ; + ZMicromega_eval_nformula_split -> _pair [] ; + ZMicromega_eval_nformula_split -> RingMicromega_NonStrict [] ; + ZMicromega_eval_nformula_split -> RingMicromega_eval_pol_opp [] ; + ZMicromega_eval_nformula_split -> ZMicromega_ZSORaddon [] ; + ZMicromega_eval_nformula_split -> ZMicromega_eval_nformula [] ; + ZMicromega_eval_nformula_split -> ZMicromega_Zsor [] ; + ZMicromega_eval_nformula_split -> Z_opp_nonneg_nonpos [] ; + ZMicromega_eval_nformula_split -> ZMicromega_popp [] ; + ZMicromega_eval_nformula_split -> Z_le_ge_cases [] ; + ZMicromega_agree_env -> _Z [] ; + ZMicromega_agree_env -> Pos_le [] ; + ZMicromega_genCuttingPlaneNone -> RingMicromega_NonEqual [] ; + ZMicromega_genCuttingPlaneNone -> RingMicromega_Strict [] ; + ZMicromega_genCuttingPlaneNone -> Bool_negb_true_iff [] ; + ZMicromega_genCuttingPlaneNone -> Bool_andb_true_iff [] ; + ZMicromega_genCuttingPlaneNone -> ZMicromega_eval_nformula [] ; + ZMicromega_genCuttingPlaneNone -> ZMicromega_genCuttingPlane [] ; + ZMicromega_genCuttingPlaneNone -> Z_gcd_opp_r [] ; + ZMicromega_genCuttingPlaneNone -> Z_gtb_lt [] ; + ZMicromega_genCuttingPlaneNone -> ZMicromega_Zgcd_pol_correct_lt [] ; + ZMicromega_genCuttingPlaneNone -> Z_eqb_neq [] ; + ZMicromega_genCuttingPlaneNone -> Z_add_move_0_l [] ; + ZMicromega_genCuttingPlaneNone -> Z_gcd_mul_diag_l [] ; + ZMicromega_ZArithProof_ind -> ZMicromega_ZArithProof [] ; + ZMicromega_ZArithProof_ind -> ZMicromega_DoneProof [] ; + ZMicromega_ZArithProof_ind -> ZMicromega_RatProof [] ; + ZMicromega_ZArithProof_ind -> ZMicromega_CutProof [] ; + ZMicromega_ZArithProof_ind -> ZMicromega_SplitProof [] ; + ZMicromega_ZArithProof_ind -> ZMicromega_deprecated_EnumProof [] ; + ZMicromega_ZArithProof_ind -> ZMicromega_ExProof [] ; + ZMicromega_SplitProof -> _list [] ; + ZMicromega_SplitProof -> ZMicromega_ZWitness [] ; + ZMicromega_deprecated_EnumProof -> _list [] ; + ZMicromega_deprecated_EnumProof -> ZMicromega_ZWitness [] ; + ZMicromega_ExProof -> _list [] ; + ZMicromega_ExProof -> ZMicromega_ZWitness [] ; + Z_gcd_opp_r -> Z_gcd_opp_l [] ; + Z_gcd_opp_r -> Z_gcd_comm [] ; + Z_gtb_lt -> Z_ltb_lt [] ; + Z_gtb_lt -> Z_gtb_ltb [] ; + ZMicromega_Zgcd_pol_correct_lt -> ZMicromega_ZSORaddon [] ; + ZMicromega_Zgcd_pol_correct_lt -> ZMicromega_Zsor [] ; + ZMicromega_Zgcd_pol_correct_lt -> RingMicromega_PsubC_ok [] ; + ZMicromega_Zgcd_pol_correct_lt -> ZMicromega_Zgcd_pol_div [] ; + ZMicromega_Zgcd_pol_correct_lt -> ZMicromega_Zdiv_pol_correct [] ; + ZMicromega_Zdiv_pol -> RingMicromega_PolC [] ; + ZMicromega_Zdiv_pol -> EnvRing_Pinj [] ; + ZMicromega_Zdiv_pol -> EnvRing_PX [] ; + ZMicromega_Zdiv_pol -> EnvRing_Pc [] ; + ZMicromega_Zdiv_pol -> Z_div [] ; + ZMicromega_Zgcd_pol -> _prod [] ; + ZMicromega_Zgcd_pol -> _pair [] ; + ZMicromega_Zgcd_pol -> RingMicromega_PolC [] ; + ZMicromega_Zgcd_pol -> ZMicromega_ZgcdM [] ; + Z_eqb_neq -> RelationClasses_reflexivity [] ; + Z_eqb_neq -> RelationClasses_iff_Reflexive [] ; + Z_eqb_neq -> RelationClasses_iff_Symmetric [] ; + Z_eqb_neq -> RelationClasses_symmetry [] ; + Z_eqb_neq -> Morphisms_Prop_not_iff_morphism [] ; + Z_eqb_neq -> Z_eqb_eq [] ; + Z_eqb_neq -> Bool_not_true_iff_false [] ; + Z_gcd -> Z_abs [] ; + Z_gcd -> Pos_gcd [] ; + Z_add_move_0_l -> Z_sub_0_l [] ; + Z_add_move_0_l -> Z_add_move_l [] ; + ZMicromega_makeCuttingPlane -> EnvRing_PsubC [] ; + ZMicromega_makeCuttingPlane -> Z_gtb [] ; + ZMicromega_makeCuttingPlane -> ZMicromega_Zdiv_pol [] ; + ZMicromega_makeCuttingPlane -> ZMicromega_Zgcd_pol [] ; + ZMicromega_makeCuttingPlane -> ZMicromega_ceiling [] ; + Z_gcd_mul_diag_l -> Z_divide_mul_l [] ; + Z_gcd_mul_diag_l -> Z_gcd_unique_alt [] ; + Z_divide -> _eq [] ; + Z_divide -> Z_mul [] ; + Z_divide -> _ex [] ; + Z_divide_mul_l -> Z_mul_shuffle0 [] ; + Z_divide_mul_l -> Z_divide [] ; + Z_gcd_unique_alt -> Z_divide_refl [] ; + Z_gcd_unique_alt -> Z_gcd_unique [] ; + Z_divide_refl -> Z_mul_1_l [] ; + Z_divide_refl -> Z_divide [] ; + Z_gcd_unique -> Z_gcd_divide_l [] ; + Z_gcd_unique -> Z_gcd_divide_r [] ; + Z_gcd_unique -> Z_divide_antisym_nonneg [] ; + Z_gcd_unique -> Z_gcd_nonneg [] ; + Z_gcd_unique -> Z_gcd_greatest [] ; + Z_gcd_divide_l -> Z_mul_comm [] ; + Z_gcd_divide_l -> Z_divide [] ; + Z_gcd_divide_l -> Z_ggcd_correct_divisors [] ; + Z_gcd_divide_l -> Z_ggcd_gcd [] ; + Z_gcd_divide_r -> Z_mul_comm [] ; + Z_gcd_divide_r -> Z_divide [] ; + Z_gcd_divide_r -> Z_ggcd_correct_divisors [] ; + Z_gcd_divide_r -> Z_ggcd_gcd [] ; + Z_divide_antisym_nonneg -> Z_mul_assoc [] ; + Z_divide_antisym_nonneg -> Z_Private_OrderTac_Tac_eq_neq [] ; + Z_divide_antisym_nonneg -> Z_mul_neg_pos [] ; + Z_divide_antisym_nonneg -> Z_divide [] ; + Z_divide_antisym_nonneg -> Z_eq_mul_1_nonneg_ [] ; + Z_divide_antisym_nonneg -> Z_Private_OrderTac_Tac_le_eq [] ; + Z_divide_antisym_nonneg -> Z_Private_OrderTac_Tac_neq_eq [] ; + Z_divide_antisym_nonneg -> Z_mul_id_l [] ; + Z_gcd_nonneg -> RelationClasses_PreOrder_Reflexive [] ; + Z_gcd_nonneg -> Z_le_preorder [] ; + Z_gcd_nonneg -> Z_gcd [] ; + Z_gcd_greatest -> Z_gcd [] ; + Z_gcd_greatest -> Pos_gcd_greatest [] ; + Z_gcd_greatest -> Z_divide_Zpos_Zneg_l [] ; + Z_gcd_greatest -> Z_divide_Zpos_Zneg_r [] ; + Z_gcd_greatest -> Z_divide_Zpos [] ; + Pos_gcd_greatest -> Pos_gcd [] ; + Pos_gcd_greatest -> Pos_gcdn_greatest [] ; + Z_divide_Zpos_Zneg_l -> Z_divide [] ; + Z_divide_Zpos_Zneg_l -> Z_mul_opp_r [] ; + Z_divide_Zpos_Zneg_r -> Z_divide [] ; + Z_divide_Zpos_Zneg_r -> Z_mul_opp_l [] ; + Z_divide_Zpos -> _False_ind [] ; + Z_divide_Zpos -> _eq_ind [] ; + Z_divide_Zpos -> _True [] ; + Z_divide_Zpos -> _I [] ; + Z_divide_Zpos -> _iff [] ; + Z_divide_Zpos -> _conj [] ; + Z_divide_Zpos -> _f_equal [] ; + Z_divide_Zpos -> _eq_trans [] ; + Z_divide_Zpos -> _ex_intro [] ; + Z_divide_Zpos -> Z_divide [] ; + Z_divide_Zpos -> Pos_divide [] ; + Pos_gcd -> Init_Nat_add [] ; + Pos_gcd -> Pos_size_nat [] ; + Pos_gcd -> Pos_gcdn [] ; + Pos_divide -> _eq [] ; + Pos_divide -> Pos_mul [] ; + Pos_divide -> _ex [] ; + Pos_size_nat -> _positive [] ; + Pos_size_nat -> _O [] ; + Pos_size_nat -> _S [] ; + Pos_size_nat -> _nat [] ; + Pos_gcdn -> _nat [] ; + Pos_gcdn -> Pos_compare [] ; + Pos_gcdn -> Pos_sub [] ; + Z_mul_opp_l -> Z_mul_add_distr_r [] ; + Z_mul_opp_l -> Z_add_opp_diag_l [] ; + Z_mul_opp_l -> Z_add_move_0_r [] ; + Z_add_opp_diag_l -> Z_sub_diag [] ; + Z_add_move_0_r -> Z_sub_0_l [] ; + Z_add_move_0_r -> Z_add_move_r [] ; + Z_sub_0_l -> Z_add_opp_r [] ; + Z_add_move_r -> Z_add_move_l [] ; + Z_add_move_l -> Z_add_sub_assoc [] ; + Z_add_move_l -> Z_sub_cancel_r [] ; + _iff_stepl -> _iff [] ; + _iff_stepl -> _conj [] ; + Z_sub_cancel_r -> Z_add_cancel_r [] ; + Z_sub_cancel_r -> Z_sub_diag [] ; + Z_sub_cancel_r -> Z_sub_sub_distr [] ; + Z_sub_cancel_r -> _iff_stepl [] ; + Z_mul_opp_r -> Z_mul_comm [] ; + Z_mul_opp_r -> Z_mul_opp_l [] ; + Pos_gcdn_greatest -> _plus_n_Sm [] ; + Pos_gcdn_greatest -> Nat_add_le_mono [] ; + Pos_gcdn_greatest -> Pos_sub_xI_xI [] ; + Pos_gcdn_greatest -> Pos_gcdn [] ; + Pos_gcdn_greatest -> Pos_sub_decr [] ; + Pos_gcdn_greatest -> _plus_Sn_m [] ; + Pos_gcdn_greatest -> Pos_size_nat_monotone [] ; + Pos_gcdn_greatest -> Pos_divide_mul_r [] ; + Pos_gcdn_greatest -> Pos_divide_xO_xI [] ; + Pos_gcdn_greatest -> Pos_divide_xO_xO [] ; + Pos_gcdn_greatest -> Pos_divide_add_cancel_l [] ; + Pos_sub_decr -> Pos_lt_add_r [] ; + Pos_sub_decr -> Pos_sub_add [] ; + Pos_sub_decr -> Pos_add_lt_mono_r [] ; + _plus_Sn_m -> _eq [] ; + _plus_Sn_m -> Init_Nat_add [] ; + _plus_Sn_m -> _eq_refl [] ; + Pos_size_nat_monotone -> _nat_ind [] ; + Pos_size_nat_monotone -> _le_ind [] ; + Pos_size_nat_monotone -> _le_n [] ; + Pos_size_nat_monotone -> _le_S [] ; + Pos_size_nat_monotone -> Pos_compare_spec [] ; + Pos_size_nat_monotone -> Pos_size_nat [] ; + Pos_divide_mul_r -> Pos_divide_mul_l [] ; + Pos_divide_xO_xI -> _False_ind [] ; + Pos_divide_xO_xI -> _True [] ; + Pos_divide_xO_xI -> _I [] ; + Pos_divide_xO_xI -> _eq_ind_r [] ; + Pos_divide_xO_xI -> _ex_intro [] ; + Pos_divide_xO_xI -> Pos_mul_1_r [] ; + Pos_divide_xO_xI -> Pos_mul_xO_r [] ; + Pos_divide_xO_xI -> Pos_divide [] ; + Pos_divide_xO_xO -> _iff [] ; + Pos_divide_xO_xO -> _conj [] ; + Pos_divide_xO_xO -> _eq_ind_r [] ; + Pos_divide_xO_xO -> _ex_intro [] ; + Pos_divide_xO_xO -> Pos_mul_xO_r [] ; + Pos_divide_xO_xO -> Pos_divide [] ; + Pos_divide_add_cancel_l -> Pos_add_sub [] ; + Pos_divide_add_cancel_l -> Pos_mul_sub_distr_r [] ; + Pos_divide_add_cancel_l -> Pos_divide [] ; + Pos_divide_add_cancel_l -> Pos_mul_lt_mono_r [] ; + Pos_mul_lt_mono_r -> Pos_mul_compare_mono_r [] ; + Pos_divide_mul_l -> _ex_intro [] ; + Pos_divide_mul_l -> Pos_mul_assoc [] ; + Pos_divide_mul_l -> Pos_divide [] ; + Z_eq_mul_1_nonneg_ -> _and_comm [] ; + Z_eq_mul_1_nonneg_ -> Z_eq_mul_1_nonneg [] ; + Z_Private_OrderTac_Tac_le_eq -> Z_Private_OrderTac_Tac_trans [] ; + Z_Private_OrderTac_Tac_neq_eq -> Z_Private_OrderTac_Tac_eq_sym [] ; + Z_Private_OrderTac_Tac_neq_eq -> Z_Private_OrderTac_Tac_eq_trans [] ; + Z_mul_id_l -> Z_mul_cancel_r [] ; + Z_mul_id_l -> Z_mul_1_l [] ; + Z_mul_id_l -> _iff_stepl [] ; + Z_lt_ge_cases -> Z_le_gt_cases [] ; + _and_comm -> _iff [] ; + _and_comm -> _conj [] ; + Z_eq_mul_1_nonneg -> Z_Private_OrderTac_Tac_eq_lt [] ; + Z_eq_mul_1_nonneg -> Z_Private_OrderTac_Tac_eq_sym [] ; + Z_eq_mul_1_nonneg -> Z_Private_OrderTac_Tac_eq_trans [] ; + Z_eq_mul_1_nonneg -> Z_mul_pos_neg [] ; + Z_eq_mul_1_nonneg -> Z_lt_ge_cases [] ; + Z_eq_mul_1_nonneg -> Z_lt_0_1 [] ; + Z_eq_mul_1_nonneg -> Z_lt_1_2 [] ; + Z_eq_mul_1_nonneg -> Z_lt_1_mul_pos [] ; + Z_lt_0_1 -> Z_one_succ [] ; + Z_lt_0_1 -> Z_lt_wd [] ; + Z_lt_0_1 -> Z_lt_succ_diag_r [] ; + Z_lt_1_2 -> Z_lt_wd [] ; + Z_lt_1_2 -> Z_lt_succ_diag_r [] ; + Z_lt_1_2 -> Z_two_succ [] ; + Z_lt_1_mul_pos -> Z_mul_lt_mono_pos_r [] ; + Z_lt_1_mul_pos -> Z_mul_1_l [] ; + Z_lt_1_mul_pos -> Z_lt_1_l [] ; + Z_lt_1_l -> Z_one_succ [] ; + Z_lt_1_l -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_lt_1_l -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_lt_1_l -> Z_Private_OrderTac_Tac_not_ge_lt [] ; + Z_two_succ -> _eq [] ; + Z_two_succ -> _eq_refl [] ; + Z_two_succ -> Z_succ [] ; + Z_ggcd_correct_divisors -> Z_mul [] ; + Z_ggcd_correct_divisors -> Z_ggcd [] ; + Z_ggcd_correct_divisors -> Pos_ggcd_correct_divisors [] ; + Z_ggcd_gcd -> Z_gcd [] ; + Z_ggcd_gcd -> Z_ggcd [] ; + Z_ggcd_gcd -> Pos_ggcd_gcd [] ; + Z_ggcd -> Z_abs [] ; + Z_ggcd -> Z_sgn [] ; + Z_ggcd -> Pos_ggcd [] ; + Z_sgn -> _Z [] ; + Z_sgn -> _Z0 [] ; + Z_sgn -> _Zpos [] ; + Z_sgn -> _xH [] ; + Z_sgn -> _Zneg [] ; + Pos_ggcd -> Init_Nat_add [] ; + Pos_ggcd -> Pos_size_nat [] ; + Pos_ggcd -> Pos_ggcdn [] ; + Pos_ggcdn -> _prod [] ; + Pos_ggcdn -> Pos_add [] ; + Pos_ggcdn -> _nat [] ; + Pos_ggcdn -> Pos_compare [] ; + Pos_ggcdn -> Pos_sub [] ; + Pos_ggcdn -> _pair [] ; + Pos_ggcd_gcd -> Pos_gcd [] ; + Pos_ggcd_gcd -> Pos_ggcd [] ; + Pos_ggcd_gcd -> Pos_ggcdn_gcdn [] ; + Pos_ggcdn_gcdn -> _nat_ind [] ; + Pos_ggcdn_gcdn -> Pos_compare_spec [] ; + Pos_ggcdn_gcdn -> _fst [] ; + Pos_ggcdn_gcdn -> Pos_gcdn [] ; + Pos_ggcdn_gcdn -> Pos_ggcdn [] ; + Pos_ggcd_correct_divisors -> Pos_ggcd [] ; + Pos_ggcd_correct_divisors -> Pos_ggcdn_correct_divisors [] ; + Pos_ggcdn_correct_divisors -> _nat_ind [] ; + Pos_ggcdn_correct_divisors -> Pos_sub_add [] ; + Pos_ggcdn_correct_divisors -> Pos_compare_spec [] ; + Pos_ggcdn_correct_divisors -> Pos_mul_comm [] ; + Pos_ggcdn_correct_divisors -> Pos_mul_add_distr_l [] ; + Pos_ggcdn_correct_divisors -> Pos_ggcdn [] ; + ZMicromega_ceiling -> Z_div_eucl [] ; + Z_div_eucl -> Z_pos_div_eucl [] ; + Z_pos_div_eucl -> _prod [] ; + Z_pos_div_eucl -> Z_leb [] ; + Z_pos_div_eucl -> Z_mul [] ; + Z_pos_div_eucl -> _pair [] ; + Z_pos_div_eucl -> Z_sub [] ; + Z_pos_div_eucl -> Z_ltb [] ; + Bool_not_true_iff_false -> _iff [] ; + Bool_not_true_iff_false -> _conj [] ; + Bool_not_true_iff_false -> _eq_sym [] ; + Bool_not_true_iff_false -> Bool_diff_false_true [] ; + ZMicromega_ZgcdM -> Z_gcd [] ; + ZMicromega_ZgcdM -> Z_max [] ; + Z_max -> Z_compare [] ; + Z_div -> Z_div_eucl [] ; + RingMicromega_PsubC_ok -> _Rth_ARth [] ; + RingMicromega_PsubC_ok -> _mk_reqe [] ; + RingMicromega_PsubC_ok -> RingMicromega_eval_pol [] ; + RingMicromega_PsubC_ok -> OrderedRing_SORsetoid [] ; + RingMicromega_PsubC_ok -> OrderedRing_SORrt [] ; + RingMicromega_PsubC_ok -> RingMicromega_SORrm [] ; + RingMicromega_PsubC_ok -> OrderedRing_SORtimes_wd [] ; + RingMicromega_PsubC_ok -> OrderedRing_SORopp_wd [] ; + RingMicromega_PsubC_ok -> OrderedRing_SORplus_wd [] ; + RingMicromega_PsubC_ok -> EnvRing_PsubC_ok [] ; + RingMicromega_PsubC_ok -> RingMicromega_psubC [] ; + RingMicromega_psubC -> EnvRing_PsubC [] ; + ZMicromega_Zgcd_pol_div -> Z_lt_le_trans [] ; + ZMicromega_Zgcd_pol_div -> ZMicromega_Zgcd_pol [] ; + ZMicromega_Zgcd_pol_div -> ZMicromega_Zdivide_pol_one [] ; + ZMicromega_Zgcd_pol_div -> ZMicromega_Zdivide_pol_sub [] ; + ZMicromega_Zgcd_pol_div -> Z_max_spec [] ; + ZMicromega_Zdiv_pol_correct -> _ring_subst_niter [] ; + ZMicromega_Zdiv_pol_correct -> RelationClasses_neq_Symmetric [] ; + ZMicromega_Zdiv_pol_correct -> _Zr_ring_lemma1 [] ; + ZMicromega_Zdiv_pol_correct -> ZMicromega_eval_pol [] ; + ZMicromega_Zdiv_pol_correct -> ZMicromega_Zdiv_pol [] ; + ZMicromega_Zdiv_pol_correct -> ZMicromega_Zdivide_pol_ind [] ; + ZMicromega_Zdiv_pol_correct -> Z_divide_div_mul_exact [] ; + ZMicromega_Zdivide_pol_ind -> ZMicromega_Zdivide_pol [] ; + Z_divide_div_mul_exact -> Z_mul_cancel_l [] ; + Z_divide_div_mul_exact -> Z_div_exact [] ; + Z_divide_div_mul_exact -> Z_divide_mul_r [] ; + Z_divide_div_mul_exact -> Z_mod_divide [] ; + Z_div_mul -> Z_Private_OrderTac_Tac_eq_neq [] ; + Z_div_mul -> Z_Private_OrderTac_Tac_eq_refl [] ; + Z_div_mul -> Z_Private_OrderTac_Tac_le_refl [] ; + Z_div_mul -> Z_lt_ge_cases [] ; + Z_div_mul -> Z_div_unique [] ; + ZMicromega_Zdivide_pol -> RingMicromega_PolC [] ; + ZMicromega_Zdivide_pol -> EnvRing_Pinj [] ; + ZMicromega_Zdivide_pol -> EnvRing_PX [] ; + ZMicromega_Zdivide_pol -> EnvRing_Pc [] ; + ZMicromega_Zdivide_pol -> Z_divide [] ; + Z_Private_OrderTac_Tac_le_neq_lt -> Z_Private_OrderTac_Tac_not_ge_lt [] ; + Z_Private_OrderTac_Tac_le_neq_lt -> Z_Private_OrderTac_Tac_le_antisym [] ; + Z_div_unique -> Z_Private_OrderTac_Tac_le_neq_lt [] ; + Z_div_unique -> Z_div_mod_unique [] ; + Z_div_unique -> Z_mod_pos_bound [] ; + Z_div_unique -> Z_Private_OrderTac_Tac_neq_sym [] ; + Z_div_unique -> Z_div_mod [] ; + Z_div_unique -> Z_mod_neg_bound [] ; + Z_div_mod_unique -> Z_Private_OrderTac_Tac_not_neq_eq [] ; + Z_div_mod_unique -> Z_opp_lt_mono [] ; + Z_div_mod_unique -> Z_opp_nonneg_nonpos [] ; + Z_div_mod_unique -> Z_mul_opp_l [] ; + Z_div_mod_unique -> Z_Private_NZDiv_div_mod_unique [] ; + Z_div_mod_unique -> Z_opp_inj_wd [] ; + Z_mod_pos_bound -> Pos_sub_decr [] ; + Z_mod_pos_bound -> Z_modulo [] ; + Z_mod_pos_bound -> Z_pos_div_eucl_bound [] ; + Z_mod_pos_bound -> Z_pos_sub_gt [] ; + Z_Private_OrderTac_Tac_neq_sym -> _not [] ; + Z_Private_OrderTac_Tac_neq_sym -> Z_Private_OrderTac_Tac_eq_sym [] ; + Z_div_mod -> Z_div [] ; + Z_div_mod -> Z_modulo [] ; + Z_div_mod -> Z_div_eucl_eq [] ; + Z_modulo -> Z_div_eucl [] ; + Z_mod_neg_bound -> Pos_sub_decr [] ; + Z_mod_neg_bound -> Z_modulo [] ; + Z_mod_neg_bound -> Z_pos_div_eucl_bound [] ; + Z_mod_neg_bound -> Z_pos_sub_lt [] ; + Z_pos_div_eucl_bound -> RelationClasses_PreOrder_Reflexive [] ; + Z_pos_div_eucl_bound -> Z_add_assoc [] ; + Z_pos_div_eucl_bound -> Z_le_preorder [] ; + Z_pos_div_eucl_bound -> Pos_add_diag [] ; + Z_pos_div_eucl_bound -> _snd [] ; + Z_pos_div_eucl_bound -> Z_leb_spec [] ; + Z_pos_div_eucl_bound -> Z_pos_div_eucl [] ; + Z_pos_div_eucl_bound -> Z_ltb_spec [] ; + Z_pos_div_eucl_bound -> Z_succ_double_spec [] ; + Z_pos_div_eucl_bound -> Pos_le_succ_l [] ; + Z_pos_sub_lt -> Z_pos_sub_spec [] ; + Z_ltb_spec -> Morphisms_iff_flip_impl_subrelation [] ; + Z_ltb_spec -> Z_compare_le_iff [] ; + Z_ltb_spec -> _BoolSpec [] ; + Z_ltb_spec -> _BoolSpecT [] ; + Z_ltb_spec -> _BoolSpecF [] ; + Z_ltb_spec -> Z_ltb_spec0 [] ; + Z_ltb_spec -> Z_compare_ngt_iff [] ; + Z_succ_double_spec -> _eq [] ; + Z_succ_double_spec -> Z_mul [] ; + Z_succ_double_spec -> Z_add [] ; + Z_succ_double_spec -> _eq_refl [] ; + Pos_le_succ_l -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Pos_le_succ_l -> Morphisms_eq_proper_proxy [] ; + Pos_le_succ_l -> RelationClasses_iff_Transitive [] ; + Pos_le_succ_l -> RelationClasses_iff_Symmetric [] ; + Pos_le_succ_l -> RelationClasses_symmetry [] ; + Pos_le_succ_l -> Pos_lt_succ_r [] ; + Pos_le_succ_l -> Pos_succ_lt_mono [] ; + Pos_succ_lt_mono -> RelationClasses_reflexivity [] ; + Pos_succ_lt_mono -> RelationClasses_iff_Reflexive [] ; + Pos_succ_lt_mono -> Pos_lt [] ; + Pos_succ_lt_mono -> Pos_compare_succ_succ [] ; + Z_ltb_spec0 -> RelationClasses_iff_Symmetric [] ; + Z_ltb_spec0 -> RelationClasses_symmetry [] ; + Z_ltb_spec0 -> Bool_iff_reflect [] ; + Z_ltb_spec0 -> Z_ltb_lt [] ; + Z_compare_ngt_iff -> Morphisms_Prop_not_iff_morphism [] ; + Z_compare_ngt_iff -> Z_compare_gt_iff [] ; + Z_compare_gt_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Z_compare_gt_iff -> Morphisms_eq_proper_proxy [] ; + Z_compare_gt_iff -> RelationClasses_Equivalence_PER [] ; + Z_compare_gt_iff -> RelationClasses_iff_equivalence [] ; + Z_compare_gt_iff -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Z_compare_gt_iff -> _CompOpp_iff [] ; + Z_compare_gt_iff -> Z_compare_antisym [] ; + Z_compare_gt_iff -> Z_compare_lt_iff [] ; + Z_div_eucl_eq -> Z_mul_1_r [] ; + Z_div_eucl_eq -> Z_div_eucl [] ; + Z_div_eucl_eq -> Z_mul_opp_comm [] ; + Z_div_eucl_eq -> Z_pos_div_eucl_eq [] ; + Z_mul_add_distr_l -> Z_mul_comm [] ; + Z_mul_add_distr_l -> Z_mul_add_distr_r [] ; + Z_add_opp_diag_r -> Z_add_opp_diag_l [] ; + Z_mul_opp_comm -> Z_mul_opp_r [] ; + Z_pos_div_eucl_eq -> Z_mul_assoc [] ; + Z_pos_div_eucl_eq -> Pos_le_1_l [] ; + Z_pos_div_eucl_eq -> Z_mul_1_l [] ; + Z_pos_div_eucl_eq -> Pos_lt_succ_r [] ; + Z_pos_div_eucl_eq -> Z_leb_spec [] ; + Z_pos_div_eucl_eq -> Z_pos_div_eucl [] ; + Z_pos_div_eucl_eq -> Z_mul_add_distr_l [] ; + Z_pos_div_eucl_eq -> Z_add_opp_diag_r [] ; + Z_pos_div_eucl_eq -> Pos_le_antisym [] ; + Pos_le_antisym -> RelationClasses_StrictOrder_Transitive [] ; + Pos_le_antisym -> Pos_lt_strorder [] ; + Pos_le_antisym -> Pos_le_lteq [] ; + Pos_lt_irrefl -> Morphisms_subrelation_proper [] ; + Pos_lt_irrefl -> Morphisms_subrelation_refl [] ; + Pos_lt_irrefl -> Morphisms_iff_flip_impl_subrelation [] ; + Pos_lt_irrefl -> Morphisms_subrelation_respectful [] ; + Pos_lt_irrefl -> _tt [] ; + Pos_lt_irrefl -> Morphisms_Prop_not_iff_morphism [] ; + Pos_lt_irrefl -> Pos_compare_lt_iff [] ; + Pos_lt_irrefl -> Pos_compare_refl [] ; + Pos_lt_strorder -> RelationClasses_StrictOrder [] ; + Pos_lt_strorder -> RelationClasses_Build_StrictOrder [] ; + Pos_lt_strorder -> Pos_lt_trans [] ; + Pos_lt_strorder -> Pos_lt_irrefl [] ; + Pos_le_lteq -> Pos_lt_eq_cases [] ; + Pos_lt_eq_cases -> Morphisms_reflexive_reflexive_proxy [] ; + Pos_lt_eq_cases -> Morphisms_Reflexive_partial_app_morphism [] ; + Pos_lt_eq_cases -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Pos_lt_eq_cases -> Morphisms_eq_proper_proxy [] ; + Pos_lt_eq_cases -> Morphisms_reflexive_proper_proxy [] ; + Pos_lt_eq_cases -> Morphisms_Prop_or_iff_morphism [] ; + Pos_lt_eq_cases -> Pos_compare_eq_iff [] ; + Pos_lt_eq_cases -> Pos_compare_lt_iff [] ; + Pos_lt_eq_cases -> Pos_compare_le_iff [] ; + Pos_compare_le_iff -> RelationClasses_reflexivity [] ; + Pos_compare_le_iff -> RelationClasses_iff_Reflexive [] ; + Pos_compare_le_iff -> Pos_le [] ; + Z_pos_sub_gt -> Z_pos_sub_spec [] ; + Z_Private_NZDiv_div_mod_unique -> Z_mul_comm [] ; + Z_Private_NZDiv_div_mod_unique -> Z_add_le_mono_l [] ; + Z_Private_NZDiv_div_mod_unique -> Z_lt_le_trans [] ; + Z_Private_NZDiv_div_mod_unique -> Z_mul_le_mono_nonneg_l [] ; + Z_Private_NZDiv_div_mod_unique -> Z_lt_neq [] ; + Z_opp_inj_wd -> Z_opp_inj [] ; + Z_opp_inj -> Z_opp_involutive [] ; + Z_div_exact -> Z_Private_OrderTac_Tac_eq_neq [] ; + Z_div_exact -> Z_Private_OrderTac_Tac_eq_refl [] ; + Z_div_exact -> Z_div_mod [] ; + Z_divide_mul_r -> Z_divide_mul_l [] ; + Z_divide_mul_r -> Z_divide_wd [] ; + Z_mod_divide -> Z_divide [] ; + Z_mod_divide -> Z_mod_wd [] ; + Z_mod_divide -> Z_mod_mul [] ; + Z_mod_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Z_mod_wd -> RelationClasses_eq_Reflexive [] ; + Z_mod_wd -> Morphisms_reflexive_proper [] ; + Z_mod_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_mod_wd -> Z_eq [] ; + Z_mod_wd -> Z_modulo [] ; + Z_mod_mul -> Z_div_mul [] ; + Z_mod_mul -> Z_mod_eq [] ; + Z_mod_eq -> Z_div_mod [] ; + Z_divide_wd -> Morphisms_Reflexive_partial_app_morphism [] ; + Z_divide_wd -> Morphisms_PER_morphism [] ; + Z_divide_wd -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Z_divide_wd -> RelationClasses_reflexivity [] ; + Z_divide_wd -> Morphisms_eq_proper_proxy [] ; + Z_divide_wd -> RelationClasses_iff_Transitive [] ; + Z_divide_wd -> RelationClasses_Equivalence_PER [] ; + Z_divide_wd -> RelationClasses_iff_Reflexive [] ; + Z_divide_wd -> Morphisms_reflexive_proper_proxy [] ; + Z_divide_wd -> RelationClasses_Equivalence_Reflexive [] ; + Z_divide_wd -> Morphisms_per_partial_app_morphism [] ; + Z_divide_wd -> Z_eq_equiv [] ; + Z_divide_wd -> Z_mul_wd [] ; + Z_divide_wd -> Z_divide [] ; + Z_divide_wd -> Morphisms_Prop_ex_iff_morphism [] ; + Morphisms_Prop_ex_iff_morphism -> Morphisms_Proper [] ; + Morphisms_Prop_ex_iff_morphism -> Morphisms_Prop_ex_iff_morphism_obligation_1 [] ; + Morphisms_Prop_ex_iff_morphism_obligation_1 -> _iff [] ; + Morphisms_Prop_ex_iff_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_Prop_ex_iff_morphism_obligation_1 -> _and_ind [] ; + Morphisms_Prop_ex_iff_morphism_obligation_1 -> _conj [] ; + Morphisms_Prop_ex_iff_morphism_obligation_1 -> Morphisms_pointwise_relation [] ; + Morphisms_Prop_ex_iff_morphism_obligation_1 -> _ex_intro [] ; + Morphisms_Prop_ex_iff_morphism_obligation_1 -> _ex_ind [] ; + _ex_ind -> _ex [] ; + ZMicromega_Zdivide_pol_one -> _ring_subst_niter [] ; + ZMicromega_Zdivide_pol_one -> _Zr_ring_lemma1 [] ; + ZMicromega_Zdivide_pol_one -> EnvRing_Pol_ind [] ; + ZMicromega_Zdivide_pol_one -> ZMicromega_Zdivide_pol [] ; + ZMicromega_Zdivide_pol_one -> ZMicromega_Zdiv_Pc [] ; + ZMicromega_Zdivide_pol_one -> ZMicromega_Zdiv_Pinj [] ; + ZMicromega_Zdivide_pol_one -> ZMicromega_Zdiv_PX [] ; + ZMicromega_Zdivide_pol_sub -> Z_lt [] ; + ZMicromega_Zdivide_pol_sub -> EnvRing_PsubC [] ; + ZMicromega_Zdivide_pol_sub -> EnvRing_Pol_ind [] ; + ZMicromega_Zdivide_pol_sub -> ZMicromega_Zdivide_pol_Zdivide [] ; + ZMicromega_Zdivide_pol_sub -> ZMicromega_Zgcd_minus [] ; + Z_max_spec -> Z_lt_total [] ; + Z_max_spec -> Z_le_lteq [] ; + Z_max_spec -> Z_max_l [] ; + Z_max_spec -> Z_max_r [] ; + ZMicromega_Zdivide_pol_Zdivide -> ZMicromega_Zdivide_pol_ind [] ; + ZMicromega_Zdivide_pol_Zdivide -> ZMicromega_Zdiv_Pc [] ; + ZMicromega_Zdivide_pol_Zdivide -> ZMicromega_Zdiv_Pinj [] ; + ZMicromega_Zdivide_pol_Zdivide -> ZMicromega_Zdiv_PX [] ; + ZMicromega_Zdivide_pol_Zdivide -> Z_divide_trans [] ; + ZMicromega_Zdiv_Pc -> RingMicromega_PolC [] ; + ZMicromega_Zdiv_Pc -> EnvRing_Pinj [] ; + ZMicromega_Zdiv_Pc -> EnvRing_PX [] ; + ZMicromega_Zdiv_Pc -> EnvRing_Pc [] ; + ZMicromega_Zdiv_Pc -> Z_divide [] ; + ZMicromega_Zdiv_Pinj -> RingMicromega_PolC [] ; + ZMicromega_Zdiv_Pinj -> EnvRing_Pinj [] ; + ZMicromega_Zdiv_Pinj -> EnvRing_PX [] ; + ZMicromega_Zdiv_Pinj -> EnvRing_Pc [] ; + ZMicromega_Zdiv_Pinj -> Z_divide [] ; + ZMicromega_Zdiv_PX -> RingMicromega_PolC [] ; + ZMicromega_Zdiv_PX -> EnvRing_Pinj [] ; + ZMicromega_Zdiv_PX -> EnvRing_PX [] ; + ZMicromega_Zdiv_PX -> EnvRing_Pc [] ; + ZMicromega_Zdiv_PX -> Z_divide [] ; + Z_divide_trans -> Z_mul_assoc [] ; + Z_divide_trans -> Z_divide [] ; + Z_max_l -> Z_le [] ; + Z_max_l -> _False_ind [] ; + Z_max_l -> Z_compare_antisym [] ; + Z_max_l -> Z_max [] ; + Z_max_r -> Z_le [] ; + Z_max_r -> Z_compare_spec [] ; + Z_max_r -> Z_max [] ; + ZMicromega_Zgcd_minus -> Z_gcd_divide_l [] ; + ZMicromega_Zgcd_minus -> Z_gcd_divide_r [] ; + ZMicromega_Zgcd_minus -> Z_divide_mul_r [] ; + ZMicromega_Zgcd_minus -> Z_divide_add_r [] ; + ZMicromega_Zgcd_minus -> Z_sub_move_r [] ; + Z_divide_add_r -> Z_mul_add_distr_r [] ; + Z_divide_add_r -> Z_divide [] ; + Z_sub_move_r -> Z_sub_opp_r [] ; + Z_sub_move_r -> Z_add_move_r [] ; + Z_gtb_ltb -> Z_compare_antisym [] ; + Z_gtb_ltb -> Z_ltb [] ; + Z_gtb_ltb -> Z_gtb [] ; + Z_gcd_opp_l -> Z_gcd_unique_alt [] ; + Z_gcd_opp_l -> Z_gcd_divide_iff [] ; + Z_gcd_opp_l -> Z_divide_opp_r [] ; + Z_gcd_comm -> Z_gcd_unique_alt [] ; + Z_gcd_comm -> Z_gcd_divide_iff [] ; + Z_gcd_divide_iff -> Z_gcd_divide_l [] ; + Z_gcd_divide_iff -> Z_gcd_divide_r [] ; + Z_gcd_divide_iff -> Z_gcd_greatest [] ; + Z_gcd_divide_iff -> Z_divide_transitive [] ; + Z_divide_transitive -> Z_divide_trans [] ; + Z_divide_opp_r -> Z_divide [] ; + Z_divide_opp_r -> Z_mul_opp_l [] ; + Z_le_ge_cases -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_le_ge_cases -> Z_Private_OrderTac_Tac_lt_trans [] ; + Z_le_ge_cases -> Z_Private_OrderTac_Tac_not_gt_le [] ; + Pos_max_1_l -> Pos_compare_spec [] ; + Pos_max_1_l -> Pos_le_1_l [] ; + Pos_max_1_l -> Pos_max [] ; + Pos_max_1_l -> Pos_lt_nle [] ; + ZMicromega_max_var_nformulae_mono_aux_ -> _list_ind [] ; + ZMicromega_max_var_nformulae_mono_aux_ -> List_fold_left [] ; + ZMicromega_max_var_nformulae_mono_aux_ -> ZMicromega_F [] ; + ZMicromega_max_var_nformulae_mono_aux_ -> Pos_max_le_compat_r [] ; + ZMicromega_max_var_nformulae_mono_aux -> _list_ind [] ; + ZMicromega_max_var_nformulae_mono_aux -> List_fold_left [] ; + ZMicromega_max_var_nformulae_mono_aux -> Pos_le_trans [] ; + ZMicromega_max_var_nformulae_mono_aux -> Pos_max_case_strong [] ; + ZMicromega_max_var_nformulae_mono_aux -> ZMicromega_F [] ; + ZMicromega_agree_env_subset -> ZMicromega_agree_env [] ; + ZMicromega_agree_env_subset -> Pos_le_trans [] ; + Pos_max -> Pos_compare [] ; + ZMicromega_max_var -> _Z [] ; + ZMicromega_max_var -> Pos_add [] ; + ZMicromega_max_var -> EnvRing_Pol [] ; + ZMicromega_max_var -> Pos_max [] ; + _and_iff_compat_l -> _iff [] ; + _and_iff_compat_l -> _conj [] ; + ZMicromega_agree_env_eval_nformula -> _pair [] ; + ZMicromega_agree_env_eval_nformula -> Pos_le_1_l [] ; + ZMicromega_agree_env_eval_nformula -> _fst [] ; + ZMicromega_agree_env_eval_nformula -> ZMicromega_eval_nformula [] ; + ZMicromega_agree_env_eval_nformula -> ZMicromega_agree_env_subset [] ; + ZMicromega_agree_env_eval_nformula -> Pos_le_refl [] ; + ZMicromega_agree_env_eval_nformula -> ZMicromega_agree_env_tail [] ; + ZMicromega_agree_env_eval_nformula -> ZMicromega_max_var_acc [] ; + ZMicromega_agree_env_eval_nformula -> Pos_le_max_l [] ; + ZMicromega_agree_env_eval_nformula -> Pos_le_max_r [] ; + ZMicromega_agree_env_eval_nformula -> _Pplus_one_succ_r [] ; + Pos_le_refl -> Pos_compare_refl [] ; + Pos_le_refl -> Pos_le [] ; + ZMicromega_agree_env_jump -> Env_jump [] ; + ZMicromega_agree_env_jump -> ZMicromega_agree_env [] ; + ZMicromega_agree_env_jump -> Pos_add_le_mono_r [] ; + ZMicromega_agree_env_tail -> Env_tail [] ; + ZMicromega_agree_env_tail -> ZMicromega_agree_env_jump [] ; + ZMicromega_max_var_acc -> EnvRing_Pol_ind [] ; + ZMicromega_max_var_acc -> ZMicromega_max_var [] ; + ZMicromega_max_var_acc -> _Pplus_one_succ_l [] ; + ZMicromega_max_var_acc -> Pos_add_max_distr_r [] ; + Pos_le_max_l -> Pos_Private_Tac_eq_lt [] ; + Pos_le_max_l -> Pos_max_spec [] ; + Pos_le_max_l -> Pos_Private_Tac_lt_irrefl [] ; + Pos_le_max_l -> Pos_Private_Tac_eq_sym [] ; + Pos_le_max_l -> Pos_Private_Tac_not_gt_le [] ; + Pos_le_max_l -> Pos_Private_Tac_lt_trans [] ; + Pos_le_max_r -> Pos_Private_Tac_eq_lt [] ; + Pos_le_max_r -> Pos_Private_Tac_le_lt_trans [] ; + Pos_le_max_r -> Pos_max_spec [] ; + Pos_le_max_r -> Pos_Private_Tac_lt_irrefl [] ; + Pos_le_max_r -> Pos_Private_Tac_eq_sym [] ; + Pos_le_max_r -> Pos_Private_Tac_not_gt_le [] ; + _Pplus_one_succ_r -> _eq_sym [] ; + _Pplus_one_succ_r -> Pos_add_1_r [] ; + Pos_Private_Tac_eq_lt -> Pos_Private_Tac_trans [] ; + Pos_Private_Tac_le_lt_trans -> Pos_Private_Tac_trans [] ; + Pos_max_spec -> Morphisms_iff_flip_impl_subrelation [] ; + Pos_max_spec -> Pos_eq_equiv [] ; + Pos_max_spec -> Pos_le_lteq [] ; + Pos_max_spec -> Pos_lt_total [] ; + Pos_max_spec -> Pos_max_l [] ; + Pos_max_spec -> Pos_max_r [] ; + Pos_Private_Tac_lt_irrefl -> RelationClasses_StrictOrder_Irreflexive [] ; + Pos_Private_Tac_lt_irrefl -> Pos_lt_strorder [] ; + Pos_Private_Tac_eq_sym -> RelationClasses_Equivalence_Symmetric [] ; + Pos_Private_Tac_eq_sym -> RelationClasses_symmetry [] ; + Pos_Private_Tac_eq_sym -> Pos_eq_equiv [] ; + Pos_Private_Tac_not_gt_le -> Morphisms_iff_flip_impl_subrelation [] ; + Pos_Private_Tac_not_gt_le -> Pos_le_lteq [] ; + Pos_Private_Tac_not_gt_le -> Pos_lt_total [] ; + Pos_lt_total -> _or [] ; + Pos_lt_total -> _or_introl [] ; + Pos_lt_total -> _or_intror [] ; + Pos_lt_total -> Pos_compare_spec [] ; + Pos_max_l -> Pos_compare_spec [] ; + Pos_max_l -> Pos_max [] ; + Pos_max_l -> Pos_le_nlt [] ; + Pos_max_r -> _False_ind [] ; + Pos_max_r -> _eq_refl [] ; + Pos_max_r -> Pos_le [] ; + Pos_max_r -> Pos_max [] ; + Pos_le_nlt -> RelationClasses_iff_Symmetric [] ; + Pos_le_nlt -> RelationClasses_symmetry [] ; + Pos_le_nlt -> Pos_lt [] ; + Pos_le_nlt -> Pos_ge_le_iff [] ; + Pos_ge_le_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Pos_ge_le_iff -> RelationClasses_reflexivity [] ; + Pos_ge_le_iff -> Morphisms_eq_proper_proxy [] ; + Pos_ge_le_iff -> RelationClasses_iff_Transitive [] ; + Pos_ge_le_iff -> RelationClasses_iff_Reflexive [] ; + Pos_ge_le_iff -> Morphisms_Prop_not_iff_morphism [] ; + Pos_ge_le_iff -> Pos_compare_antisym [] ; + Pos_ge_le_iff -> _CompOpp_iff [] ; + Pos_ge_le_iff -> Pos_le [] ; + Pos_ge_le_iff -> Pos_ge [] ; + Pos_ge -> _eq [] ; + Pos_ge -> _not [] ; + Pos_ge -> Pos_compare [] ; + Pos_Private_Tac_trans -> OrdersTac_OEQ [] ; + Pos_Private_Tac_trans -> RelationClasses_StrictOrder_Transitive [] ; + Pos_Private_Tac_trans -> OrdersTac_trans_ord [] ; + Pos_Private_Tac_trans -> Pos_lt_strorder [] ; + Pos_Private_Tac_trans -> Pos_le_lteq [] ; + Pos_Private_Tac_trans -> Pos_lt_compat [] ; + Pos_Private_Tac_trans -> Pos_Private_Tac_interp_ord [] ; + Pos_lt_compat -> _iff [] ; + Pos_lt_compat -> Morphisms_Proper [] ; + Pos_lt_compat -> Morphisms_respectful [] ; + Pos_lt_compat -> _conj [] ; + Pos_lt_compat -> _eq_ind_r [] ; + Pos_lt_compat -> Pos_lt [] ; + Pos_Private_Tac_interp_ord -> OrdersTac_ord [] ; + Pos_Private_Tac_interp_ord -> Pos_lt [] ; + Pos_Private_Tac_interp_ord -> Pos_le [] ; + Pos_Private_Tac_lt_trans -> Pos_Private_Tac_trans [] ; + _Pplus_one_succ_l -> _eq_sym [] ; + _Pplus_one_succ_l -> Pos_add_1_l [] ; + Pos_add_max_distr_r -> Pos_add_max_distr_l [] ; + Pos_add_max_distr_l -> Pos_add_le_mono_l [] ; + Pos_add_max_distr_l -> Pos_max_monotone [] ; + Pos_add_le_mono_l -> _iff_refl [] ; + Pos_add_le_mono_l -> Pos_add_compare_mono_l [] ; + Pos_add_le_mono_l -> Pos_le [] ; + Pos_max_monotone -> Pos_max_mono [] ; + Pos_max_mono -> Pos_Private_Tac_le_lt_trans [] ; + Pos_max_mono -> Pos_max_spec [] ; + Pos_max_mono -> Pos_Private_Tac_not_gt_le [] ; + Pos_max_mono -> Pos_Private_Tac_lt_trans [] ; + Pos_max_mono -> Pos_Private_Tac_eq_neq [] ; + Pos_max_mono -> Pos_Private_Tac_neq_eq [] ; + Pos_max_mono -> Pos_Private_Tac_not_neq_eq [] ; + Pos_max_mono -> Pos_Private_Tac_eq_refl [] ; + Pos_max_mono -> Pos_Private_Tac_le_neq_lt [] ; + Pos_Private_Tac_le_antisym -> RelationClasses_StrictOrder_Irreflexive [] ; + Pos_Private_Tac_le_antisym -> RelationClasses_StrictOrder_Transitive [] ; + Pos_Private_Tac_le_antisym -> Pos_lt_strorder [] ; + Pos_Private_Tac_le_antisym -> Pos_le_lteq [] ; + Pos_Private_Tac_eq_neq -> Pos_Private_Tac_eq_sym [] ; + Pos_Private_Tac_eq_neq -> Pos_Private_Tac_eq_trans [] ; + Pos_Private_Tac_neq_eq -> Pos_Private_Tac_eq_sym [] ; + Pos_Private_Tac_neq_eq -> Pos_Private_Tac_eq_trans [] ; + Pos_Private_Tac_not_neq_eq -> Pos_Private_Tac_lt_irrefl [] ; + Pos_Private_Tac_not_neq_eq -> Pos_lt_total [] ; + Pos_Private_Tac_not_neq_eq -> Pos_lt_compat [] ; + Pos_Private_Tac_eq_refl -> RelationClasses_reflexivity [] ; + Pos_Private_Tac_eq_refl -> RelationClasses_Equivalence_Reflexive [] ; + Pos_Private_Tac_eq_refl -> Pos_eq_equiv [] ; + Pos_Private_Tac_le_neq_lt -> Pos_Private_Tac_le_antisym [] ; + Pos_Private_Tac_le_neq_lt -> Pos_Private_Tac_not_ge_lt [] ; + Pos_Private_Tac_not_ge_lt -> Morphisms_iff_flip_impl_subrelation [] ; + Pos_Private_Tac_not_ge_lt -> Pos_eq_equiv [] ; + Pos_Private_Tac_not_ge_lt -> Pos_le_lteq [] ; + Pos_Private_Tac_not_ge_lt -> Pos_lt_total [] ; + Pos_Private_Tac_eq_trans -> Pos_Private_Tac_trans [] ; + Pos_add_le_mono_r -> _iff_refl [] ; + Pos_add_le_mono_r -> Pos_add_compare_mono_r [] ; + Pos_add_le_mono_r -> Pos_le [] ; + Pos_le_trans -> Pos_lt_le_trans [] ; + Pos_lt_le_trans -> Pos_lt_trans [] ; + Pos_lt_le_trans -> Pos_le_lteq [] ; + Pos_max_case_strong -> _eq_rect [] ; + Pos_max_case_strong -> Pos_Private_Dec_max_case_strong [] ; + ZMicromega_F -> _fst [] ; + ZMicromega_F -> RingMicromega_Op1 [] ; + ZMicromega_F -> ZMicromega_max_var [] ; + Pos_Private_Dec_max_case_strong -> Morphisms_iff_flip_impl_subrelation [] ; + Pos_Private_Dec_max_case_strong -> Pos_eq_equiv [] ; + Pos_Private_Dec_max_case_strong -> Pos_le_lteq [] ; + Pos_Private_Dec_max_case_strong -> Pos_max_l [] ; + Pos_Private_Dec_max_case_strong -> Pos_max_r [] ; + Pos_Private_Dec_max_case_strong -> _CompSpec2Type [] ; + _CompSpec2Type -> _CompSpec [] ; + _CompSpec2Type -> _CompSpecT [] ; + _CompSpec2Type -> _CompareSpec2Type [] ; + _CompareSpecT -> _Eq [] ; + _CompareSpecT -> _Lt [] ; + _CompareSpecT -> _Gt [] ; + _CompSpec -> _comparison [] ; + _CompSpec -> _CompareSpec [] ; + _CompSpecT -> _comparison [] ; + _CompSpecT -> _CompareSpecT [] ; + _CompareSpec2Type -> _comparison [] ; + _CompareSpec2Type -> _False_ind [] ; + _CompareSpec2Type -> _eq_ind [] ; + _CompareSpec2Type -> _True [] ; + _CompareSpec2Type -> _eq_refl [] ; + _CompareSpec2Type -> _I [] ; + _CompareSpec2Type -> _CompareSpec [] ; + _CompareSpec2Type -> _CompareSpecT [] ; + _CompareSpec2Type -> _CompEqT [] ; + _CompareSpec2Type -> _CompLtT [] ; + _CompareSpec2Type -> _CompGtT [] ; + _CompEqT -> _Eq [] ; + _CompEqT -> _Lt [] ; + _CompEqT -> _Gt [] ; + _CompLtT -> _Eq [] ; + _CompLtT -> _Lt [] ; + _CompLtT -> _Gt [] ; + _CompGtT -> _Eq [] ; + _CompGtT -> _Lt [] ; + _CompGtT -> _Gt [] ; + Pos_max_le_compat_r -> Pos_Private_Tac_eq_lt [] ; + Pos_max_le_compat_r -> Pos_max_lub_iff [] ; + Pos_max_lub_iff -> Pos_Private_Tac_le_lt_trans [] ; + Pos_max_lub_iff -> Pos_max_spec [] ; + Pos_max_lub_iff -> Pos_Private_Tac_lt_irrefl [] ; + Pos_max_lub_iff -> Pos_Private_Tac_eq_sym [] ; + Pos_max_lub_iff -> Pos_Private_Tac_not_gt_le [] ; + Pos_max_lub_iff -> Pos_Private_Tac_lt_trans [] ; + Pos_max_lub_iff -> Pos_Private_Tac_eq_le [] ; + Pos_max_lub_iff -> Pos_Private_Tac_lt_eq [] ; + Pos_Private_Tac_eq_le -> Pos_Private_Tac_trans [] ; + Pos_Private_Tac_lt_eq -> Pos_Private_Tac_trans [] ; + Pos_lt_nle -> _False_ind [] ; + Pos_lt_nle -> _True [] ; + Pos_lt_nle -> _I [] ; + Pos_lt_nle -> _iff [] ; + Pos_lt_nle -> _conj [] ; + Pos_lt_nle -> Pos_lt [] ; + Pos_lt_nle -> Pos_compare_antisym [] ; + Pos_lt_nle -> Pos_le [] ; + Pos_leb_spec0 -> RelationClasses_iff_Symmetric [] ; + Pos_leb_spec0 -> RelationClasses_symmetry [] ; + Pos_leb_spec0 -> Bool_iff_reflect [] ; + Pos_leb_spec0 -> Pos_leb_le [] ; + Pos_compare_nge_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Pos_compare_nge_iff -> Morphisms_eq_proper_proxy [] ; + Pos_compare_nge_iff -> Pos_compare_antisym [] ; + Pos_compare_nge_iff -> _CompOpp_iff [] ; + Pos_compare_nge_iff -> Pos_compare_nle_iff [] ; + Pos_compare_nle_iff -> _eq_ind [] ; + Pos_compare_nle_iff -> _True [] ; + Pos_compare_nle_iff -> _eq_refl [] ; + Pos_compare_nle_iff -> _I [] ; + Pos_compare_nle_iff -> RelationClasses_Equivalence_PER [] ; + Pos_compare_nle_iff -> RelationClasses_iff_equivalence [] ; + Pos_compare_nle_iff -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Pos_compare_nle_iff -> Morphisms_Prop_not_iff_morphism [] ; + Pos_compare_nle_iff -> Pos_compare_le_iff [] ; + Pos_leb_le -> _False_ind [] ; + Pos_leb_le -> _eq_ind [] ; + Pos_leb_le -> _True [] ; + Pos_leb_le -> _eq_refl [] ; + Pos_leb_le -> _I [] ; + Pos_leb_le -> _iff [] ; + Pos_leb_le -> _conj [] ; + Pos_leb_le -> Pos_le [] ; + Pos_leb_le -> Pos_leb [] ; + ZMicromega_eval_pol_add -> ZMicromega_ZSORaddon [] ; + ZMicromega_eval_pol_add -> ZMicromega_Zsor [] ; + ZMicromega_eval_pol_add -> ZMicromega_eval_pol [] ; + ZMicromega_eval_pol_add -> ZMicromega_padd [] ; + ZMicromega_eval_pol_add -> RingMicromega_eval_pol_add [] ; + Bool_negb_false_iff -> _iff [] ; + Bool_negb_false_iff -> _conj [] ; + Bool_negb_false_iff -> _eq_sym [] ; + Bool_negb_false_iff -> _negb [] ; + RingMicromega_padd -> EnvRing_Padd [] ; + ZMicromega_Zdivide_ceiling -> Z_divide [] ; + ZMicromega_Zdivide_ceiling -> ZMicromega_ceiling [] ; + ZMicromega_Zdivide_ceiling -> Z_mod_mul [] ; + ZMicromega_Zdivide_ceiling -> Z_eqb_spec [] ; + ZMicromega_Zdivide_ceiling -> Z_div_0_r [] ; + ZMicromega_Zdivide_ceiling -> Z_div_eucl_0_r [] ; + Z_lt_le_pred -> Morphisms_PER_morphism [] ; + Z_lt_le_pred -> Z_pred_succ [] ; + Z_lt_le_pred -> Z_pred_wd [] ; + Z_lt_le_pred -> Z_succ_pred [] ; + Z_lt_le_pred -> Z_le_wd [] ; + ZMicromega_makeCuttingPlane_ns_sound -> RingMicromega_NonStrict [] ; + ZMicromega_makeCuttingPlane_ns_sound -> Z_ge_le [] ; + ZMicromega_makeCuttingPlane_ns_sound -> ZMicromega_eval_nformula [] ; + ZMicromega_makeCuttingPlane_ns_sound -> Z_le_ge [] ; + ZMicromega_makeCuttingPlane_ns_sound -> Z_lt_gt [] ; + ZMicromega_makeCuttingPlane_ns_sound -> ZMicromega_nformula_of_cutting_plane [] ; + ZMicromega_makeCuttingPlane_ns_sound -> ZMicromega_Zgcd_pol_correct_lt [] ; + ZMicromega_makeCuttingPlane_ns_sound -> ZMicromega_makeCuttingPlane [] ; + ZMicromega_makeCuttingPlane_ns_sound -> RingMicromega_eval_pol_add [] ; + ZMicromega_makeCuttingPlane_ns_sound -> Z_le_sub_le_add_r [] ; + ZMicromega_makeCuttingPlane_ns_sound -> ZMicromega_narrow_interval_lower_bound [] ; + ZMicromega_makeCuttingPlane_ns_sound -> Z_gtb_spec [] ; + ZMicromega_makeCuttingPlane_ns_sound -> Z_add_nonneg_nonneg [] ; + ZMicromega_makeCuttingPlane_ns_sound -> Z_le_add_le_sub_l [] ; + Z_div_unique_exact -> Z_div_mul [] ; + Z_div_unique_exact -> Z_div_wd [] ; + Bool_andb_false_iff -> _eq [] ; + Bool_andb_false_iff -> _true [] ; + Bool_andb_false_iff -> _eq_refl [] ; + Bool_andb_false_iff -> _iff [] ; + Bool_andb_false_iff -> _conj [] ; + Bool_andb_false_iff -> _or_ind [] ; + Bool_andb_false_iff -> _or_introl [] ; + Bool_andb_false_iff -> _or_intror [] ; + Bool_andb_false_iff -> _andb [] ; + ZMicromega_padd -> Z_add [] ; + ZMicromega_padd -> Z_eqb [] ; + ZMicromega_padd -> RingMicromega_padd [] ; + RingMicromega_eval_pol_add -> _Rth_ARth [] ; + RingMicromega_eval_pol_add -> RingMicromega_eval_pol [] ; + RingMicromega_eval_pol_add -> OrderedRing_SORsetoid [] ; + RingMicromega_eval_pol_add -> OrderedRing_SORrt [] ; + RingMicromega_eval_pol_add -> RingMicromega_Rops_wd [] ; + RingMicromega_eval_pol_add -> RingMicromega_SORrm [] ; + RingMicromega_eval_pol_add -> EnvRing_Padd_ok [] ; + RingMicromega_eval_pol_add -> RingMicromega_padd [] ; + Z_sub_move_0_r -> Z_sub_move_r [] ; + Z_div_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Z_div_wd -> RelationClasses_eq_Reflexive [] ; + Z_div_wd -> Morphisms_reflexive_proper [] ; + Z_div_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_div_wd -> Z_eq [] ; + Z_div_wd -> Z_div [] ; + Z_le_sub_le_add_r -> Z_add_le_mono_r [] ; + Z_le_sub_le_add_r -> Z_sub_simpl_r [] ; + ZMicromega_narrow_interval_lower_bound -> Z_mul_le_mono_pos_l [] ; + ZMicromega_narrow_interval_lower_bound -> Z_lt_le_trans [] ; + ZMicromega_narrow_interval_lower_bound -> Z_ge_le_iff [] ; + ZMicromega_narrow_interval_lower_bound -> Z_add_1_r [] ; + ZMicromega_narrow_interval_lower_bound -> Z_gt_lt_iff [] ; + ZMicromega_narrow_interval_lower_bound -> ZMicromega_ceiling [] ; + ZMicromega_narrow_interval_lower_bound -> Z_mul_div_le [] ; + ZMicromega_narrow_interval_lower_bound -> Z_lt_add_pos_r [] ; + Z_gtb_spec -> Z_ltb_spec [] ; + Z_gtb_spec -> Z_gtb_ltb [] ; + Z_add_nonneg_nonneg -> Z_add_le_mono [] ; + Z_le_add_le_sub_l -> Z_le_add_le_sub_r [] ; + Z_le_add_le_sub_r -> Z_add_simpl_r [] ; + Z_le_add_le_sub_r -> Z_sub_le_mono_r [] ; + Z_add_simpl_r -> Z_sub_diag [] ; + Z_add_simpl_r -> Z_add_sub_assoc [] ; + Z_sub_le_mono_r -> Z_add_le_mono_r [] ; + Z_sub_le_mono_r -> Z_add_opp_r [] ; + _Fdiv_correct -> Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_correct [] ; + _Fdiv_correct -> _Fdiv [] ; + Z_mul_div_le -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_mul_div_le -> Z_Private_OrderTac_Tac_lt_eq [] ; + Z_mul_div_le -> Z_add_le_mono_l [] ; + Z_mul_div_le -> Z_mod_pos_bound [] ; + Z_mul_div_le -> Z_div_mod [] ; + Z_le -> _eq [] ; + Z_le -> Z_compare [] ; + Z_le -> _not [] ; + Z_lt_add_pos_r -> Z_lt_add_pos_l [] ; + _IZR -> _Ropp [] ; + _IZR -> _R0 [] ; + _IZR -> _IPR [] ; + Z_lt_add_pos_l -> Z_add_lt_mono_r [] ; + _Rdiv -> RinvImpl_Rinv [] ; + _Rdiv -> _Rmult [] ; + Z_eqb_spec -> RelationClasses_iff_Symmetric [] ; + Z_eqb_spec -> RelationClasses_symmetry [] ; + Z_eqb_spec -> Z_eqb_eq [] ; + Z_eqb_spec -> Bool_iff_reflect [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_correct -> _cexp [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_correct -> _inbetween_float [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_correct -> Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv [] ; + Z_div_0_r -> _eq [] ; + Z_div_0_r -> _eq_refl [] ; + Z_div_0_r -> Z_div [] ; + _Fdiv -> _float [] ; + _Fdiv -> Z_min [] ; + _Fdiv -> _Zdigits [] ; + _Fdiv -> _Fdiv_core [] ; + Z_div_eucl_0_r -> _eq [] ; + Z_div_eucl_0_r -> _eq_refl [] ; + Z_div_eucl_0_r -> Z_div_eucl [] ; + _F2R -> _bpow [] ; + _F2R -> _Fexp [] ; + _F2R -> _Fnum [] ; + Z_opp_le_mono -> Z_le_0_sub [] ; + Z_opp_le_mono -> Z_sub_opp_r [] ; + Z_opp_le_mono -> Z_add_opp_l [] ; + _cexp -> _mag [] ; + _cexp -> _mag_val [] ; + Z_leb_spec0 -> RelationClasses_iff_Symmetric [] ; + Z_leb_spec0 -> RelationClasses_symmetry [] ; + Z_leb_spec0 -> Bool_iff_reflect [] ; + Z_leb_spec0 -> Z_leb_le [] ; + _inbetween_float -> _F2R [] ; + _inbetween_float -> SpecFloat_location [] ; + _inbetween_float -> _inbetween [] ; + _inbetween_float -> _Float [] ; + Z_compare_nge_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Z_compare_nge_iff -> Morphisms_eq_proper_proxy [] ; + Z_compare_nge_iff -> _CompOpp_iff [] ; + Z_compare_nge_iff -> Z_compare_antisym [] ; + Z_compare_nge_iff -> Z_compare_nle_iff [] ; + _Rlt -> ConstructiveCauchyReals_CRealLtProp [] ; + _Rlt -> _R [] ; + _Rlt -> _Rrepr [] ; + Z_compare_nle_iff -> _eq_ind [] ; + Z_compare_nle_iff -> _True [] ; + Z_compare_nle_iff -> _eq_refl [] ; + Z_compare_nle_iff -> _I [] ; + Z_compare_nle_iff -> RelationClasses_Equivalence_PER [] ; + Z_compare_nle_iff -> RelationClasses_iff_equivalence [] ; + Z_compare_nle_iff -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Z_compare_nle_iff -> Morphisms_Prop_not_iff_morphism [] ; + Z_compare_nle_iff -> Z_compare_le_iff [] ; + Pos_le_lt_trans -> Pos_lt_trans [] ; + Pos_le_lt_trans -> Pos_le_lteq [] ; + _Z -> _positive [] ; + Z_le_neq -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_le_neq -> Z_Private_OrderTac_Tac_not_ge_lt [] ; + Z_le_neq -> Z_Private_OrderTac_Tac_lt_trans [] ; + Z_le_neq -> Z_Private_OrderTac_Tac_not_gt_le [] ; + Z_le_neq -> Z_Private_OrderTac_Tac_eq_lt [] ; + Z_le_neq -> Z_Private_OrderTac_Tac_le_antisym [] ; + Z_le_neq -> Z_Private_OrderTac_Tac_eq_neq [] ; + Z_le_neq -> Z_Private_OrderTac_Tac_eq_refl [] ; + _float -> _radix [] ; + _Zsth -> _Z [] ; + _Zsth -> _Eqsth [] ; + _Zsth -> Setoid_Setoid_Theory [] ; + _radix -> Z_leb [] ; + _radix -> _eq [] ; + _radix -> _Zpos [] ; + _radix -> _xO [] ; + _radix -> _xH [] ; + ZMicromega_Zeval_op2_hold -> Tauto_isBool [] ; + ZMicromega_Zeval_op2_hold -> Tauto_hold [] ; + ZMicromega_Zeval_op2_hold -> ZMicromega_Zeval_op2 [] ; + ZMicromega_Zeval_op2_hold -> ZMicromega_pop2_bop2 [] ; + SpecFloat_location -> _comparison [] ; + ZMicromega_pop2_bop2 -> RelationClasses_Equivalence_PER [] ; + ZMicromega_pop2_bop2 -> RelationClasses_iff_equivalence [] ; + ZMicromega_pop2_bop2 -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + ZMicromega_pop2_bop2 -> Z_eqb_eq [] ; + ZMicromega_pop2_bop2 -> RingMicromega_OpEq [] ; + ZMicromega_pop2_bop2 -> RingMicromega_OpLt [] ; + ZMicromega_pop2_bop2 -> _is_true [] ; + ZMicromega_pop2_bop2 -> RingMicromega_OpNEq [] ; + ZMicromega_pop2_bop2 -> RingMicromega_OpLe [] ; + ZMicromega_pop2_bop2 -> RingMicromega_OpGe [] ; + ZMicromega_pop2_bop2 -> RingMicromega_OpGt [] ; + ZMicromega_pop2_bop2 -> Bool_negb_true_iff [] ; + ZMicromega_pop2_bop2 -> Z_ltb_lt [] ; + ZMicromega_pop2_bop2 -> Z_ge_le_iff [] ; + ZMicromega_pop2_bop2 -> ZMicromega_Zeval_pop2 [] ; + ZMicromega_pop2_bop2 -> ZMicromega_Zeval_bop2 [] ; + ZMicromega_pop2_bop2 -> Z_geb_le [] ; + ZMicromega_pop2_bop2 -> Z_gtb_gt [] ; + _Z0 -> _positive [] ; + Z_geb_le -> Z_leb_le [] ; + Z_geb_le -> Z_geb_leb [] ; + Z_gtb_gt -> _False_ind [] ; + Z_gtb_gt -> _eq_ind [] ; + Z_gtb_gt -> _True [] ; + Z_gtb_gt -> _eq_refl [] ; + Z_gtb_gt -> _I [] ; + Z_gtb_gt -> _iff [] ; + Z_gtb_gt -> _conj [] ; + Z_gtb_gt -> Z_gt [] ; + Z_gtb_gt -> Z_gtb [] ; + Z_geb_leb -> Z_leb [] ; + Z_geb_leb -> Z_compare_antisym [] ; + Z_geb_leb -> Z_geb [] ; + ZMicromega_xnormalise -> _list [] ; + ZMicromega_xnormalise -> _nil [] ; + ZMicromega_xnormalise -> _cons [] ; + ZMicromega_xnormalise -> _pair [] ; + ZMicromega_xnormalise -> RingMicromega_NFormula [] ; + ZMicromega_xnormalise -> RingMicromega_Equal [] ; + ZMicromega_xnormalise -> RingMicromega_NonStrict [] ; + ZMicromega_xnormalise -> ZMicromega_psub [] ; + Z_leb -> _bool [] ; + Z_leb -> _true [] ; + Z_leb -> Z_compare [] ; + Z_leb -> _false [] ; + ZMicromega_xnormalise_correct -> Refl_make_conj [] ; + ZMicromega_xnormalise_correct -> RingMicromega_NonEqual [] ; + ZMicromega_xnormalise_correct -> RingMicromega_Strict [] ; + ZMicromega_xnormalise_correct -> ZMicromega_eval_nformula [] ; + ZMicromega_xnormalise_correct -> ZMicromega_eval_pol_sub [] ; + ZMicromega_xnormalise_correct -> ZMicromega_eval_pol_Pc [] ; + ZMicromega_xnormalise_correct -> ZMicromega_eq_cnf [] ; + ZMicromega_xnormalise_correct -> Z_sub_0_l [] ; + ZMicromega_xnormalise_correct -> ZMicromega_xnormalise [] ; + ZMicromega_xnormalise_correct -> ZMicromega_le_neg [] ; + ZMicromega_le_neg -> Z_nle_gt [] ; + ZMicromega_le_neg -> Z_opp_pos_neg [] ; + Z_le_ind -> Z_right_induction [] ; + _Zpos -> _positive [] ; + Z_pow_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Z_pow_wd -> RelationClasses_eq_Reflexive [] ; + Z_pow_wd -> Morphisms_reflexive_proper [] ; + Z_pow_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_pow_wd -> Z_eq [] ; + Z_pow_wd -> Z_pow [] ; + Z_pow_neg_r -> Z_lt [] ; + Z_pow_neg_r -> _False_ind [] ; + Z_pow_neg_r -> _eq_ind [] ; + Z_pow_neg_r -> _True [] ; + Z_pow_neg_r -> _eq_refl [] ; + Z_pow_neg_r -> _I [] ; + Z_pow_neg_r -> Z_pow [] ; + Z_pow_succ_r -> Z_le [] ; + Z_pow_succ_r -> Z_succ [] ; + Z_pow_succ_r -> Z_pow [] ; + Z_pow_succ_r -> Pos_iter_add [] ; + Z_pow_0_r -> _eq [] ; + Z_pow_0_r -> _eq_refl [] ; + Z_pow_0_r -> Z_pow [] ; + Z_compare -> _Z [] ; + Z_compare -> _CompOpp [] ; + Z_compare -> PosDef_Pos_compare [] ; + Pos_iter -> _positive [] ; + Pos_iter_add -> Pos_add_1_l [] ; + Pos_iter_add -> Pos_peano_ind [] ; + Pos_iter_add -> Pos_add_succ_l [] ; + Pos_iter_add -> Pos_iter_succ [] ; + _CompOpp -> _comparison [] ; + _CompOpp -> _Eq [] ; + _CompOpp -> _Lt [] ; + _CompOpp -> _Gt [] ; + Pos_iter_succ -> Pos_succ [] ; + Pos_iter_succ -> Pos_iter_swap [] ; + PosDef_Pos_compare -> _Eq [] ; + PosDef_Pos_compare -> PosDef_Pos_compare_cont [] ; + Pos_iter_swap -> Pos_iter_swap_gen [] ; + Pos_iter_swap_gen -> _eq_ind_r [] ; + Pos_iter_swap_gen -> _positive_ind [] ; + Pos_iter_swap_gen -> Pos_iter [] ; + PosDef_Pos_compare_cont -> _positive [] ; + PosDef_Pos_compare_cont -> _comparison [] ; + PosDef_Pos_compare_cont -> _Lt [] ; + PosDef_Pos_compare_cont -> _Gt [] ; + QArith_base_Qinv_lt_0_compat -> QArith_base_Qlt [] ; + QArith_base_Qinv_lt_0_compat -> QArith_base_Qinv [] ; + QArith_base_Qmult_lt_0_le_reg_r -> QArith_base_Qlt [] ; + QArith_base_Qmult_lt_0_le_reg_r -> QArith_base_Qmult [] ; + QArith_base_Qmult_lt_0_le_reg_r -> QArith_base_Qle [] ; + QArith_base_Qmult_lt_0_le_reg_r -> Z_mul_1_r [] ; + QArith_base_Qmult_lt_0_le_reg_r -> Z_mul_le_mono_pos_r [] ; + QArith_base_Qmult_lt_0_le_reg_r -> Pos2Z_inj_mul [] ; + QArith_base_Qmult_lt_0_le_reg_r -> Z_mul_shuffle1 [] ; + QArith_base_Qmult_lt_0_le_reg_r -> Z_mul_pos_pos [] ; + ConstructiveCauchyReals_CRealLtProp -> _ex [] ; + ConstructiveCauchyReals_CRealLtProp -> ConstructiveCauchyReals_seq [] ; + _R -> ClassicalDedekindReals_DReal [] ; + QArith_base_Qlt_not_le -> QArith_base_Qlt [] ; + QArith_base_Qlt_not_le -> QArith_base_Qle [] ; + QArith_base_Qlt_not_le -> Z_lt_nge [] ; + _Rrepr -> ClassicalDedekindReals_DRealRepr [] ; + QArith_base_Qdiv_mult_l -> QArith_base_Q_Setoid [] ; + QArith_base_Qdiv_mult_l -> QArith_base_Qdiv [] ; + QArith_base_Qdiv_mult_l -> QArith_base_Qmult_comp [] ; + QArith_base_Qdiv_mult_l -> QArith_base_Qmult_inv_r [] ; + QArith_base_Qdiv_mult_l -> QArith_base_Qmult_assoc [] ; + QArith_base_Qdiv_mult_l -> QArith_base_Qmult_1_r [] ; + QArith_base_Qmult_1_r -> QArith_base_Qmult [] ; + QArith_base_Qmult_1_r -> QArith_base_Qeq [] ; + QArith_base_Qmult_1_r -> Z_mul_1_r [] ; + ClassicalDedekindReals_DRealRepr -> ConstructiveCauchyReals_CReal [] ; + ClassicalDedekindReals_DRealRepr -> ClassicalDedekindReals_CReal_of_DReal_bound [] ; + ClassicalDedekindReals_DRealRepr -> ConstructiveCauchyReals_mkCReal [] ; + Z_lt_nge -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_lt_nge -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_lt_nge -> Z_Private_OrderTac_Tac_not_ge_lt [] ; + ClassicalDedekindReals_DReal -> ClassicalDedekindReals_isLowerCut [] ; + ClassicalDedekindReals_DReal -> _sig [] ; + ConstructiveCauchyReals_CReal -> ConstructiveCauchyReals_QCauchySeq [] ; + ConstructiveCauchyReals_CReal -> ConstructiveCauchyReals_QBound [] ; + Pos2Z_inj_pow_pos -> Z_pow_pos [] ; + Pos2Z_inj_pow_pos -> Pos_pow [] ; + Pos2Z_inj_pow_pos -> Pos_iter_swap_gen [] ; + Datatypes_id -> _ID [] ; + ConstructiveCauchyReals_QCauchySeq -> Z_le [] ; + ConstructiveCauchyReals_QCauchySeq -> QArith_base_Qlt [] ; + ConstructiveCauchyReals_QCauchySeq -> Qabs_Qabs [] ; + ConstructiveCauchyReals_QCauchySeq -> QArith_base_Qpower [] ; + ConstructiveCauchyReals_QCauchySeq -> QArith_base_Qminus [] ; + Pos_iter_invariant -> Pos_iter_ind [] ; + ConstructiveCauchyReals_QBound -> QArith_base_Qlt [] ; + ConstructiveCauchyReals_QBound -> Qabs_Qabs [] ; + ConstructiveCauchyReals_QBound -> QArith_base_Qpower [] ; + QArith_base_Q -> _Z [] ; + Pos_iter_ind -> Pos_peano_ind [] ; + Pos_iter_ind -> Pos_iter_succ [] ; + QArith_base_Qlt -> Z_mul [] ; + QArith_base_Qlt -> QArith_base_Qden [] ; + QArith_base_Qlt -> QArith_base_Qnum [] ; + QArith_base_Qlt -> Z_lt [] ; + Qpower_Qpower_decomp_positive -> QArith_base_Qpower_positive [] ; + Qpower_Qpower_decomp_positive -> Pos2Z_inj_mul [] ; + Qpower_Qpower_decomp_positive -> Pos2Z_inj_pow [] ; + Qpower_Qpower_decomp_positive -> IntDef_Z_mul [] ; + Qpower_Qpower_decomp_positive -> Pos_pow_1_r [] ; + Qpower_Qpower_decomp_positive -> Pos2Z_inj [] ; + Qpower_Qpower_decomp_positive -> Z_pow_twice_r [] ; + Qpower_Qpower_decomp_positive -> Z_pow_1_r [] ; + Qabs_Qabs -> QArith_base_Q [] ; + Qabs_Qabs -> QArith_base_Qmake [] ; + Qabs_Qabs -> Z_abs [] ; + Pos_pow_1_r -> Pos_mul_comm [] ; + Pos_pow_1_r -> Pos_pow [] ; + QArith_base_Qpower -> QArith_base_Qinv [] ; + QArith_base_Qpower -> QArith_base_Qpower_positive [] ; + QArith_base_Qmake -> _Z [] ; + Pos2Z_inj -> _Z [] ; + Pos2Z_inj -> _Zpos [] ; + Pos2Z_inj -> _f_equal [] ; + Z_pow_twice_r -> Z_mul_0_r [] ; + Z_pow_twice_r -> Z_pow_add_r [] ; + Z_pow_twice_r -> Z_two_succ [] ; + Z_pow_twice_r -> Z_pow_neg_r [] ; + Z_pow_twice_r -> Z_add_neg_neg [] ; + QArith_base_Qinv -> _Z0 [] ; + QArith_base_Qinv -> _Zpos [] ; + QArith_base_Qinv -> _xH [] ; + QArith_base_Qinv -> QArith_base_Qmake [] ; + QArith_base_Qinv -> QArith_base_Qden [] ; + QArith_base_Qinv -> QArith_base_Qnum [] ; + QArith_base_Qinv -> _Zneg [] ; + Z_pow_1_r -> RelationClasses_PreOrder_Reflexive [] ; + Z_pow_1_r -> Z_mul_1_r [] ; + Z_pow_1_r -> Z_le_preorder [] ; + Z_pow_1_r -> Z_pow_wd [] ; + Z_pow_1_r -> Z_pow_succ_r [] ; + Z_pow_1_r -> Z_pow_0_r [] ; + QArith_base_Qpower_positive -> _pow_pos [] ; + QArith_base_Qpower_positive -> QArith_base_Qmult [] ; + _pow_pos -> _positive [] ; + Z_add_neg_neg -> Z_add_lt_mono [] ; + Pos_pow_succ_r -> Pos_pow [] ; + Pos_pow_succ_r -> Pos_iter_succ [] ; + QArith_base_Qmult -> QArith_base_Qmake [] ; + QArith_base_Qmult -> Pos_mul [] ; + QArith_base_Qmult -> Z_mul [] ; + QArith_base_Qmult -> QArith_base_Qden [] ; + QArith_base_Qmult -> QArith_base_Qnum [] ; + ZifyClasses_rew_iff_rev -> _iff [] ; + ZifyClasses_rew_iff_rev -> _proj2 [] ; + Pos_mul -> Pos_add [] ; + Z_mul -> _Z [] ; + Z_mul -> _Z0 [] ; + Z_mul -> _Zpos [] ; + Z_mul -> PosDef_Pos_mul [] ; + Z_mul -> _Zneg [] ; + ZifyClasses_mkapp -> _eq_ind [] ; + QArith_base_Qden -> QArith_base_Q [] ; + _Fnorm -> Ring_polynom_PEX [] ; + _Fnorm -> _nil [] ; + _Fnorm -> _app [] ; + _Fnorm -> _denum [] ; + _Fnorm -> _condition [] ; + _Fnorm -> _num [] ; + _Fnorm -> _mk_linear [] ; + _Fnorm -> _NPEadd [] ; + _Fnorm -> _NPEopp [] ; + _Fnorm -> _NPEsub [] ; + _Fnorm -> _FExpr [] ; + _Fnorm -> _split [] ; + QArith_base_Qnum -> QArith_base_Q [] ; + _PCond -> _and [] ; + _PCond -> _not [] ; + _PCond -> _True [] ; + _PCond -> Ring_polynom_PEeval [] ; + PosDef_Pos_mul -> PosDef_Pos_add [] ; + _denum -> _linear [] ; + _Zneg -> _positive [] ; + Qfield_Qfield_field_lemma1 -> QArith_base_Qplus_comp [] ; + Qfield_Qfield_field_lemma1 -> Qfield_Qpower_theory [] ; + Qfield_Qfield_field_lemma1 -> _triv_div_th [] ; + Qfield_Qfield_field_lemma1 -> QArith_base_Qopp_comp [] ; + Qfield_Qfield_field_lemma1 -> Qfield_Qsft [] ; + Qfield_Qfield_field_lemma1 -> QArith_base_Qmult_comp [] ; + Qfield_Qfield_field_lemma1 -> QArith_base_Qeq_bool_eq [] ; + Qfield_Qfield_field_lemma1 -> QArith_base_Qinv_comp [] ; + Qfield_Qfield_field_lemma1 -> _F2AF [] ; + Qfield_Qfield_field_lemma1 -> _Field_correct [] ; + PosDef_Pos_add -> PosDef_Pos_succ [] ; + _FEeval -> BinList_nth [] ; + _FEeval -> _FExpr [] ; + PosDef_Pos_succ -> _positive [] ; + PosDef_Pos_succ -> _xO [] ; + PosDef_Pos_succ -> _xH [] ; + PosDef_Pos_succ -> _xI [] ; + _Fcons2 -> _Fcons1 [] ; + _Fcons2 -> _PEsimp [] ; + _condition -> _linear [] ; + Pos_add -> Pos_succ [] ; + Qpower_Qpower_opp -> QArith_base_Qpower [] ; + Qpower_Qpower_opp -> QArith_base_Q_Setoid [] ; + Qpower_Qpower_opp -> QArith_base_Qinv_involutive [] ; + Pos_succ -> _positive [] ; + Pos_succ -> _xO [] ; + Pos_succ -> _xH [] ; + Pos_succ -> _xI [] ; + Qfield_Qfield_lemma5 -> QArith_base_Qplus_comp [] ; + Qfield_Qfield_lemma5 -> Qfield_Qpower_theory [] ; + Qfield_Qfield_lemma5 -> _triv_div_th [] ; + Qfield_Qfield_lemma5 -> QArith_base_Qopp_comp [] ; + Qfield_Qfield_lemma5 -> Qfield_Qsft [] ; + Qfield_Qfield_lemma5 -> QArith_base_Qmult_comp [] ; + Qfield_Qfield_lemma5 -> QArith_base_Qeq_bool_eq [] ; + Qfield_Qfield_lemma5 -> QArith_base_Qeq_eq_bool [] ; + Qfield_Qfield_lemma5 -> _Pcond_simpl_complete [] ; + Qfield_Qfield_lemma5 -> _F2AF [] ; + Z_abs -> _Z [] ; + Z_abs -> _Z0 [] ; + Z_abs -> _Zpos [] ; + Qpower_Qpower_plus -> Qfield_Qfield_field_lemma1 [] ; + Qpower_Qpower_plus -> Qfield_Qfield_lemma5 [] ; + Qpower_Qpower_plus -> QArith_base_Qinv_mult_distr [] ; + Qpower_Qpower_plus -> Qfield_Qfield_ring_lemma1 [] ; + Qpower_Qpower_plus -> Qpower_Qpower_minus_positive [] ; + _num -> _linear [] ; + Z_lt -> _eq [] ; + Z_lt -> Z_compare [] ; + QArith_base_Qminus -> QArith_base_Qopp [] ; + QArith_base_Qminus -> QArith_base_Qplus [] ; + _Fapp -> Ring_polynom_PExpr [] ; + _Fapp -> _list [] ; + _linear -> Ring_polynom_PExpr [] ; + _linear -> _list [] ; + QArith_base_Qopp -> QArith_base_Qmake [] ; + QArith_base_Qopp -> QArith_base_Qden [] ; + QArith_base_Qopp -> QArith_base_Qnum [] ; + QArith_base_Qopp -> Z_opp [] ; + _FEX -> _N [] ; + QArith_base_Qplus -> QArith_base_Qmake [] ; + QArith_base_Qplus -> Pos_mul [] ; + QArith_base_Qplus -> Z_mul [] ; + QArith_base_Qplus -> QArith_base_Qden [] ; + QArith_base_Qplus -> QArith_base_Qnum [] ; + QArith_base_Qplus -> Z_add [] ; + _FEmul -> _N [] ; + Z_add -> PosDef_Pos_add [] ; + Z_add -> Z_pos_sub [] ; + _FEinv -> _N [] ; + Z_pos_sub -> Z_pred_double [] ; + Z_pos_sub -> Z_double [] ; + Z_pos_sub -> Z_succ_double [] ; + _FEdiv -> _N [] ; + PosDef_Pos_pred_double -> _positive [] ; + PosDef_Pos_pred_double -> _xO [] ; + PosDef_Pos_pred_double -> _xH [] ; + PosDef_Pos_pred_double -> _xI [] ; + _mk_linear -> Ring_polynom_PExpr [] ; + _mk_linear -> _list [] ; + Z_pred_double -> _Z [] ; + Z_pred_double -> _Zpos [] ; + Z_pred_double -> _Zneg [] ; + Z_pred_double -> PosDef_Pos_pred_double [] ; + Z_double -> _Z [] ; + Z_double -> _Z0 [] ; + Z_double -> _Zpos [] ; + Z_double -> _xO [] ; + Z_double -> _Zneg [] ; + Qpower_Qpower_plus_positive -> QArith_base_Qpower_positive [] ; + Qpower_Qpower_plus_positive -> QArith_base_Q_Setoid [] ; + Qpower_Qpower_plus_positive -> QArith_base_Qmult_comp [] ; + Qpower_Qpower_plus_positive -> QArith_base_Qmult_assoc [] ; + Z_succ_double -> _Z [] ; + Z_succ_double -> _Zpos [] ; + Z_succ_double -> _Zneg [] ; + Z_succ_double -> PosDef_Pos_pred_double [] ; + QArith_base_Qinv_mult_distr -> QArith_base_Qinv [] ; + QArith_base_Qinv_mult_distr -> QArith_base_Qmult [] ; + QArith_base_Qinv_mult_distr -> _eq_refl [] ; + QArith_base_Qinv_mult_distr -> QArith_base_Qeq [] ; + Z_opp -> _Z [] ; + Z_opp -> _Z0 [] ; + Z_opp -> _Zpos [] ; + Z_opp -> _Zneg [] ; + Qfield_Qfield_ring_lemma1 -> QArith_base_Qplus_comp [] ; + Qfield_Qfield_ring_lemma1 -> Setoid_Build_Setoid_Theory [] ; + Qfield_Qfield_ring_lemma1 -> Qfield_Qpower_theory [] ; + Qfield_Qfield_ring_lemma1 -> _triv_div_th [] ; + Qfield_Qfield_ring_lemma1 -> QArith_base_Qopp_comp [] ; + Qfield_Qfield_ring_lemma1 -> Qfield_Qsft [] ; + Qfield_Qfield_ring_lemma1 -> QArith_base_Qmult_comp [] ; + Qfield_Qfield_ring_lemma1 -> Morphisms_proper_prf [] ; + Qfield_Qfield_ring_lemma1 -> QArith_base_Qeq_bool_eq [] ; + Qfield_Qfield_ring_lemma1 -> _F_R [] ; + ClassicalDedekindReals_isLowerCut -> _and [] ; + ClassicalDedekindReals_isLowerCut -> _bool [] ; + ClassicalDedekindReals_isLowerCut -> _true [] ; + ClassicalDedekindReals_isLowerCut -> _false [] ; + ClassicalDedekindReals_isLowerCut -> QArith_base_Qle [] ; + ClassicalDedekindReals_isLowerCut -> _or [] ; + Qpower_Qpower_minus_positive -> Qpower_Qpower_not_0_positive [] ; + Qpower_Qpower_minus_positive -> QArith_base_Qdiv_mult_l [] ; + Qpower_Qpower_minus_positive -> Qpower_Qpower_plus_positive [] ; + Qpower_Qpower_minus_positive -> QArith_base_Qdiv_comp [] ; + Qpower_Qpower_minus_positive -> QArith_base_Qeq_dec [] ; + Qpower_Qpower_minus_positive -> QArith_base_Qpower_positive_comp [] ; + Qpower_Qpower_minus_positive -> Qpower_Qpower_positive_0 [] ; + QArith_base_Qinv_comp -> QArith_base_Qinv [] ; + QArith_base_Qinv_comp -> QArith_base_Qeq [] ; + QArith_base_Qinv_comp -> Z_eq_mul_0 [] ; + _FEc -> _N [] ; + _not -> _False [] ; + QArith_base_Qle -> Z_le [] ; + QArith_base_Qle -> Z_mul [] ; + QArith_base_Qle -> QArith_base_Qden [] ; + QArith_base_Qle -> QArith_base_Qnum [] ; + QArith_base_Qdiv_comp -> QArith_base_Q_Setoid [] ; + QArith_base_Qdiv_comp -> QArith_base_Qdiv [] ; + QArith_base_Qdiv_comp -> QArith_base_Qmult_comp [] ; + QArith_base_Qdiv_comp -> QArith_base_Qinv_comp [] ; + QArith_base_Qeq_dec -> QArith_base_Qeq [] ; + QArith_base_Qeq_dec -> Z_eq_dec [] ; + QArith_base_Qpower_positive_comp -> QArith_base_Qpower_positive [] ; + QArith_base_Qpower_positive_comp -> QArith_base_Q_Setoid [] ; + QArith_base_Qpower_positive_comp -> QArith_base_Qmult_comp [] ; + Qpower_Qpower_positive_0 -> QArith_base_Qpower_positive [] ; + Qpower_Qpower_positive_0 -> QArith_base_Q_Setoid [] ; + Qpower_Qpower_positive_0 -> QArith_base_Qmult_comp [] ; + ClassicalDedekindReals_CReal_of_DReal_cauchy -> ConstructiveCauchyReals_QCauchySeq [] ; + ClassicalDedekindReals_CReal_of_DReal_cauchy -> ClassicalDedekindReals_CReal_of_DReal_seq [] ; + ClassicalDedekindReals_CReal_of_DReal_cauchy -> VarMap_Branch [] ; + ClassicalDedekindReals_CReal_of_DReal_cauchy -> ClassicalDedekindReals_Qpower_2_invneg_le_pow [] ; + ClassicalDedekindReals_CReal_of_DReal_cauchy -> Qabs_Qabs_case [] ; + ClassicalDedekindReals_CReal_of_DReal_cauchy -> ClassicalDedekindReals_UpperAboveLower [] ; + ClassicalDedekindReals_CReal_of_DReal_cauchy -> Qpower_Qpower_le_compat_l [] ; + QArith_base_Qeq_eq_bool -> QArith_base_Qeq_bool_iff [] ; + ClassicalDedekindReals_CReal_of_DReal_bound -> ConstructiveCauchyReals_QBound [] ; + ClassicalDedekindReals_CReal_of_DReal_bound -> ClassicalDedekindReals_CReal_of_DReal_scale [] ; + ClassicalDedekindReals_CReal_of_DReal_bound -> Qabs_Qabs_triangle_reverse [] ; + ClassicalDedekindReals_CReal_of_DReal_bound -> ConstructiveRcomplete_Qlt_trans_swap_hyp [] ; + ClassicalDedekindReals_CReal_of_DReal_bound -> ClassicalDedekindReals_CReal_of_DReal_seq_bound [] ; + ClassicalDedekindReals_CReal_of_DReal_bound -> QExtra_Qbound_lt_ZExp2_spec [] ; + _Pcond_simpl_complete -> _PFcons2_fcons_inv [] ; + _Pcond_simpl_complete -> _fcons_ok [] ; + ClassicalDedekindReals_CReal_of_DReal_scale -> Qabs_Qabs [] ; + ClassicalDedekindReals_CReal_of_DReal_scale -> ClassicalDedekindReals_CReal_of_DReal_seq [] ; + ClassicalDedekindReals_CReal_of_DReal_scale -> QExtra_Qbound_lt_ZExp2 [] ; + _F2AF -> _Rth_ARth [] ; + _F2AF -> _F_R [] ; + _F2AF -> _Finv_l [] ; + _F2AF -> _F_1_neq_0 [] ; + _F2AF -> _Fdiv_def [] ; + _F2AF -> _almost_field_theory [] ; + _F2AF -> _mk_afield [] ; + ClassicalDedekindReals_CReal_of_DReal_seq -> ClassicalDedekindReals_DRealQlimExp2 [] ; + ClassicalDedekindReals_CReal_of_DReal_seq -> Z_to_nat [] ; + ConstructiveCauchyReals_mkCReal -> ConstructiveCauchyReals_QCauchySeq [] ; + ConstructiveCauchyReals_mkCReal -> ConstructiveCauchyReals_QBound [] ; + _Finv_l -> _field_theory [] ; + _proj1_sig -> _sig [] ; + _F_1_neq_0 -> _field_theory [] ; + Nat_pow -> Nat_mul [] ; + _Fdiv_def -> _field_theory [] ; + _almost_field_theory -> _not [] ; + _almost_field_theory -> _almost_ring_theory [] ; + ClassicalDedekindReals_DRealQlimExp2 -> Nat_succ_pred_pos [] ; + ClassicalDedekindReals_DRealQlimExp2 -> ClassicalDedekindReals_DRealQlim [] ; + ClassicalDedekindReals_DRealQlimExp2 -> Nat_neq_0_lt_0 [] ; + ClassicalDedekindReals_DRealQlimExp2 -> Nat_pow_nonzero [] ; + _mk_afield -> _not [] ; + _mk_afield -> _almost_ring_theory [] ; + Z_to_nat -> _Z [] ; + Z_to_nat -> PosDef_Pos_to_nat [] ; + Pos_of_nat -> Pos_succ [] ; + Pos_of_nat -> _nat [] ; + _AF_AR -> _almost_field_theory [] ; + _AFinv_l -> _almost_field_theory [] ; + _PFcons2_fcons_inv -> _Fcons2 [] ; + _PFcons2_fcons_inv -> _PEsimp_ok [] ; + _PFcons2_fcons_inv -> _PFcons1_fcons_inv [] ; + _fcons_ok -> _eq [] ; + _fcons_ok -> _eq_refl [] ; + _fcons_ok -> _and_ind [] ; + _fcons_ok -> _conj [] ; + _fcons_ok -> _list_ind [] ; + _fcons_ok -> _PCond [] ; + _fcons_ok -> _Fapp [] ; + PosDef_Pos_to_nat -> _O [] ; + PosDef_Pos_to_nat -> PosDef_Pos_iter_op [] ; + PosDef_Pos_to_nat -> Init_Nat_add [] ; + Setoid_Seq_sym -> RelationClasses_Equivalence_Symmetric [] ; + Setoid_Seq_sym -> RelationClasses_symmetry [] ; + Setoid_Seq_sym -> Setoid_Setoid_Theory [] ; + PosDef_Pos_iter_op -> _positive [] ; + _ARopp_zero -> Morphisms_subrelation_proper [] ; + _ARopp_zero -> Morphisms_subrelation_refl [] ; + _ARopp_zero -> Morphisms_PER_morphism [] ; + _ARopp_zero -> RelationClasses_Equivalence_PER [] ; + _ARopp_zero -> Morphisms_iff_flip_impl_subrelation [] ; + _ARopp_zero -> Morphisms_subrelation_respectful [] ; + _ARopp_zero -> _tt [] ; + _ARopp_zero -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _ARopp_zero -> _ropp_ext2_Proper [] ; + _ARopp_zero -> _ARopp_mul_l [] ; + _ARopp_zero -> _ARmul_0_r [] ; + Init_Nat_add -> _S [] ; + Init_Nat_add -> _nat [] ; + Setoid_Seq_trans -> RelationClasses_Equivalence_Transitive [] ; + Setoid_Seq_trans -> RelationClasses_transitivity [] ; + Setoid_Seq_trans -> Setoid_Setoid_Theory [] ; + Nat_succ_pred_pos -> Nat_succ_pred [] ; + _AF_1_neq_0 -> _almost_field_theory [] ; + _PEsimp_ok -> _PEsimp [] ; + _PEsimp_ok -> _PEsub_ext [] ; + _PEsimp_ok -> _PEadd_ext [] ; + _PEsimp_ok -> _NPEadd_ok [] ; + _PEsimp_ok -> _NPEmul_ok [] ; + _PEsimp_ok -> _NPEopp_ok [] ; + _PEsimp_ok -> _NPEsub_ok [] ; + _PEsimp_ok -> _NPEequiv_eq [] ; + _PEsimp_ok -> _PEmul_ext [] ; + _PEsimp_ok -> _PEopp_ext [] ; + _PEsimp_ok -> _PEpow_ext [] ; + ClassicalDedekindReals_DRealQlim -> ClassicalDedekindReals_DReal [] ; + ClassicalDedekindReals_DRealQlim -> ClassicalDedekindReals_lowerCutAbove [] ; + ClassicalDedekindReals_DRealQlim -> ClassicalDedekindReals_DRealQlim_rec [] ; + ClassicalDedekindReals_DRealQlim -> Nat2Z_inj_mul [] ; + ClassicalDedekindReals_DRealQlim -> Pos_succ_of_nat [] ; + Nat_pred -> _nat [] ; + _PFcons1_fcons_inv -> Morphisms_per_partial_app_morphism [] ; + _PFcons1_fcons_inv -> _Fcons1 [] ; + _PFcons1_fcons_inv -> _ropp_neq_0 [] ; + _PFcons1_fcons_inv -> _PFcons0_fcons_inv [] ; + _PFcons1_fcons_inv -> _ceqb_spec_ [] ; + _PFcons1_fcons_inv -> _absurd_PCond_bottom [] ; + _PFcons1_fcons_inv -> _PEpow_nz [] ; + _Fcons1 -> _Fcons0 [] ; + _Fcons1 -> _absurd_PCond [] ; + _False_ind -> _False [] ; + _lt -> _le [] ; + _PEsimp -> _NPEadd [] ; + _PEsimp -> _NPEmul [] ; + _PEsimp -> _NPEopp [] ; + _PEsimp -> _NPEsub [] ; + _eq_ind -> _eq [] ; + _NPEadd -> _bool [] ; + _NPEadd -> Ring_polynom_PExpr [] ; + _NPEadd -> Ring_polynom_PEadd [] ; + _NPEadd -> Ring_polynom_PEc [] ; + Nat_neq_0_lt_0 -> Nat_lt_0_succ [] ; + Nat_neq_0_lt_0 -> Nat_case_analysis [] ; + _NPEmul -> Ring_polynom_PEmul [] ; + _NPEmul -> _NPEpow [] ; + _NPEmul -> N_eqb [] ; + Nat_pow_nonzero -> Nat_le_0_l [] ; + Nat_pow_nonzero -> Nat_Private_NZPow_pow_nonzero [] ; + _NPEopp -> Ring_polynom_PExpr [] ; + _NPEopp -> Ring_polynom_PEc [] ; + _NPEopp -> Ring_polynom_PEopp [] ; + _NPEpow -> _xH [] ; + _NPEpow -> _pow_pos [] ; + _NPEpow -> Ring_polynom_PExpr [] ; + _NPEpow -> Ring_polynom_PEc [] ; + _NPEpow -> Ring_polynom_PEpow [] ; + _NPEpow -> Pos_eqb [] ; + _NPEsub -> _bool [] ; + _NPEsub -> Ring_polynom_PExpr [] ; + _NPEsub -> Ring_polynom_PEsub [] ; + _NPEsub -> Ring_polynom_PEc [] ; + _NPEsub -> Ring_polynom_PEopp [] ; + N_eqb -> _N [] ; + N_eqb -> PosDef_Pos_eqb [] ; + _Fcons0 -> _O [] ; + _Fcons0 -> Ring_polynom_norm_subst [] ; + _Fcons0 -> _nil [] ; + _Fcons0 -> _cons [] ; + Nat_le_0_l -> Nat_le_le_succ_r [] ; + Nat_le_0_l -> Nat_le_succ_r [] ; + Nat_le_0_l -> Nat_eq_le_incl [] ; + Nat_le_0_l -> Nat_neq_succ_0 [] ; + _absurd_PCond -> Ring_polynom_PExpr [] ; + _absurd_PCond -> _list [] ; + _absurd_PCond -> _nil [] ; + _absurd_PCond -> _cons [] ; + _absurd_PCond -> Ring_polynom_PEc [] ; + Nat_Private_NZPow_pow_nonzero -> Nat_Private_NZPow_pow_eq_0 [] ; + _field_is_integral_domain -> Morphisms_reflexive_reflexive_proxy [] ; + _field_is_integral_domain -> Morphisms_Reflexive_partial_app_morphism [] ; + _field_is_integral_domain -> RelationClasses_Equivalence_PER [] ; + _field_is_integral_domain -> Morphisms_reflexive_proper_proxy [] ; + _field_is_integral_domain -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _field_is_integral_domain -> _ARmul_assoc [] ; + _field_is_integral_domain -> _ARmul_1_l [] ; + _field_is_integral_domain -> _ARmul_0_r [] ; + _field_is_integral_domain -> _AF_AR [] ; + _field_is_integral_domain -> _AFinv_l [] ; + _field_is_integral_domain -> Field_theory_rmul_ext_Proper [] ; + _ropp_neq_0 -> Morphisms_subrelation_proper [] ; + _ropp_neq_0 -> Morphisms_subrelation_refl [] ; + _ropp_neq_0 -> Morphisms_PER_morphism [] ; + _ropp_neq_0 -> Morphisms_iff_flip_impl_subrelation [] ; + _ropp_neq_0 -> Morphisms_subrelation_respectful [] ; + _ropp_neq_0 -> _tt [] ; + _ropp_neq_0 -> Morphisms_Prop_not_iff_morphism [] ; + _ropp_neq_0 -> SetoidTactics_default_relation [] ; + _ropp_neq_0 -> SetoidTactics_equivalence_default [] ; + _ropp_neq_0 -> Setoid_Seq_refl [] ; + _ropp_neq_0 -> _ARopp_mul_l [] ; + _ropp_neq_0 -> _field_is_integral_domain [] ; + _ropp_neq_0 -> Field_theory_ropp_ext_Proper [] ; + Nat_Private_NZPow_pow_eq_0 -> Nat_le_ind [] ; + Nat_Private_NZPow_pow_eq_0 -> Nat_lt_0_1 [] ; + Nat_Private_NZPow_pow_eq_0 -> Nat_lt_1_2 [] ; + Nat_Private_NZPow_pow_eq_0 -> Nat_eq_mul_0 [] ; + Nat_Private_NZPow_pow_eq_0 -> Nat_pow_wd [] ; + Nat_Private_NZPow_pow_eq_0 -> Nat_Private_OrderTac_Tac_not_neq_eq [] ; + Nat_Private_NZPow_pow_eq_0 -> Nat_pow_succ_r [] ; + Nat_Private_NZPow_pow_eq_0 -> Nat_pow_0_r [] ; + _le -> _S [] ; + _le -> _nat [] ; + _PFcons0_fcons_inv -> Morphisms_Prop_not_iff_morphism [] ; + _PFcons0_fcons_inv -> Morphisms_Prop_and_iff_morphism [] ; + _PFcons0_fcons_inv -> Ring_polynom_ring_correct [] ; + _PFcons0_fcons_inv -> _AF_AR [] ; + _PFcons0_fcons_inv -> _Fcons0 [] ; + _PFcons0_fcons_inv -> _PCond_cons [] ; + Nat_le_ind -> Nat_right_induction [] ; + _ceqb_spec_ -> _False_ind [] ; + _ceqb_spec_ -> _eq_ind [] ; + _ceqb_spec_ -> _True [] ; + _ceqb_spec_ -> _eq_refl [] ; + _ceqb_spec_ -> _I [] ; + _ceqb_spec_ -> _morph_eq [] ; + _ceqb_spec_ -> _reflect [] ; + _ceqb_spec_ -> _ReflectT [] ; + _ceqb_spec_ -> _ReflectF [] ; + Nat_lt_0_1 -> Morphisms_subrelation_proper [] ; + Nat_lt_0_1 -> Morphisms_subrelation_refl [] ; + Nat_lt_0_1 -> Morphisms_subrelation_respectful [] ; + Nat_lt_0_1 -> _tt [] ; + Nat_lt_0_1 -> Nat_lt_wd [] ; + Nat_lt_0_1 -> Nat_lt_succ_diag_r [] ; + Nat_lt_0_1 -> Nat_one_succ [] ; + _absurd_PCond_bottom -> _morph0 [] ; + _absurd_PCond_bottom -> _PCond [] ; + _absurd_PCond_bottom -> _absurd_PCond [] ; + Field_theory_ropp_ext_Proper -> _Ropp_ext [] ; + Nat_lt_1_2 -> Morphisms_subrelation_proper [] ; + Nat_lt_1_2 -> Morphisms_subrelation_refl [] ; + Nat_lt_1_2 -> Morphisms_subrelation_respectful [] ; + Nat_lt_1_2 -> _tt [] ; + Nat_lt_1_2 -> Nat_lt_wd [] ; + Nat_lt_1_2 -> Nat_lt_succ_diag_r [] ; + Nat_lt_1_2 -> Nat_two_succ [] ; + Nat_eq_equiv -> _nat [] ; + Nat_eq_equiv -> RelationClasses_eq_equivalence [] ; + _PEpow_nz -> Morphisms_subrelation_proper [] ; + _PEpow_nz -> Morphisms_subrelation_refl [] ; + _PEpow_nz -> Morphisms_PER_morphism [] ; + _PEpow_nz -> Morphisms_iff_flip_impl_subrelation [] ; + _PEpow_nz -> Morphisms_subrelation_respectful [] ; + _PEpow_nz -> _tt [] ; + _PEpow_nz -> Morphisms_Prop_not_iff_morphism [] ; + _PEpow_nz -> Ring_polynom_PEeval [] ; + _PEpow_nz -> _N0 [] ; + _PEpow_nz -> _Npos [] ; + _PEpow_nz -> _rpow_pow_N [] ; + _PEpow_nz -> Ring_polynom_PEpow [] ; + _PEpow_nz -> _AF_1_neq_0 [] ; + _PEpow_nz -> _pow_pos_nz [] ; + _pow_pos_nz -> _pow_pos [] ; + _pow_pos_nz -> _positive_ind [] ; + _pow_pos_nz -> _field_is_integral_domain [] ; + Nat_eq_mul_0 -> Nat_lt_neq [] ; + Nat_eq_mul_0 -> Nat_mul_neg_neg [] ; + Nat_eq_mul_0 -> Nat_mul_neg_pos [] ; + Nat_eq_mul_0 -> Nat_mul_pos_pos [] ; + _PCond_cons -> _I [] ; + _PCond_cons -> RelationClasses_reflexivity [] ; + _PCond_cons -> RelationClasses_iff_Reflexive [] ; + _PCond_cons -> _cons [] ; + _PCond_cons -> _PCond [] ; + Field_theory_rmul_ext_Proper -> _Rmul_ext [] ; + Nat_Private_OrderTac_Tac_eq_lt -> Nat_Private_OrderTac_Tac_trans [] ; + _PEsub_ext -> Ring_polynom_PEsub [] ; + _PEsub_ext -> _NPEeval_ext [] ; + _PEsub_ext -> Field_theory_rsub_ext_Proper [] ; + Morphisms_subrelation_proper -> Morphisms_Proper [] ; + Morphisms_subrelation_proper -> RelationClasses_subrelation [] ; + Morphisms_subrelation_proper -> Init_Unconvertible [] ; + _PEadd_ext -> Morphisms_reflexive_reflexive_proxy [] ; + _PEadd_ext -> Morphisms_Reflexive_partial_app_morphism [] ; + _PEadd_ext -> Morphisms_reflexive_proper_proxy [] ; + _PEadd_ext -> Ring_polynom_PEadd [] ; + _PEadd_ext -> _NPEeval_ext [] ; + _PEadd_ext -> Field_theory_radd_ext_Proper [] ; + Nat_pow_wd -> Morphisms_Proper [] ; + Nat_pow_wd -> PeanoNat_Nat_pow_wd_obligation_1 [] ; + _NPEadd_ok -> _ring_subst_niter [] ; + _NPEadd_ok -> _NPEadd [] ; + _NPEadd_ok -> _NPEequiv [] ; + _NPEadd_ok -> _ceqb_spec [] ; + _NPEadd_ok -> _Rring_ring_lemma1 [] ; + Nat_Private_OrderTac_Tac_lt_eq -> Nat_Private_OrderTac_Tac_trans [] ; + _NPEequiv -> Ring_polynom_PEeval [] ; + Morphisms_reflexive_reflexive_proxy -> RelationClasses_Reflexive [] ; + Morphisms_reflexive_reflexive_proxy -> Morphisms_ReflexiveProxy [] ; + _NPEmul_ok -> _NPEmul [] ; + _NPEmul_ok -> _NPEpow_ok [] ; + _NPEmul_ok -> _NPEeval_ext [] ; + _NPEmul_ok -> N_eqb_spec [] ; + _NPEmul_ok -> _pow_pos_mul_l [] ; + Morphisms_subrelation_refl -> RelationClasses_subrelation [] ; + _NPEopp_ok -> Ring_polynom_PEX [] ; + _NPEopp_ok -> Ring_polynom_PEadd [] ; + _NPEopp_ok -> Ring_polynom_PEsub [] ; + _NPEopp_ok -> Ring_polynom_PEmul [] ; + _NPEopp_ok -> Setoid_Seq_refl [] ; + _NPEopp_ok -> Ring_polynom_PEO [] ; + _NPEopp_ok -> Ring_polynom_PEI [] ; + _NPEopp_ok -> Ring_polynom_PEpow [] ; + _NPEopp_ok -> _morph_opp [] ; + _NPEopp_ok -> _NPEopp [] ; + _NPEopp_ok -> _NPEequiv [] ; + Nat_mul -> _O [] ; + Nat_mul -> Nat_add [] ; + _NPEpow_ok -> _NPEpow [] ; + _NPEpow_ok -> _NPEequiv [] ; + _NPEpow_ok -> _pow_N_ext [] ; + _NPEpow_ok -> _ceqb_spec [] ; + _NPEpow_ok -> Pos_eqb_spec [] ; + _NPEpow_ok -> _pow_pos_0 [] ; + _NPEpow_ok -> _pow_pos_1 [] ; + _NPEpow_ok -> _pow_pos_cst [] ; + Morphisms_Reflexive_partial_app_morphism -> Morphisms_Proper [] ; + Morphisms_Reflexive_partial_app_morphism -> Morphisms_respectful [] ; + Morphisms_Reflexive_partial_app_morphism -> Morphisms_ProperProxy [] ; + _NPEsub_ok -> _NPEsub [] ; + _NPEsub_ok -> _NPEequiv [] ; + _NPEsub_ok -> _ceqb_spec [] ; + _NPEsub_ok -> _rsub_0_l [] ; + _NPEsub_ok -> _rsub_0_r [] ; + _NPEsub_ok -> Field_theory_rsub_ext_Proper [] ; + Nat_Private_OrderTac_Tac_lt_irrefl -> RelationClasses_StrictOrder_Irreflexive [] ; + Nat_Private_OrderTac_Tac_lt_irrefl -> Nat_Private_OrderTac_IsTotal_lt_strorder [] ; + _NPEequiv_eq -> RelationClasses_Build_Equivalence [] ; + _NPEequiv_eq -> Setoid_Seq_refl [] ; + _NPEequiv_eq -> Setoid_Seq_sym [] ; + _NPEequiv_eq -> Setoid_Seq_trans [] ; + _NPEequiv_eq -> _NPEequiv [] ; + Nat_Private_OrderTac_Tac_eq_sym -> RelationClasses_Equivalence_Symmetric [] ; + Nat_Private_OrderTac_Tac_eq_sym -> Nat_Private_OrderTac_IsTotal_eq_equiv [] ; + Nat_Private_OrderTac_Tac_eq_sym -> RelationClasses_symmetry [] ; + _PEmul_ext -> Morphisms_reflexive_reflexive_proxy [] ; + _PEmul_ext -> Morphisms_Reflexive_partial_app_morphism [] ; + _PEmul_ext -> Morphisms_reflexive_proper_proxy [] ; + _PEmul_ext -> Ring_polynom_PEmul [] ; + _PEmul_ext -> Field_theory_rmul_ext_Proper [] ; + _PEmul_ext -> _NPEeval_ext [] ; + _iff -> _and [] ; + _PEopp_ext -> Morphisms_Reflexive_partial_app_morphism [] ; + _PEopp_ext -> Ring_polynom_PEopp [] ; + _PEopp_ext -> Field_theory_ropp_ext_Proper [] ; + _PEopp_ext -> _NPEeval_ext [] ; + Morphisms_Proper -> Relation_Definitions_relation [] ; + _PEpow_ext -> RelationClasses_Equivalence_PER [] ; + _PEpow_ext -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _PEpow_ext -> _rpow_pow_N [] ; + _PEpow_ext -> Ring_polynom_PEpow [] ; + _PEpow_ext -> _NPEequiv [] ; + _PEpow_ext -> _pow_N_ext [] ; + _pow_N_ext -> _N0 [] ; + _pow_N_ext -> _Npos [] ; + _pow_N_ext -> _pow_N [] ; + _pow_N_ext -> _pow_ext [] ; + Morphisms_PER_morphism -> Morphisms_Proper [] ; + Morphisms_PER_morphism -> Morphisms_PER_morphism_obligation_1 [] ; + Morphisms_respectful -> Relation_Definitions_relation [] ; + _pow_ext -> _pow_pos [] ; + _pow_ext -> _eq_ind [] ; + _pow_ext -> Morphisms_reflexive_reflexive_proxy [] ; + _pow_ext -> Morphisms_Reflexive_partial_app_morphism [] ; + _pow_ext -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _pow_ext -> Morphisms_eq_proper_proxy [] ; + _pow_ext -> Morphisms_reflexive_proper_proxy [] ; + _pow_ext -> RelationClasses_Equivalence_Transitive [] ; + _pow_ext -> _positive_ind [] ; + _pow_ext -> Setoid_Seq_refl [] ; + _pow_ext -> Field_theory_rmul_ext_Proper [] ; + Morphisms_trans_co_eq_inv_impl_morphism -> Morphisms_Proper [] ; + Morphisms_trans_co_eq_inv_impl_morphism -> Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 [] ; + _NPEeval_ext -> _eq_ind [] ; + _NPEeval_ext -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _NPEeval_ext -> Morphisms_eq_proper_proxy [] ; + _NPEeval_ext -> RelationClasses_Equivalence_Transitive [] ; + _NPEeval_ext -> Setoid_Seq_refl [] ; + _NPEeval_ext -> _NPEequiv [] ; + Nat_Private_OrderTac_Tac_not_neq_eq -> Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Nat_Private_OrderTac_Tac_not_neq_eq -> Nat_Private_OrderTac_IsTotal_lt_total [] ; + Nat_Private_OrderTac_Tac_not_neq_eq -> Nat_Private_OrderTac_IsTotal_lt_compat [] ; + Nat_Private_OrderTac_Tac_not_neq_eq -> Nat_Private_OrderTac_IsTotal_eq_equiv [] ; + _ceqb_spec -> _True [] ; + _ceqb_spec -> _eq_refl [] ; + _ceqb_spec -> _I [] ; + _ceqb_spec -> _BoolSpec [] ; + _ceqb_spec -> _BoolSpecT [] ; + _ceqb_spec -> _BoolSpecF [] ; + _ceqb_spec -> _morph_eq [] ; + _rsub_0_l -> _ring_subst_niter [] ; + _rsub_0_l -> _Rring_ring_lemma1 [] ; + RelationClasses_reflexivity -> RelationClasses_Reflexive [] ; + _rsub_0_r -> _ring_subst_niter [] ; + _rsub_0_r -> _ARopp_zero [] ; + _rsub_0_r -> _Rring_ring_lemma1 [] ; + Morphisms_eq_proper_proxy -> _eq [] ; + Morphisms_eq_proper_proxy -> _eq_refl [] ; + Morphisms_eq_proper_proxy -> Morphisms_ProperProxy [] ; + Field_theory_rsub_ext_Proper -> _ARsub_ext [] ; + Field_theory_rsub_ext_Proper -> _AF_AR [] ; + RelationClasses_iff_Transitive -> RelationClasses_Transitive [] ; + RelationClasses_iff_Transitive -> _iff_trans [] ; + _Rring_ring_lemma1 -> Ring_polynom_ring_correct [] ; + _Rring_ring_lemma1 -> Setoid_Build_Setoid_Theory [] ; + _Rring_ring_lemma1 -> Morphisms_proper_prf [] ; + _Rring_ring_lemma1 -> _pow_N_th [] ; + _Rring_ring_lemma1 -> _AF_AR [] ; + _Rring_ring_lemma1 -> Field_theory_rmul_ext_Proper [] ; + _Rring_ring_lemma1 -> Field_theory_radd_ext_Proper [] ; + _Rring_ring_lemma1 -> _gen_phiN_morph [] ; + _Rring_ring_lemma1 -> _ARth_SRth [] ; + _Rring_ring_lemma1 -> _Ntriv_div_th [] ; + _Rring_ring_lemma1 -> _mk_seqe [] ; + RelationClasses_Equivalence_PER -> RelationClasses_Equivalence_Transitive [] ; + RelationClasses_Equivalence_PER -> RelationClasses_Equivalence_Symmetric [] ; + RelationClasses_Equivalence_PER -> RelationClasses_PER [] ; + RelationClasses_Equivalence_PER -> RelationClasses_Build_PER [] ; + Field_theory_radd_ext_Proper -> _Radd_ext [] ; + RelationClasses_iff_Reflexive -> RelationClasses_Reflexive [] ; + RelationClasses_iff_Reflexive -> _iff_refl [] ; + Morphisms_iff_flip_impl_subrelation -> Basics_flip [] ; + Morphisms_iff_flip_impl_subrelation -> Basics_impl [] ; + Morphisms_iff_flip_impl_subrelation -> _iff [] ; + Morphisms_iff_flip_impl_subrelation -> RelationClasses_subrelation [] ; + Morphisms_iff_flip_impl_subrelation -> _and_ind [] ; + N_div_eucl -> N_pos_div_eucl [] ; + Morphisms_reflexive_proper_proxy -> Morphisms_ReflexiveProxy [] ; + Morphisms_reflexive_proper_proxy -> Morphisms_ProperProxy [] ; + _Nopp -> _N [] ; + _Nopp -> _SRopp [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism -> Morphisms_Proper [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism -> Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 [] ; + _Nsub -> N_add [] ; + _Nsub -> _SRsub [] ; + Nat_pow_succ_r -> _eq [] ; + Nat_pow_succ_r -> Nat_pow [] ; + Nat_pow_succ_r -> _eq_refl [] ; + Nat_pow_succ_r -> _le [] ; + _SRsub -> _SRopp [] ; + Nat_pow_0_r -> _eq [] ; + Nat_pow_0_r -> Nat_pow [] ; + Nat_pow_0_r -> _eq_refl [] ; + _gen_phiN_morph -> _ring_morph [] ; + _gen_phiN_morph -> _mkmorph [] ; + _gen_phiN_morph -> _Nopp [] ; + _gen_phiN_morph -> _gen_phiN_sub [] ; + _gen_phiN_morph -> N_eqb_eq [] ; + _gen_phiN_morph -> _gen_phiN_mult [] ; + RelationClasses_Equivalence_Reflexive -> RelationClasses_Equivalence [] ; + Morphisms_subrelation_respectful -> Morphisms_respectful [] ; + Morphisms_subrelation_respectful -> RelationClasses_subrelation [] ; + _gen_phiN -> _N [] ; + _gen_phiN -> _gen_phiPOS [] ; + _SRth_ARth -> _almost_ring_theory [] ; + _SRth_ARth -> _mk_art [] ; + _SRth_ARth -> _SRmul_0_l [] ; + _SRth_ARth -> _SRmul_1_l [] ; + _SRth_ARth -> _SRopp_add [] ; + _SRth_ARth -> _SRopp_mul_l [] ; + _SRth_ARth -> _SRadd_assoc [] ; + _SRth_ARth -> _SRsub_def [] ; + _SRth_ARth -> _SRadd_0_l [] ; + _SRth_ARth -> _SRmul_assoc [] ; + _SRth_ARth -> _SRdistr_l [] ; + _SRth_ARth -> _SRmul_comm [] ; + _SRth_ARth -> _SRadd_comm [] ; + _ARth_SRth -> _almost_ring_theory [] ; + _ARth_SRth -> _semi_ring_theory [] ; + _ARth_SRth -> _mk_srt [] ; + RelationClasses_subrelation -> Relation_Definitions_relation [] ; + _SReqe_Reqe -> _ring_eq_ext [] ; + _SReqe_Reqe -> _mk_reqe [] ; + _SReqe_Reqe -> _SRmul_ext [] ; + _SReqe_Reqe -> _SRopp_ext [] ; + _SReqe_Reqe -> _SRadd_ext [] ; + RelationClasses_Reflexive -> Relation_Definitions_relation [] ; + _Ntriv_div_th -> _div_theory [] ; + _Ntriv_div_th -> Setoid_Seq_refl [] ; + _Ntriv_div_th -> _mkdiv_th [] ; + _Ntriv_div_th -> N_div_eucl_spec [] ; + _mk_seqe -> Morphisms_Proper [] ; + _mk_seqe -> Morphisms_respectful [] ; + RelationClasses_Equivalence -> RelationClasses_Reflexive [] ; + RelationClasses_Equivalence -> RelationClasses_Symmetric [] ; + RelationClasses_Equivalence -> RelationClasses_Transitive [] ; + N_mul_comm -> N_mul_0_r [] ; + N_mul_comm -> N_mul_succ_r [] ; + RelationClasses_Symmetric -> Relation_Definitions_relation [] ; + N_div_eucl_spec -> N_pos_div_eucl_spec [] ; + N_div_eucl_spec -> N_div_eucl [] ; + N_div_eucl_spec -> N_mul_comm [] ; + RelationClasses_Transitive -> Relation_Definitions_relation [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> Basics_impl [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> _iff [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> _and_ind [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> _conj [] ; + N_add_cancel_r -> N_add_comm [] ; + N_add_cancel_r -> N_add_cancel_l [] ; + N_mul_0_l -> _eq [] ; + N_mul_0_l -> _eq_refl [] ; + N_mul_0_l -> N_mul [] ; + _and_ind -> _and [] ; + N_mul_0_r -> N_add_0_r [] ; + N_mul_0_r -> N_mul_0_l [] ; + N_mul_0_r -> N_mul_wd [] ; + N_mul_0_r -> N_mul_succ_l [] ; + N_mul_wd -> Morphisms_reflexive_reflexive_proxy [] ; + N_mul_wd -> RelationClasses_eq_Reflexive [] ; + N_mul_wd -> Morphisms_reflexive_proper [] ; + N_mul_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + N_mul_wd -> N_mul [] ; + N_mul_wd -> N_eq [] ; + Morphisms_ReflexiveProxy -> Relation_Definitions_relation [] ; + N_mul_succ_l -> PosDef_Pos_mul [] ; + N_mul_succ_l -> N_mul [] ; + N_mul_succ_l -> Pos_mul_succ_l [] ; + N_mul_succ_l -> N_add [] ; + N_mul_succ_l -> N_succ [] ; + Morphisms_ProperProxy -> Relation_Definitions_relation [] ; + N_mul_succ_r -> N_add_assoc [] ; + N_mul_succ_r -> N_add_cancel_r [] ; + N_mul_succ_r -> N_mul_0_l [] ; + N_mul_succ_r -> N_mul_wd [] ; + N_mul_succ_r -> N_mul_succ_l [] ; + _iff_refl -> _iff [] ; + _iff_refl -> _conj [] ; + N_add_cancel_l -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + N_add_cancel_l -> RelationClasses_reflexivity [] ; + N_add_cancel_l -> Morphisms_eq_proper_proxy [] ; + N_add_cancel_l -> RelationClasses_iff_equivalence [] ; + N_add_cancel_l -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + N_add_cancel_l -> Morphisms_per_partial_app_morphism [] ; + N_add_cancel_l -> N_bi_induction [] ; + N_add_cancel_l -> N_add_wd [] ; + N_add_cancel_l -> N_succ_inj_wd [] ; + N_add_cancel_l -> N_add_succ_l [] ; + N_add_cancel_l -> N_add_0_l [] ; + RelationClasses_Equivalence_Transitive -> RelationClasses_Equivalence [] ; + _SRmul_ext -> _sring_eq_ext [] ; + RelationClasses_Equivalence_Symmetric -> RelationClasses_Equivalence [] ; + RelationClasses_PER -> RelationClasses_Symmetric [] ; + RelationClasses_PER -> RelationClasses_Transitive [] ; + _SRopp_ext -> _SRopp [] ; + RelationClasses_Build_PER -> RelationClasses_Symmetric [] ; + RelationClasses_Build_PER -> RelationClasses_Transitive [] ; + _SRadd_ext -> _sring_eq_ext [] ; + _sring_eq_ext -> Morphisms_Proper [] ; + _sring_eq_ext -> Morphisms_respectful [] ; + _iff_trans -> _iff [] ; + _iff_trans -> _conj [] ; + Nat_Private_OrderTac_IsTotal_lt_total -> Nat_lt_total [] ; + Nat_Private_OrderTac_IsTotal_lt_compat -> Nat_lt_compat [] ; + Nat_Private_OrderTac_IsTotal_eq_equiv -> Nat_eq_equiv [] ; + _SRmul_0_l -> _semi_ring_theory [] ; + Morphisms_iff_impl_subrelation -> Basics_impl [] ; + Morphisms_iff_impl_subrelation -> _iff [] ; + Morphisms_iff_impl_subrelation -> RelationClasses_subrelation [] ; + Morphisms_iff_impl_subrelation -> _and_ind [] ; + _SRmul_1_l -> _semi_ring_theory [] ; + Nat_lt_compat -> Nat_lt_wd [] ; + _SRopp_add -> RelationClasses_reflexivity [] ; + _SRopp_add -> RelationClasses_Equivalence_Reflexive [] ; + _SRopp_add -> _SRopp [] ; + Nat_lt_wd -> Morphisms_Proper [] ; + Nat_lt_wd -> PeanoNat_Nat_lt_wd_obligation_1 [] ; + _SRopp_mul_l -> RelationClasses_reflexivity [] ; + _SRopp_mul_l -> RelationClasses_Equivalence_Reflexive [] ; + _SRopp_mul_l -> _SRopp [] ; + PeanoNat_Nat_lt_wd_obligation_1 -> _lt [] ; + PeanoNat_Nat_lt_wd_obligation_1 -> _iff [] ; + PeanoNat_Nat_lt_wd_obligation_1 -> Morphisms_respectful [] ; + PeanoNat_Nat_lt_wd_obligation_1 -> _conj [] ; + PeanoNat_Nat_lt_wd_obligation_1 -> _eq_ind_r [] ; + _SRadd_assoc -> _semi_ring_theory [] ; + _eq_ind_r -> _eq_ind [] ; + _eq_ind_r -> _eq_sym [] ; + _SRsub_def -> RelationClasses_reflexivity [] ; + _SRsub_def -> RelationClasses_Equivalence_Reflexive [] ; + _SRsub_def -> _SRsub [] ; + _eq_sym -> _eq [] ; + _eq_sym -> _eq_refl [] ; + _SRadd_0_l -> _semi_ring_theory [] ; + Nat_lt_total -> Nat_lt_trichotomy [] ; + _SRmul_assoc -> _semi_ring_theory [] ; + Nat_lt_trichotomy -> Nat_le_gt_cases [] ; + _SRdistr_l -> _semi_ring_theory [] ; + _or_ind -> _or [] ; + _SRmul_comm -> _semi_ring_theory [] ; + Nat_le_gt_cases -> Nat_le_succ_l [] ; + _SRadd_comm -> _semi_ring_theory [] ; + Nat_lt_eq_cases -> Morphisms_reflexive_reflexive_proxy [] ; + Nat_lt_eq_cases -> Morphisms_Reflexive_partial_app_morphism [] ; + Nat_lt_eq_cases -> RelationClasses_Equivalence_PER [] ; + Nat_lt_eq_cases -> Morphisms_reflexive_proper_proxy [] ; + Nat_lt_eq_cases -> Morphisms_Prop_or_iff_morphism [] ; + Nat_lt_eq_cases -> RelationClasses_iff_equivalence [] ; + Nat_lt_eq_cases -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_lt_eq_cases -> Nat_compare_eq_iff [] ; + Nat_lt_eq_cases -> Nat_compare_le_iff [] ; + Nat_lt_eq_cases -> Nat_compare_lt_iff [] ; + _gen_phiN_add -> _ARadd_0_r [] ; + _gen_phiN_add -> N_add [] ; + _gen_phiN_add -> _ARgen_phiPOS_add [] ; + _gen_phiN_add -> _same_genN [] ; + _gen_phiN_add -> _R_setoid4_Transitive [] ; + _gen_phiN_add -> _radd_ext4_Proper [] ; + Morphisms_Prop_or_iff_morphism -> Morphisms_Proper [] ; + Morphisms_Prop_or_iff_morphism -> Morphisms_Prop_or_iff_morphism_obligation_1 [] ; + _gen_phiN_sub -> _Nsub [] ; + _gen_phiN_sub -> _gen_phiN_add [] ; + _R_setoid4_Reflexive -> RelationClasses_Equivalence_Reflexive [] ; + _R_setoid4_Reflexive -> Setoid_Setoid_Theory [] ; + N_eqb_eq -> _eq_ind_r [] ; + N_eqb_eq -> _N0 [] ; + N_eqb_eq -> _Npos [] ; + N_eqb_eq -> Pos_eqb_eq [] ; + N_eqb_eq -> N_eqb [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _iff [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _and_ind [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _conj [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _or_ind [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _or_introl [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _or_intror [] ; + _gen_phiN_mult -> N_mul [] ; + _gen_phiN_mult -> _ARmul_0_r [] ; + _gen_phiN_mult -> _ARgen_phiPOS_mult [] ; + _gen_phiN_mult -> _same_genN [] ; + _gen_phiN_mult -> _R_setoid4_Transitive [] ; + _gen_phiN_mult -> _rmul_ext4_Proper [] ; + RelationClasses_iff_equivalence -> RelationClasses_iff_Transitive [] ; + RelationClasses_iff_equivalence -> RelationClasses_iff_Reflexive [] ; + RelationClasses_iff_equivalence -> RelationClasses_Equivalence [] ; + RelationClasses_iff_equivalence -> RelationClasses_iff_Symmetric [] ; + RelationClasses_iff_equivalence -> RelationClasses_Build_Equivalence [] ; + _gen_phiN1 -> _N [] ; + _gen_phiN1 -> _gen_phiPOS1 [] ; + Morphisms_trans_sym_co_inv_impl_morphism -> Morphisms_Proper [] ; + Morphisms_trans_sym_co_inv_impl_morphism -> Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 [] ; + _R_setoid4 -> RelationClasses_Equivalence_Reflexive [] ; + _R_setoid4 -> RelationClasses_Equivalence_Transitive [] ; + _R_setoid4 -> RelationClasses_Equivalence_Symmetric [] ; + _R_setoid4 -> RelationClasses_Build_Equivalence [] ; + _R_setoid4 -> Setoid_Setoid_Theory [] ; + _same_genN -> RelationClasses_Equivalence_PER [] ; + _same_genN -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _same_genN -> _N0 [] ; + _same_genN -> _Npos [] ; + _same_genN -> _same_gen [] ; + _same_genN -> _gen_phiN [] ; + _same_genN -> _SRth_ARth [] ; + _same_genN -> _SReqe_Reqe [] ; + _same_genN -> _R_setoid4_Reflexive [] ; + _same_genN -> _gen_phiN1 [] ; + _same_genN -> _R_setoid4 [] ; + RelationClasses_iff_Symmetric -> RelationClasses_Symmetric [] ; + RelationClasses_iff_Symmetric -> _iff_sym [] ; + RelationClasses_symmetry -> RelationClasses_Symmetric [] ; + _R_setoid4_Transitive -> RelationClasses_Equivalence_Transitive [] ; + _R_setoid4_Transitive -> Setoid_Setoid_Theory [] ; + _rmul_ext4_Proper -> _Rmul_ext [] ; + _rmul_ext4_Proper -> _SReqe_Reqe [] ; + Nat_compare -> _comparison [] ; + Nat_compare -> _Eq [] ; + Nat_compare -> _Lt [] ; + Nat_compare -> _Gt [] ; + Nat_compare -> _nat [] ; + _radd_ext4_Proper -> _Radd_ext [] ; + _radd_ext4_Proper -> _SReqe_Reqe [] ; + Nat_compare_eq_iff -> _False_ind [] ; + Nat_compare_eq_iff -> _eq_ind [] ; + Nat_compare_eq_iff -> _True [] ; + Nat_compare_eq_iff -> _I [] ; + Nat_compare_eq_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_compare_eq_iff -> Morphisms_eq_proper_proxy [] ; + Nat_compare_eq_iff -> RelationClasses_iff_Transitive [] ; + Nat_compare_eq_iff -> Nat_compare [] ; + Nat_compare_eq_iff -> _nat_ind [] ; + Nat_compare_eq_iff -> _f_equal_nat [] ; + Nat_compare_eq_iff -> _eq_add_S [] ; + Pos_eqb_spec -> RelationClasses_iff_Symmetric [] ; + Pos_eqb_spec -> RelationClasses_symmetry [] ; + Pos_eqb_spec -> Pos_eqb_eq [] ; + Pos_eqb_spec -> Bool_iff_reflect [] ; + Nat_compare_le_iff -> _not [] ; + Nat_compare_le_iff -> _False_ind [] ; + Nat_compare_le_iff -> _eq_ind [] ; + Nat_compare_le_iff -> _True [] ; + Nat_compare_le_iff -> _I [] ; + Nat_compare_le_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_compare_le_iff -> Morphisms_eq_proper_proxy [] ; + Nat_compare_le_iff -> RelationClasses_iff_Transitive [] ; + Nat_compare_le_iff -> Nat_compare [] ; + Nat_compare_le_iff -> _le_0_n [] ; + Nat_compare_le_iff -> _le_S_n [] ; + Nat_compare_le_iff -> _le_n_S [] ; + _pow_pos_0 -> _pow_pos [] ; + _pow_pos_0 -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _pow_pos_0 -> Morphisms_eq_proper_proxy [] ; + _pow_pos_0 -> RelationClasses_Equivalence_Transitive [] ; + _pow_pos_0 -> _positive_ind [] ; + _pow_pos_0 -> Setoid_Seq_refl [] ; + _pow_pos_0 -> _ARmul_0_l [] ; + _pow_pos_0 -> _AF_AR [] ; + _pow_pos_0 -> Field_theory_rmul_ext_Proper [] ; + Nat_compare_lt_iff -> _False_ind [] ; + Nat_compare_lt_iff -> _lt [] ; + Nat_compare_lt_iff -> _eq_ind [] ; + Nat_compare_lt_iff -> _True [] ; + Nat_compare_lt_iff -> _I [] ; + Nat_compare_lt_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_compare_lt_iff -> Morphisms_eq_proper_proxy [] ; + Nat_compare_lt_iff -> RelationClasses_iff_Transitive [] ; + Nat_compare_lt_iff -> Nat_compare [] ; + Nat_compare_lt_iff -> _le_0_n [] ; + Nat_compare_lt_iff -> _le_S_n [] ; + Nat_compare_lt_iff -> _le_n_S [] ; + _pow_pos_1 -> _ring_subst_niter [] ; + _pow_pos_1 -> _Rring_ring_lemma1 [] ; + _nat_ind -> _O [] ; + _nat_ind -> _S [] ; + _nat_ind -> _nat [] ; + _pow_pos_cst -> _pow_pos [] ; + _pow_pos_cst -> Morphisms_reflexive_reflexive_proxy [] ; + _pow_pos_cst -> Morphisms_Reflexive_partial_app_morphism [] ; + _pow_pos_cst -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _pow_pos_cst -> Morphisms_eq_proper_proxy [] ; + _pow_pos_cst -> RelationClasses_Equivalence_PER [] ; + _pow_pos_cst -> Morphisms_reflexive_proper_proxy [] ; + _pow_pos_cst -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _pow_pos_cst -> _positive_ind [] ; + _pow_pos_cst -> Setoid_Seq_refl [] ; + _pow_pos_cst -> _morph_mul [] ; + _pow_pos_cst -> Field_theory_rmul_ext_Proper [] ; + _le_0_n -> _le [] ; + _le_0_n -> _nat_ind [] ; + _le_0_n -> _le_n [] ; + _le_0_n -> _le_S [] ; + _le_S_n -> _le_pred [] ; + N_eqb_spec -> RelationClasses_iff_Symmetric [] ; + N_eqb_spec -> RelationClasses_symmetry [] ; + N_eqb_spec -> Bool_iff_reflect [] ; + N_eqb_spec -> N_eqb_eq [] ; + _pow_pos_mul_l -> _ring_subst_niter [] ; + _pow_pos_mul_l -> _Rring_ring_lemma1 [] ; + _le_n_S -> _le_ind [] ; + _le_n_S -> _le_n [] ; + _le_n_S -> _le_S [] ; + _le_ind -> _le [] ; + QArith_base_Qinv_involutive -> QArith_base_Qinv [] ; + QArith_base_Qinv_involutive -> _eq_refl [] ; + QArith_base_Qinv_involutive -> QArith_base_Qeq [] ; + _le_n -> _S [] ; + _le_n -> _nat [] ; + _FExpr -> _N [] ; + _le_S -> _S [] ; + _le_S -> _nat [] ; + _Field_correct -> _Fnorm_crossproduct [] ; + _le_pred -> _O [] ; + _le_pred -> _le_ind [] ; + _le_pred -> _le_n [] ; + _le_pred -> _le_S [] ; + _le_pred -> Init_Nat_pred [] ; + _AFdiv_def -> _almost_field_theory [] ; + Init_Nat_pred -> _nat [] ; + _Fnorm_crossproduct -> _cross_product_eq [] ; + _Fnorm_crossproduct -> _Fnorm_FEeval_PEeval [] ; + _f_equal_nat -> _nat [] ; + _f_equal_nat -> _f_equal [] ; + _Pcond_Fnorm -> _Fnorm [] ; + _Pcond_Fnorm -> _PEpow_nz [] ; + _Pcond_Fnorm -> _PCond_app [] ; + _Pcond_Fnorm -> _FExpr_ind [] ; + _Pcond_Fnorm -> _split_nz_l [] ; + _Pcond_Fnorm -> _split_nz_r [] ; + _eq_add_S -> _S [] ; + _eq_add_S -> Init_Nat_pred [] ; + _eq_add_S -> _f_equal [] ; + _cross_product_eq -> _rdiv_ext [] ; + _cross_product_eq -> _rdiv4 [] ; + _cross_product_eq -> _rdiv_r_r [] ; + _f_equal -> _eq [] ; + _f_equal -> _eq_refl [] ; + _Fnorm_FEeval_PEeval -> _FEeval [] ; + _Fnorm_FEeval_PEeval -> _NPEadd_ok [] ; + _Fnorm_FEeval_PEeval -> _NPEopp_ok [] ; + _Fnorm_FEeval_PEeval -> _NPEsub_ok [] ; + _Fnorm_FEeval_PEeval -> _Pcond_Fnorm [] ; + _Fnorm_FEeval_PEeval -> _rdiv1 [] ; + _Fnorm_FEeval_PEeval -> _rdiv3b [] ; + _Fnorm_FEeval_PEeval -> _rdiv4b [] ; + _Fnorm_FEeval_PEeval -> _rdiv7b [] ; + _Fnorm_FEeval_PEeval -> _pow_pos_div [] ; + _iff_sym -> _iff [] ; + _iff_sym -> _conj [] ; + _PCond_app -> Morphisms_reflexive_reflexive_proxy [] ; + _PCond_app -> Morphisms_Reflexive_partial_app_morphism [] ; + _PCond_app -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _PCond_app -> Morphisms_eq_proper_proxy [] ; + _PCond_app -> RelationClasses_Equivalence_PER [] ; + _PCond_app -> Morphisms_reflexive_proper_proxy [] ; + _PCond_app -> RelationClasses_iff_equivalence [] ; + _PCond_app -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _PCond_app -> Morphisms_Prop_and_iff_morphism [] ; + _PCond_app -> _list_ind [] ; + _PCond_app -> _app [] ; + _PCond_app -> _PCond_cons [] ; + _PCond_app -> _and_assoc [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Basics_flip [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Basics_impl [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> RelationClasses_symmetry [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> RelationClasses_PER_Symmetric [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> RelationClasses_PER_Transitive [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> RelationClasses_transitivity [] ; + _and_assoc -> _iff [] ; + _and_assoc -> _conj [] ; + _rdiv1 -> _AF_1_neq_0 [] ; + _rdiv1 -> _rdiv_simpl [] ; + RelationClasses_PER_Symmetric -> RelationClasses_PER [] ; + _rdiv5 -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _rdiv5 -> Morphisms_eq_proper_proxy [] ; + _rdiv5 -> RelationClasses_Equivalence_PER [] ; + _rdiv5 -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _rdiv5 -> Setoid_Seq_refl [] ; + _rdiv5 -> _ARopp_mul_l [] ; + _rdiv5 -> _AF_AR [] ; + _rdiv5 -> Field_theory_ropp_ext_Proper [] ; + _rdiv5 -> _AFdiv_def [] ; + RelationClasses_PER_Transitive -> RelationClasses_PER [] ; + RelationClasses_transitivity -> RelationClasses_Transitive [] ; + _rdiv6 -> _rmul_reg_l [] ; + RelationClasses_Build_Equivalence -> RelationClasses_Reflexive [] ; + RelationClasses_Build_Equivalence -> RelationClasses_Symmetric [] ; + RelationClasses_Build_Equivalence -> RelationClasses_Transitive [] ; + _split -> _split_aux [] ; + Nat_lt_succ_r -> _lt [] ; + Nat_lt_succ_r -> _iff [] ; + Nat_lt_succ_r -> _conj [] ; + Nat_lt_succ_r -> _le_S_n [] ; + _FExpr_ind -> _FEX [] ; + _FExpr_ind -> _FEmul [] ; + _FExpr_ind -> _FEinv [] ; + _FExpr_ind -> _FEdiv [] ; + _FExpr_ind -> _FEc [] ; + _FExpr_ind -> _FExpr [] ; + _FExpr_ind -> _FEO [] ; + _FExpr_ind -> _FEI [] ; + _FExpr_ind -> _FEadd [] ; + _FExpr_ind -> _FEsub [] ; + _FExpr_ind -> _FEopp [] ; + _FExpr_ind -> _FEpow [] ; + _rdiv2b -> _field_is_integral_domain [] ; + _rdiv2b -> _rmul_reg_l [] ; + _rdiv2b -> Field_theory_radd_ext [] ; + Nat_le_succ_l -> Nat_central_induction [] ; + Nat_le_succ_l -> Nat_le_wd [] ; + Nat_le_succ_l -> Nat_succ_inj_wd [] ; + Nat_le_succ_l -> Morphisms_per_partial_app_morphism [] ; + Nat_le_succ_l -> Nat_nle_succ_diag_l [] ; + Nat_le_succ_l -> _or_cancel_r [] ; + _rdiv3b -> _rdiv5 [] ; + _rdiv3b -> _rdiv2b [] ; + _rdiv3b -> _rdiv_ext [] ; + Nat_central_induction -> Morphisms_reflexive_reflexive_proxy [] ; + Nat_central_induction -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_central_induction -> RelationClasses_reflexivity [] ; + Nat_central_induction -> Morphisms_eq_proper_proxy [] ; + Nat_central_induction -> RelationClasses_iff_Transitive [] ; + Nat_central_induction -> RelationClasses_iff_Reflexive [] ; + Nat_central_induction -> Morphisms_reflexive_proper_proxy [] ; + Nat_central_induction -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + Nat_central_induction -> Nat_bi_induction [] ; + _rdiv4b -> _rdiv_ext [] ; + _rdiv4b -> _rdiv4 [] ; + _rdiv4b -> _rdiv_r_r [] ; + Nat_le_refl -> Nat_eq_equiv [] ; + Nat_le_refl -> RelationClasses_reflexivity [] ; + Nat_le_refl -> RelationClasses_Equivalence_Reflexive [] ; + Nat_le_refl -> Nat_lt_eq_cases [] ; + _rdiv7b -> _rdiv_ext [] ; + _rdiv7b -> _rdiv7 [] ; + _rdiv7b -> _rdiv_r_r [] ; + Nat_le_wd -> Nat_eq_equiv [] ; + Nat_le_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Nat_le_wd -> Morphisms_Reflexive_partial_app_morphism [] ; + Nat_le_wd -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_le_wd -> RelationClasses_reflexivity [] ; + Nat_le_wd -> Morphisms_eq_proper_proxy [] ; + Nat_le_wd -> RelationClasses_Equivalence_PER [] ; + Nat_le_wd -> Morphisms_reflexive_proper_proxy [] ; + Nat_le_wd -> RelationClasses_Equivalence_Reflexive [] ; + Nat_le_wd -> Nat_lt_wd [] ; + Nat_le_wd -> RelationClasses_iff_equivalence [] ; + Nat_le_wd -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_le_wd -> Nat_lt_succ_r [] ; + Nat_le_wd -> Nat_succ_wd [] ; + Nat_succ_wd -> Morphisms_Proper [] ; + Nat_succ_wd -> PeanoNat_Nat_succ_wd_obligation_1 [] ; + _rsplit_common -> _rsplit [] ; + PeanoNat_Nat_succ_wd_obligation_1 -> _S [] ; + PeanoNat_Nat_succ_wd_obligation_1 -> _nat [] ; + PeanoNat_Nat_succ_wd_obligation_1 -> Morphisms_respectful [] ; + PeanoNat_Nat_succ_wd_obligation_1 -> _eq_ind_r [] ; + _rdiv_ext -> Morphisms_reflexive_reflexive_proxy [] ; + _rdiv_ext -> Morphisms_Reflexive_partial_app_morphism [] ; + _rdiv_ext -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _rdiv_ext -> Morphisms_eq_proper_proxy [] ; + _rdiv_ext -> RelationClasses_Equivalence_PER [] ; + _rdiv_ext -> Morphisms_reflexive_proper_proxy [] ; + _rdiv_ext -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _rdiv_ext -> Setoid_Seq_refl [] ; + _rdiv_ext -> Field_theory_rmul_ext_Proper [] ; + _rdiv_ext -> _AFdiv_def [] ; + _rdiv_ext -> _rinv_ext_Proper [] ; + _rinv_ext_Proper -> Morphisms_Proper [] ; + _rinv_ext_Proper -> Morphisms_respectful [] ; + Nat_bi_induction -> _eq [] ; + Nat_bi_induction -> _iff [] ; + Nat_bi_induction -> Morphisms_Proper [] ; + Nat_bi_induction -> Morphisms_respectful [] ; + Nat_bi_induction -> _nat_ind [] ; + _split_ok_l -> _split [] ; + _split_ok_l -> _split_aux_ok [] ; + Nat_lt_irrefl -> Morphisms_subrelation_proper [] ; + Nat_lt_irrefl -> Morphisms_subrelation_refl [] ; + Nat_lt_irrefl -> Morphisms_iff_flip_impl_subrelation [] ; + Nat_lt_irrefl -> Morphisms_subrelation_respectful [] ; + Nat_lt_irrefl -> _tt [] ; + Nat_lt_irrefl -> _eq_ind_r [] ; + Nat_lt_irrefl -> RelationClasses_iff_Symmetric [] ; + Nat_lt_irrefl -> RelationClasses_symmetry [] ; + Nat_lt_irrefl -> Nat_compare_lt_iff [] ; + Nat_lt_irrefl -> Nat_compare_refl [] ; + Nat_lt_irrefl -> Morphisms_Prop_not_iff_morphism [] ; + Nat_succ_inj_wd -> Nat_succ_wd [] ; + Nat_succ_inj_wd -> Nat_succ_inj [] ; + _split_ok_r -> _split [] ; + _split_ok_r -> _split_aux_ok [] ; + _rsplit_right -> _rsplit [] ; + Morphisms_per_partial_app_morphism -> Morphisms_Proper [] ; + Morphisms_per_partial_app_morphism -> Morphisms_per_partial_app_morphism_obligation_1 [] ; + _rsplit_left -> _rsplit [] ; + Nat_nle_succ_diag_l -> Morphisms_iff_impl_subrelation [] ; + Nat_nle_succ_diag_l -> Nat_neq_succ_diag_l [] ; + Nat_nle_succ_diag_l -> Nat_nlt_succ_diag_l [] ; + _pow_pos_div -> _pow_pos_nz [] ; + _pow_pos_div -> _rdiv4 [] ; + _or_cancel_r -> _not [] ; + _or_cancel_r -> _or_iff_compat_r [] ; + _FEO -> _N [] ; + _or_iff_compat_r -> _or [] ; + _or_iff_compat_r -> _iff [] ; + _or_iff_compat_r -> _conj [] ; + _or_iff_compat_r -> _or_introl [] ; + _or_iff_compat_r -> _or_intror [] ; + _FEI -> _N [] ; + Nat_neq_succ_diag_l -> Nat_lt_wd [] ; + Nat_neq_succ_diag_l -> Nat_lt_irrefl [] ; + Nat_neq_succ_diag_l -> Nat_lt_succ_diag_r [] ; + _FEadd -> _N [] ; + Nat_nlt_succ_diag_l -> Nat_lt_succ_r [] ; + Nat_nlt_succ_diag_l -> Nat_lt_irrefl [] ; + Nat_nlt_succ_diag_l -> Nat_lt_le_incl [] ; + _FEsub -> _N [] ; + Nat_lt_le_incl -> Nat_lt_eq_cases [] ; + _FEopp -> _N [] ; + Nat_lt_succ_diag_r -> Morphisms_iff_flip_impl_subrelation [] ; + Nat_lt_succ_diag_r -> Nat_lt_succ_r [] ; + Nat_lt_succ_diag_r -> Nat_le_refl [] ; + _FEpow -> _N [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> _iff [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> _conj [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> RelationClasses_symmetry [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> RelationClasses_PER_Symmetric [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> RelationClasses_PER_Transitive [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> RelationClasses_transitivity [] ; + Nat_succ_inj -> Nat_eq_equiv [] ; + Nat_succ_inj -> Morphisms_subrelation_proper [] ; + Nat_succ_inj -> Morphisms_reflexive_reflexive_proxy [] ; + Nat_succ_inj -> Morphisms_subrelation_refl [] ; + Nat_succ_inj -> Morphisms_PER_morphism [] ; + Nat_succ_inj -> RelationClasses_Equivalence_PER [] ; + Nat_succ_inj -> Morphisms_reflexive_proper_proxy [] ; + Nat_succ_inj -> RelationClasses_Equivalence_Reflexive [] ; + Nat_succ_inj -> Morphisms_subrelation_respectful [] ; + Nat_succ_inj -> _tt [] ; + Nat_succ_inj -> Morphisms_iff_impl_subrelation [] ; + Nat_succ_inj -> Morphisms_trans_co_impl_morphism [] ; + Nat_succ_inj -> Nat_pred_succ [] ; + Nat_succ_inj -> Nat_pred_wd [] ; + _rdiv4 -> _field_is_integral_domain [] ; + _rdiv4 -> _rmul_reg_l [] ; + Morphisms_trans_co_impl_morphism -> Morphisms_Proper [] ; + Morphisms_trans_co_impl_morphism -> Morphisms_trans_co_impl_morphism_obligation_1 [] ; + _rmul_reg_l -> _rdiv_simpl [] ; + _rdiv_simpl -> _ring_subst_niter [] ; + _rdiv_simpl -> _AFinv_l [] ; + _rdiv_simpl -> _Rring_ring_lemma1 [] ; + _rdiv_simpl -> _AFdiv_def [] ; + Nat_pred_succ -> _eq [] ; + Nat_pred_succ -> _S [] ; + Nat_pred_succ -> Nat_pred [] ; + Nat_pred_succ -> _eq_refl [] ; + _rsplit -> Ring_polynom_PExpr [] ; + Nat_pred_wd -> Morphisms_Proper [] ; + Nat_pred_wd -> PeanoNat_Nat_pred_wd_obligation_1 [] ; + _split_aux -> Pos_sub [] ; + _split_aux -> _rsplit_common [] ; + _split_aux -> _rsplit_right [] ; + _split_aux -> _rsplit_left [] ; + _split_aux -> _mk_rsplit [] ; + _split_aux -> _isIn [] ; + PeanoNat_Nat_pred_wd_obligation_1 -> Nat_pred [] ; + PeanoNat_Nat_pred_wd_obligation_1 -> Morphisms_respectful [] ; + PeanoNat_Nat_pred_wd_obligation_1 -> _eq_ind_r [] ; + Morphisms_trans_co_impl_morphism_obligation_1 -> Basics_impl [] ; + Morphisms_trans_co_impl_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_trans_co_impl_morphism_obligation_1 -> RelationClasses_transitivity [] ; + _split_aux_ok -> _split_aux [] ; + _split_aux_ok -> _split_aux_ok1 [] ; + _split_aux_ok -> _PEpow_0_r [] ; + _split_aux_ok -> _PEpow_1_l [] ; + Nat_compare_refl -> Nat_eq_equiv [] ; + Nat_compare_refl -> RelationClasses_reflexivity [] ; + Nat_compare_refl -> RelationClasses_Equivalence_Reflexive [] ; + Nat_compare_refl -> Nat_compare_eq_iff [] ; + _PE_1_r -> Morphisms_reflexive_reflexive_proxy [] ; + _PE_1_r -> Morphisms_Reflexive_partial_app_morphism [] ; + _PE_1_r -> Morphisms_reflexive_proper_proxy [] ; + _PE_1_r -> Ring_polynom_PEmul [] ; + _PE_1_r -> _morph1 [] ; + _PE_1_r -> Ring_polynom_PEc [] ; + _PE_1_r -> _ARmul_1_r [] ; + _PE_1_r -> _AF_AR [] ; + _PE_1_r -> Field_theory_rmul_ext_Proper [] ; + _PE_1_r -> _NPEequiv [] ; + _split_aux_ok1 -> Z_gt_lt [] ; + _split_aux_ok1 -> _rsplit_common [] ; + _split_aux_ok1 -> _rsplit_right [] ; + _split_aux_ok1 -> _rsplit_left [] ; + _split_aux_ok1 -> _mk_rsplit [] ; + _split_aux_ok1 -> _PE_1_l [] ; + _split_aux_ok1 -> _isIn_ok [] ; + _split_aux_ok1 -> _PEpow_1_r [] ; + Morphisms_Prop_not_iff_morphism -> Morphisms_Proper [] ; + Morphisms_Prop_not_iff_morphism -> Morphisms_Prop_not_iff_morphism_obligation_1 [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> _not [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> _False_ind [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> _iff [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> _and_ind [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> _conj [] ; + _PEpow_mul_l -> _NPEequiv [] ; + _PEpow_mul_l -> _pow_pos_mul_l [] ; + Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> _eq [] ; + Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Basics_flip [] ; + Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Basics_impl [] ; + Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> RelationClasses_transitivity [] ; + _PEpow_mul_r -> _NPEequiv [] ; + _PEpow_mul_r -> _pow_N_ext [] ; + _PEpow_mul_r -> _pow_pos_1 [] ; + _PEpow_mul_r -> _pow_pos_mul_r [] ; + _PEpow_0_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _PEpow_0_r -> Morphisms_eq_proper_proxy [] ; + _PEpow_0_r -> RelationClasses_Equivalence_Transitive [] ; + _PEpow_0_r -> RelationClasses_Equivalence_Symmetric [] ; + _PEpow_0_r -> RelationClasses_symmetry [] ; + _PEpow_0_r -> _N0 [] ; + _PEpow_0_r -> _morph1 [] ; + _PEpow_0_r -> _rpow_pow_N [] ; + _PEpow_0_r -> Ring_polynom_PEc [] ; + _PEpow_0_r -> Ring_polynom_PEpow [] ; + _PEpow_0_r -> _NPEequiv [] ; + Morphisms_PER_morphism_obligation_1 -> _iff [] ; + Morphisms_PER_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_PER_morphism_obligation_1 -> _conj [] ; + Morphisms_PER_morphism_obligation_1 -> RelationClasses_symmetry [] ; + Morphisms_PER_morphism_obligation_1 -> RelationClasses_PER_Symmetric [] ; + Morphisms_PER_morphism_obligation_1 -> RelationClasses_PER_Transitive [] ; + Morphisms_PER_morphism_obligation_1 -> RelationClasses_transitivity [] ; + RelationClasses_StrictOrder_Irreflexive -> RelationClasses_StrictOrder [] ; + _PEpow_1_l -> _NPEequiv [] ; + _PEpow_1_l -> _pow_ext [] ; + _PEpow_1_l -> _pow_pos_1 [] ; + _mk_rsplit -> Ring_polynom_PExpr [] ; + Nat_Private_OrderTac_IsTotal_lt_strorder -> Nat_lt_strorder [] ; + _pow_pos_mul_r -> _pow_pos_mul_l [] ; + _pow_pos_mul_r -> _pow_pos_add_r [] ; + Nat_lt_strorder -> RelationClasses_StrictOrder [] ; + Nat_lt_strorder -> Nat_lt_trans [] ; + Nat_lt_strorder -> RelationClasses_Build_StrictOrder [] ; + RelationClasses_StrictOrder -> RelationClasses_Transitive [] ; + RelationClasses_StrictOrder -> RelationClasses_Irreflexive [] ; + _pow_pos_add_r -> _ARmul_assoc [] ; + _pow_pos_add_r -> _pow_pos_add [] ; + _pow_pos_add_r -> _AF_AR [] ; + _pow_pos_add_r -> Field_theory_rmul_ext [] ; + Field_theory_rmul_ext -> Morphisms_proper_prf [] ; + Field_theory_rmul_ext -> Field_theory_rmul_ext_Proper [] ; + RelationClasses_Irreflexive -> RelationClasses_Reflexive [] ; + RelationClasses_Irreflexive -> RelationClasses_complement [] ; + RelationClasses_complement -> _False [] ; + RelationClasses_complement -> Relation_Definitions_relation [] ; + _PE_1_l -> Morphisms_reflexive_reflexive_proxy [] ; + _PE_1_l -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _PE_1_l -> Morphisms_eq_proper_proxy [] ; + _PE_1_l -> Morphisms_reflexive_proper_proxy [] ; + _PE_1_l -> RelationClasses_Equivalence_Reflexive [] ; + _PE_1_l -> RelationClasses_Equivalence_Transitive [] ; + _PE_1_l -> Ring_polynom_PEmul [] ; + _PE_1_l -> _morph1 [] ; + _PE_1_l -> Ring_polynom_PEc [] ; + _PE_1_l -> _ARmul_1_l [] ; + _PE_1_l -> _AF_AR [] ; + _PE_1_l -> Field_theory_rmul_ext_Proper [] ; + _PE_1_l -> _NPEequiv [] ; + Nat_lt_trans -> Morphisms_impl_pars [] ; + Nat_lt_trans -> Nat_lt_asymm [] ; + _Z_pos_sub_gt -> Pos_gt_lt [] ; + _Z_pos_sub_gt -> Z_pos_sub_gt [] ; + RelationClasses_Build_StrictOrder -> RelationClasses_Transitive [] ; + RelationClasses_Build_StrictOrder -> RelationClasses_Irreflexive [] ; + _PEpow_add_r -> _N0 [] ; + _PEpow_add_r -> Ring_polynom_PEmul [] ; + _PEpow_add_r -> _rpow_pow_N [] ; + _PEpow_add_r -> Setoid_Seq_refl [] ; + _PEpow_add_r -> Ring_polynom_PEpow [] ; + _PEpow_add_r -> _ARmul_1_r [] ; + _PEpow_add_r -> N_add [] ; + _PEpow_add_r -> _NPEequiv [] ; + _PEpow_add_r -> _pow_pos_add_r [] ; + _isIn_ok -> Z_lt_trans [] ; + _isIn_ok -> _NPEmul_ok [] ; + _isIn_ok -> _PEpow_mul_l [] ; + _isIn_ok -> _PEpow_mul_r [] ; + _isIn_ok -> _Z_pos_sub_gt [] ; + _isIn_ok -> _isIn [] ; + _isIn_ok -> _default_isIn_ok [] ; + Morphisms_impl_pars -> _O [] ; + Morphisms_impl_pars -> Basics_impl [] ; + Morphisms_impl_pars -> Morphisms_Params [] ; + Morphisms_impl_pars -> Morphisms_Build_Params [] ; + Nat_lt_asymm -> Nat_le_succ_l [] ; + _PEpow_1_r -> _xH [] ; + _PEpow_1_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _PEpow_1_r -> Morphisms_eq_proper_proxy [] ; + _PEpow_1_r -> RelationClasses_Equivalence_Transitive [] ; + _PEpow_1_r -> _Npos [] ; + _PEpow_1_r -> _rpow_pow_N [] ; + _PEpow_1_r -> Setoid_Seq_refl [] ; + _PEpow_1_r -> Ring_polynom_PEpow [] ; + _PEpow_1_r -> _NPEequiv [] ; + Morphisms_Params -> _nat [] ; + _NtoZ -> _Z [] ; + _NtoZ -> _Z0 [] ; + _NtoZ -> _Zpos [] ; + _NtoZ -> _N [] ; + Morphisms_Build_Params -> _nat [] ; + _ZtoN -> _Z [] ; + _ZtoN -> _N [] ; + _ZtoN -> _N0 [] ; + _ZtoN -> _Npos [] ; + _isIn -> Pos_mul [] ; + _isIn -> _NPEmul [] ; + _isIn -> _default_isIn [] ; + Nat_add -> _S [] ; + Nat_add -> _nat [] ; + Nat_Private_OrderTac_Tac_trans -> Nat_Private_OrderTac_IsTotal_lt_compat [] ; + Nat_Private_OrderTac_Tac_trans -> Nat_Private_OrderTac_IsTotal_eq_equiv [] ; + Nat_Private_OrderTac_Tac_trans -> Nat_Private_OrderTac_IsTotal_lt_strorder [] ; + Nat_Private_OrderTac_Tac_trans -> OrdersTac_OEQ [] ; + Nat_Private_OrderTac_Tac_trans -> RelationClasses_StrictOrder_Transitive [] ; + Nat_Private_OrderTac_Tac_trans -> Nat_Private_OrderTac_IsTotal_le_lteq [] ; + Nat_Private_OrderTac_Tac_trans -> Nat_Private_OrderTac_Tac_interp_ord [] ; + Nat_Private_OrderTac_Tac_trans -> OrdersTac_trans_ord [] ; + _default_isIn -> _prod [] ; + _default_isIn -> Z_pos_sub [] ; + _default_isIn -> _option [] ; + _default_isIn -> _pair [] ; + _default_isIn -> _Some [] ; + _default_isIn -> _None [] ; + _default_isIn -> _N0 [] ; + _default_isIn -> _Npos [] ; + _default_isIn -> _NPEpow [] ; + _default_isIn -> _PExpr_eq [] ; + _PExpr_eq -> Ring_polynom_PExpr [] ; + _PExpr_eq -> Pos_eqb [] ; + _PExpr_eq -> N_eqb [] ; + _default_isIn_ok -> RelationClasses_equivalence_rewrite_relation [] ; + _default_isIn_ok -> Morphisms_rewrite_relation_eq_dom [] ; + _default_isIn_ok -> Pos_add_sub [] ; + _default_isIn_ok -> Pos_sub_sub_distr [] ; + _default_isIn_ok -> Z_sub [] ; + _default_isIn_ok -> Z_lt_gt [] ; + _default_isIn_ok -> Pos_sub_decr [] ; + _default_isIn_ok -> Z_pos_sub_gt [] ; + _default_isIn_ok -> _NPEpow_ok [] ; + _default_isIn_ok -> _PE_1_r [] ; + _default_isIn_ok -> _PEpow_add_r [] ; + _default_isIn_ok -> _NtoZ [] ; + _default_isIn_ok -> _ZtoN [] ; + _default_isIn_ok -> _default_isIn [] ; + _default_isIn_ok -> _PExpr_eq_spec [] ; + RelationClasses_StrictOrder_Transitive -> RelationClasses_StrictOrder [] ; + _PExpr_eq_spec -> _BoolSpec [] ; + _PExpr_eq_spec -> _BoolSpecT [] ; + _PExpr_eq_spec -> _BoolSpecF [] ; + _PExpr_eq_spec -> _PExpr_eq_semi_ok [] ; + Nat_Private_OrderTac_IsTotal_le_lteq -> Nat_le_lteq [] ; + _PExpr_eq_semi_ok -> Ring_polynom_PExpr_ind [] ; + _PExpr_eq_semi_ok -> _morph_eq [] ; + _PExpr_eq_semi_ok -> _PEsub_ext [] ; + _PExpr_eq_semi_ok -> _PEadd_ext [] ; + _PExpr_eq_semi_ok -> _NPEequiv_eq [] ; + _PExpr_eq_semi_ok -> _PEmul_ext [] ; + _PExpr_eq_semi_ok -> _PEopp_ext [] ; + _PExpr_eq_semi_ok -> _PEpow_ext [] ; + _PExpr_eq_semi_ok -> N_eqb_eq [] ; + _PExpr_eq_semi_ok -> Pos_eqb_spec [] ; + _PExpr_eq_semi_ok -> _PExpr_eq [] ; + _PExpr_eq_semi_ok -> _if_true [] ; + Nat_Private_OrderTac_Tac_interp_ord -> _eq [] ; + Nat_Private_OrderTac_Tac_interp_ord -> _lt [] ; + Nat_Private_OrderTac_Tac_interp_ord -> OrdersTac_ord [] ; + _if_true -> _and [] ; + _if_true -> _bool [] ; + _if_true -> _eq [] ; + _if_true -> _true [] ; + _if_true -> _false [] ; + _if_true -> _eq_refl [] ; + _if_true -> _conj [] ; + OrdersTac_trans_ord -> OrdersTac_OLT [] ; + OrdersTac_trans_ord -> OrdersTac_ord [] ; + OrdersTac_trans_ord -> OrdersTac_OLE [] ; + _rdiv7 -> _rdiv6 [] ; + _rdiv7 -> _rdiv4 [] ; + _rdiv_r_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _rdiv_r_r -> Morphisms_eq_proper_proxy [] ; + _rdiv_r_r -> RelationClasses_Equivalence_Transitive [] ; + _rdiv_r_r -> _ARmul_comm [] ; + _rdiv_r_r -> _AF_AR [] ; + _rdiv_r_r -> _AFinv_l [] ; + _rdiv_r_r -> _AFdiv_def [] ; + Field_theory_radd_ext -> Morphisms_proper_prf [] ; + Field_theory_radd_ext -> Field_theory_radd_ext_Proper [] ; + _split_nz_l -> _split_ok_l [] ; + Nat_le_lteq -> Nat_lt_eq_cases [] ; + _split_nz_r -> _split_ok_r [] ; + PeanoNat_Nat_pow_wd_obligation_1 -> Nat_pow [] ; + PeanoNat_Nat_pow_wd_obligation_1 -> Morphisms_respectful [] ; + PeanoNat_Nat_pow_wd_obligation_1 -> _eq_ind_r [] ; + Init_Unconvertible -> _unit [] ; + _Z_gt_le_dec -> Z_le [] ; + _Z_gt_le_dec -> _Z_gt_dec [] ; + Nat_lt_neq -> Nat_Private_OrderTac_Tac_eq_lt [] ; + Nat_lt_neq -> Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Nat_lt_neq -> Nat_Private_OrderTac_Tac_eq_sym [] ; + ClassicalDedekindReals_CReal_of_DReal_seq_max_prec_1 -> ClassicalDedekindReals_CReal_of_DReal_seq [] ; + ClassicalDedekindReals_CReal_of_DReal_seq_max_prec_1 -> VarMap_find [] ; + ClassicalDedekindReals_CReal_of_DReal_seq_max_prec_1 -> VarMap_Elt [] ; + ClassicalDedekindReals_CReal_of_DReal_seq_max_prec_1 -> Pos2Z_pos_is_pos [] ; + ClassicalDedekindReals_CReal_of_DReal_seq_max_prec_1 -> ZMicromega_ZTautoChecker_sound [] ; + Nat_mul_wd -> Morphisms_Proper [] ; + Nat_mul_wd -> PeanoNat_Nat_mul_wd_obligation_1 [] ; + _Z_gt_dec -> _not [] ; + _Z_gt_dec -> _False_ind [] ; + _Z_gt_dec -> _eq_ind [] ; + _Z_gt_dec -> _True [] ; + _Z_gt_dec -> _eq_refl [] ; + _Z_gt_dec -> _I [] ; + _Z_gt_dec -> _sumbool [] ; + _Z_gt_dec -> _left [] ; + _Z_gt_dec -> _right [] ; + _Z_gt_dec -> Z_gt [] ; + Nat_mul_neg_neg -> Nat_mul_lt_mono_neg_r [] ; + QArith_base_Qle_minus_iff -> QArith_base_Qopp [] ; + QArith_base_Qle_minus_iff -> QArith_base_Qplus [] ; + QArith_base_Qle_minus_iff -> QArith_base_Qle [] ; + QArith_base_Qle_minus_iff -> Z_mul_1_r [] ; + QArith_base_Qle_minus_iff -> Z_mul_opp_l [] ; + QArith_base_Qle_minus_iff -> Z_le_sub_le_add_r [] ; + Nat_mul_neg_pos -> Nat_mul_pos_neg [] ; + Qabs_Qabs_wd -> Morphisms_proper_prf [] ; + Qabs_Qabs_wd -> Qabs_Qabs_wd_Proper [] ; + Nat_mul_0_l -> _eq [] ; + Nat_mul_0_l -> _eq_refl [] ; + Nat_mul_0_l -> Nat_mul [] ; + Qabs_Qabs_triangle -> Qabs_Qabs [] ; + Qabs_Qabs_triangle -> QArith_base_Qplus [] ; + Qabs_Qabs_triangle -> QArith_base_Qle [] ; + Qabs_Qabs_triangle -> Pos2Z_is_nonneg [] ; + Qabs_Qabs_triangle -> Z_abs_mul [] ; + Qabs_Qabs_triangle -> Z_abs_triangle [] ; + Nat_mul_0_r -> Nat_mul_wd [] ; + Nat_mul_0_r -> Nat_mul_0_l [] ; + Nat_mul_0_r -> Nat_mul_succ_l [] ; + Nat_mul_0_r -> Nat_add_0_r [] ; + Z_abs_mul -> Z_mul_nonneg_nonneg [] ; + Z_abs_mul -> Z_abs_wd [] ; + Z_abs_mul -> Z_abs_opp [] ; + Z_abs_mul -> Z_eq_refl [] ; + Z_abs_mul -> Z_mul_nonneg_nonpos [] ; + Z_abs_mul -> Z_mul_opp_opp [] ; + Nat_mul_pos_neg -> Nat_mul_lt_mono_neg_r [] ; + Z_abs_triangle -> Z_opp_nonneg_nonpos [] ; + Z_abs_triangle -> Z_le_ge_cases [] ; + Z_abs_triangle -> Z_add_nonneg_nonneg [] ; + Z_abs_triangle -> Z_abs_eq [] ; + Z_abs_triangle -> Z_add_nonpos_nonpos [] ; + Z_abs_triangle -> Z_abs_neq [] ; + Z_abs_triangle -> Z_opp_nonpos_nonneg [] ; + Nat_mul_pos_pos -> Nat_mul_lt_mono_pos_r [] ; + Z_abs_eq -> Z_le [] ; + Z_abs_eq -> _Zneg [] ; + Z_abs_eq -> Z_abs [] ; + Z_abs_eq -> _eq_refl [] ; + Nat_mul_lt_mono_pos_r -> Nat_mul_lt_mono_pos_l [] ; + Nat_mul_lt_mono_pos_r -> Nat_mul_comm [] ; + Z_add_nonpos_nonpos -> Z_add_le_mono [] ; + Nat_mul_lt_mono_pos_l -> Nat_mul_wd [] ; + Nat_mul_lt_mono_pos_l -> Nat_mul_0_l [] ; + Nat_mul_lt_mono_pos_l -> Nat_mul_succ_l [] ; + Nat_mul_lt_mono_pos_l -> Nat_lt_ind [] ; + Nat_mul_lt_mono_pos_l -> Nat_add_lt_mono [] ; + Z_abs_neq -> Z_le [] ; + Z_abs_neq -> Z_abs [] ; + Z_abs_neq -> Z_opp [] ; + Z_abs_neq -> _eq_refl [] ; + Z_opp_nonpos_nonneg -> Z_opp_le_mono [] ; + Nat_mul_comm -> Nat_mul_0_r [] ; + Nat_mul_comm -> Nat_mul_succ_r [] ; + Nat_mul_succ_l -> Nat_mul [] ; + Nat_mul_succ_l -> _eq_ind_r [] ; + Nat_mul_succ_l -> _plus_n_Sm [] ; + Nat_mul_succ_l -> _eq_trans [] ; + Nat_mul_succ_l -> _plus_n_O [] ; + Z_abs_wd -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_abs_wd -> Z_Private_OrderTac_Tac_eq_sym [] ; + Z_abs_wd -> Z_opp_inj_wd [] ; + Z_abs_wd -> Z_le_ge_cases [] ; + Z_abs_wd -> Z_abs_eq [] ; + Z_abs_wd -> Z_abs_neq [] ; + Z_abs_wd -> Z_Private_OrderTac_Tac_eq_le [] ; + Nat_mul_succ_r -> Nat_mul_wd [] ; + Nat_mul_succ_r -> Nat_mul_0_l [] ; + Nat_mul_succ_r -> Nat_mul_succ_l [] ; + Nat_mul_succ_r -> Nat_add_cancel_r [] ; + Nat_mul_succ_r -> Nat_add_assoc [] ; + Z_abs_opp -> Z_opp_nonneg_nonpos [] ; + Z_abs_opp -> Z_le_ge_cases [] ; + Z_abs_opp -> Z_abs_eq [] ; + Z_abs_opp -> Z_abs_neq [] ; + Z_abs_opp -> Z_opp_nonpos_nonneg [] ; + Z_eq_refl -> RelationClasses_Equivalence_Reflexive [] ; + Z_eq_refl -> Z_eq_equiv [] ; + Nat_add_cancel_r -> Nat_add_comm [] ; + Nat_add_cancel_r -> Nat_add_cancel_l [] ; + Z_mul_nonneg_nonpos -> Z_mul_le_mono_nonpos_r [] ; + Nat_add_comm -> Morphisms_Reflexive_partial_app_morphism [] ; + Nat_add_comm -> Nat_add_succ_r [] ; + Nat_add_comm -> Nat_add_0_r [] ; + Z_mul_opp_opp -> Z_mul_opp_r [] ; + Nat_add_cancel_l -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_add_cancel_l -> RelationClasses_reflexivity [] ; + Nat_add_cancel_l -> Morphisms_eq_proper_proxy [] ; + Nat_add_cancel_l -> RelationClasses_iff_equivalence [] ; + Nat_add_cancel_l -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_add_cancel_l -> Nat_bi_induction [] ; + Nat_add_cancel_l -> Nat_succ_inj_wd [] ; + Nat_add_cancel_l -> Morphisms_per_partial_app_morphism [] ; + Nat_add_cancel_l -> Nat_add_wd [] ; + Nat_add_cancel_l -> Nat_add_succ_l [] ; + Nat_add_cancel_l -> Nat_add_0_l [] ; + Z_mul_le_mono_nonpos_r -> Z_mul_comm [] ; + Z_mul_le_mono_nonpos_r -> Z_mul_le_mono_nonpos_l [] ; + Nat_add_wd -> Morphisms_Proper [] ; + Nat_add_wd -> PeanoNat_Nat_add_wd_obligation_1 [] ; + Z_mul_le_mono_nonpos_l -> Z_mul_lt_mono_neg_l [] ; + Nat_add_succ_l -> _eq [] ; + Nat_add_succ_l -> _eq_refl [] ; + Nat_add_succ_l -> Nat_add [] ; + Z_Private_OrderTac_Tac_eq_le -> Z_Private_OrderTac_Tac_trans [] ; + Nat_add_0_l -> _eq [] ; + Nat_add_0_l -> _O [] ; + Nat_add_0_l -> _eq_refl [] ; + Nat_add_0_l -> Nat_add [] ; + PeanoNat_Nat_add_wd_obligation_1 -> Init_Nat_add [] ; + PeanoNat_Nat_add_wd_obligation_1 -> Morphisms_respectful [] ; + PeanoNat_Nat_add_wd_obligation_1 -> _eq_ind_r [] ; + Qabs_Qabs_wd_Proper -> Qabs_Qabs [] ; + Qabs_Qabs_wd_Proper -> QArith_base_Qeq [] ; + Qabs_Qabs_wd_Proper -> Z_abs_mul [] ; + Nat_add_succ_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_add_succ_r -> RelationClasses_reflexivity [] ; + Nat_add_succ_r -> Morphisms_eq_proper_proxy [] ; + Nat_add_succ_r -> RelationClasses_iff_equivalence [] ; + Nat_add_succ_r -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_add_succ_r -> Nat_bi_induction [] ; + Nat_add_succ_r -> Nat_succ_inj_wd [] ; + Nat_add_succ_r -> Morphisms_per_partial_app_morphism [] ; + Nat_add_succ_r -> Nat_add_wd [] ; + Nat_add_succ_r -> Nat_add_succ_l [] ; + Nat_add_succ_r -> Nat_add_0_l [] ; + ClassicalDedekindReals_Qpower_2_invneg_le_pow -> Qminmax_Q_Proper_instance_0 [] ; + ClassicalDedekindReals_Qpower_2_invneg_le_pow -> VarMap_find [] ; + ClassicalDedekindReals_Qpower_2_invneg_le_pow -> QMicromega_QTautoChecker_sound [] ; + ClassicalDedekindReals_Qpower_2_invneg_le_pow -> VarMap_Empty [] ; + ClassicalDedekindReals_Qpower_2_invneg_le_pow -> VarMap_Elt [] ; + ClassicalDedekindReals_Qpower_2_invneg_le_pow -> Pos2Z_pos_is_pos [] ; + ClassicalDedekindReals_Qpower_2_invneg_le_pow -> ZMicromega_ZTautoChecker_sound [] ; + ClassicalDedekindReals_Qpower_2_invneg_le_pow -> Qpower_Qpower_1_le_pos [] ; + ClassicalDedekindReals_Qpower_2_invneg_le_pow -> Z2Nat_id [] ; + ClassicalDedekindReals_Qpower_2_invneg_le_pow -> ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv [] ; + Nat_add_0_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_add_0_r -> RelationClasses_reflexivity [] ; + Nat_add_0_r -> Morphisms_eq_proper_proxy [] ; + Nat_add_0_r -> RelationClasses_iff_equivalence [] ; + Nat_add_0_r -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_add_0_r -> Nat_bi_induction [] ; + Nat_add_0_r -> Nat_succ_inj_wd [] ; + Nat_add_0_r -> Nat_add_wd [] ; + Nat_add_0_r -> Nat_add_succ_l [] ; + Nat_add_0_r -> Nat_add_0_l [] ; + Qabs_Qabs_case -> Qabs_Qabs [] ; + Qabs_Qabs_case -> QArith_base_Qopp [] ; + Qabs_Qabs_case -> Qabs_Qabs_case_subproof [] ; + Qabs_Qabs_case -> Qabs_Qabs_case_subproof0 [] ; + Qabs_Qabs_case -> Qabs_Qabs_case_subproof1 [] ; + Nat_add_assoc -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_add_assoc -> RelationClasses_reflexivity [] ; + Nat_add_assoc -> Morphisms_eq_proper_proxy [] ; + Nat_add_assoc -> RelationClasses_iff_equivalence [] ; + Nat_add_assoc -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_add_assoc -> Nat_bi_induction [] ; + Nat_add_assoc -> Nat_succ_inj_wd [] ; + Nat_add_assoc -> Morphisms_per_partial_app_morphism [] ; + Nat_add_assoc -> Nat_add_wd [] ; + Nat_add_assoc -> Nat_add_succ_l [] ; + Nat_add_assoc -> Nat_add_0_l [] ; + QArith_base_Qlt_le_trans -> QArith_base_Qlt [] ; + QArith_base_Qlt_le_trans -> QArith_base_Qmake [] ; + QArith_base_Qlt_le_trans -> QArith_base_Qle [] ; + QArith_base_Qlt_le_trans -> Z_mul_le_mono_pos_r [] ; + QArith_base_Qlt_le_trans -> Z_mul_lt_mono_pos_r [] ; + QArith_base_Qlt_le_trans -> Z_mul_shuffle0 [] ; + QArith_base_Qlt_le_trans -> Z_lt_le_trans [] ; + _plus_n_Sm -> Init_Nat_add [] ; + _plus_n_Sm -> _nat_ind [] ; + _plus_n_Sm -> _f_equal_nat [] ; + ClassicalDedekindReals_UpperAboveLower -> ClassicalDedekindReals_isLowerCut [] ; + ClassicalDedekindReals_UpperAboveLower -> QArith_base_Qnot_le_lt [] ; + _eq_trans -> _eq [] ; + Qpower_Qpower_le_compat_l -> Qpower_Qpower_0_lt [] ; + Qpower_Qpower_le_compat_l -> Z_le_0_sub [] ; + Qpower_Qpower_le_compat_l -> Qpower_Qpower_plus [] ; + Qpower_Qpower_le_compat_l -> QArith_base_Qlt_le_trans [] ; + Qpower_Qpower_le_compat_l -> QArith_base_Qmult_le_l [] ; + Qpower_Qpower_le_compat_l -> Qpower_Qpower_1_le [] ; + _plus_n_O -> Init_Nat_add [] ; + _plus_n_O -> _nat_ind [] ; + _plus_n_O -> _f_equal_nat [] ; + QArith_base_Qmult_le_l -> QArith_base_Qle_comp [] ; + QArith_base_Qmult_le_l -> QArith_base_Qmult_comm [] ; + QArith_base_Qmult_le_l -> QArith_base_Qmult_le_r [] ; + Nat_lt_ind -> Nat_right_induction [] ; + Qpower_Qpower_1_le -> QArith_base_Qle_refl [] ; + Qpower_Qpower_1_le -> Qpower_Qpower_1_le_pos [] ; + Qpower_Qpower_1_le -> Pos2Z_neg_is_neg [] ; + Nat_Private_OrderTac_Tac_lt_trans -> Nat_Private_OrderTac_Tac_trans [] ; + Qpower_Qpower_1_le_pos -> QArith_base_Qpower [] ; + Qpower_Qpower_1_le_pos -> QArith_base_Qmult_le_1_compat [] ; + Pos2Z_neg_is_neg -> _Z0 [] ; + Pos2Z_neg_is_neg -> _Zneg [] ; + Pos2Z_neg_is_neg -> Z_lt [] ; + Pos2Z_neg_is_neg -> _eq_refl [] ; + Nat_add_lt_mono -> Nat_lt_trans [] ; + Nat_add_lt_mono -> Nat_add_lt_mono_r [] ; + Morphisms_Prop_all_iff_morphism -> Morphisms_Proper [] ; + Morphisms_Prop_all_iff_morphism -> Morphisms_Prop_all_iff_morphism_obligation_1 [] ; + QArith_base_Qmult_le_1_compat -> QArith_base_Qmult [] ; + QArith_base_Qmult_le_1_compat -> QArith_base_Qle [] ; + QArith_base_Qmult_le_1_compat -> Z_mul_1_r [] ; + QArith_base_Qmult_le_1_compat -> Pos2Z_inj_mul [] ; + QArith_base_Qmult_le_1_compat -> Z_mul_le_mono_nonneg [] ; + QArith_base_Qmult_le_1_compat -> Z_mul_1_l [] ; + QArith_base_Qmult_le_1_compat -> Pos2Z_is_nonneg [] ; + Nat_Private_OrderTac_Tac_not_ge_lt -> Nat_Private_OrderTac_IsTotal_lt_total [] ; + Nat_Private_OrderTac_Tac_not_ge_lt -> Nat_Private_OrderTac_IsTotal_eq_equiv [] ; + Nat_Private_OrderTac_Tac_not_ge_lt -> Nat_Private_OrderTac_IsTotal_le_lteq [] ; + QArith_base_Qmult_le_r -> QArith_base_Qlt_le_weak [] ; + QArith_base_Qmult_le_r -> QArith_base_Qmult_lt_0_le_reg_r [] ; + QArith_base_Qmult_le_r -> QArith_base_Qmult_le_compat_r [] ; + QArith_base_Qmult_le_compat_r -> QArith_base_Qmult [] ; + QArith_base_Qmult_le_compat_r -> QArith_base_Qle [] ; + QArith_base_Qmult_le_compat_r -> Z_mul_1_r [] ; + QArith_base_Qmult_le_compat_r -> Pos2Z_inj_mul [] ; + QArith_base_Qmult_le_compat_r -> Z_mul_shuffle1 [] ; + QArith_base_Qmult_le_compat_r -> Z_mul_nonneg_nonneg [] ; + Morphisms_Prop_all_iff_morphism_obligation_1 -> _iff [] ; + Morphisms_Prop_all_iff_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_Prop_all_iff_morphism_obligation_1 -> _and_ind [] ; + Morphisms_Prop_all_iff_morphism_obligation_1 -> _conj [] ; + Morphisms_Prop_all_iff_morphism_obligation_1 -> _all [] ; + Morphisms_Prop_all_iff_morphism_obligation_1 -> Morphisms_pointwise_relation [] ; + Qabs_Qabs_case_subproof -> QArith_base_Qmake [] ; + Qabs_Qabs_case_subproof -> QArith_base_Qle [] ; + Qabs_Qabs_case_subproof -> _False_ind [] ; + Qabs_Qabs_case_subproof -> _eq_ind [] ; + Qabs_Qabs_case_subproof -> _True [] ; + Qabs_Qabs_case_subproof -> _I [] ; + Morphisms_pointwise_relation -> Relation_Definitions_relation [] ; + Qabs_Qabs_case_subproof0 -> QArith_base_Qmake [] ; + Qabs_Qabs_case_subproof0 -> QArith_base_Qle [] ; + Qabs_Qabs_case_subproof0 -> _False_ind [] ; + Qabs_Qabs_case_subproof0 -> _eq_ind [] ; + Qabs_Qabs_case_subproof0 -> _True [] ; + Qabs_Qabs_case_subproof0 -> _I [] ; + Nat_add_lt_mono_l -> Nat_add_wd [] ; + Nat_add_lt_mono_l -> Nat_add_succ_l [] ; + Nat_add_lt_mono_l -> Nat_add_0_l [] ; + Nat_add_lt_mono_l -> Nat_succ_lt_mono [] ; + Qabs_Qabs_case_subproof1 -> QArith_base_Qmake [] ; + Qabs_Qabs_case_subproof1 -> QArith_base_Qle [] ; + Qabs_Qabs_case_subproof1 -> _False_ind [] ; + Qabs_Qabs_case_subproof1 -> _eq_ind [] ; + Qabs_Qabs_case_subproof1 -> _True [] ; + Qabs_Qabs_case_subproof1 -> _I [] ; + Z2Nat_id -> _nat_N_Z [] ; + Z2Nat_id -> Nnat_N2Nat_id [] ; + Z2Nat_id -> Z2N_id [] ; + Z2Nat_id -> _Z_N_nat [] ; + Nat_add_lt_mono_r -> Nat_add_comm [] ; + Nat_add_lt_mono_r -> Nat_add_lt_mono_l [] ; + Nat_succ_lt_mono -> Nat_le_succ_l [] ; + ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv -> Nat_pow_nonzero [] ; + ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv -> Qminmax_Q_OT_eq_equiv [] ; + ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv -> Z_sub_1_r [] ; + ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv -> QArith_base_Qmult_frac_l [] ; + ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv -> Nat2Pos_inj_mul [] ; + ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv -> Qpower_Qpower_minus_pos [] ; + ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv -> Nat_pow_succ_r_ [] ; + ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv -> Nat2Z_inj_succ [] ; + Nat_right_induction -> Nat_lt_exists_pred [] ; + Nat_right_induction -> Nat_strong_right_induction [] ; + QArith_base_Qmult_frac_l -> QArith_base_Qmult [] ; + QArith_base_Qmult_frac_l -> _eq_refl [] ; + QArith_base_Qmult_frac_l -> QArith_base_Qeq [] ; + Nat_lt_exists_pred -> Morphisms_Prop_all_iff_morphism [] ; + Nat_lt_exists_pred -> _ex [] ; + Nat_lt_exists_pred -> Nat_Private_OrderTac_Tac_le_lt_trans [] ; + Nat_lt_exists_pred -> Nat_le_preorder [] ; + Nat_lt_exists_pred -> RelationClasses_PreOrder_Reflexive [] ; + Nat_lt_exists_pred -> Nat_le_le_succ_r [] ; + Nat_lt_exists_pred -> Nat_le_succ_r [] ; + Nat_lt_exists_pred -> _ex_intro [] ; + Nat2Pos_inj_mul -> Nat_eq_mul_0 [] ; + Nat2Pos_inj_mul -> Pos2Nat_inj [] ; + Nat2Pos_inj_mul -> Nat2Pos_id [] ; + Nat2Pos_inj_mul -> Pos2Nat_inj_mul [] ; + Nat_strong_right_induction -> Nat_Private_OrderTac_Tac_not_ge_lt [] ; + Nat_strong_right_induction -> _well_founded_induction [] ; + Nat_strong_right_induction -> Nat_lt_wf [] ; + Qpower_Qpower_minus_pos -> Qpower_Qpower_minus [] ; + Qpower_Qpower_minus_pos -> QArith_base_Qinv_pos [] ; + Qpower_Qpower_minus_pos -> QArith_base_Qpower_comp [] ; + Qpower_Qpower_minus_pos -> Qpower_Qinv_power [] ; + Nat_pow_succ_r_ -> Nat_le_0_l [] ; + Nat_pow_succ_r_ -> Nat_pow_succ_r [] ; + Nat_Private_OrderTac_Tac_le_lt_trans -> Nat_Private_OrderTac_Tac_trans [] ; + Nat2Z_inj_succ -> _O [] ; + Nat2Z_inj_succ -> _S [] ; + Nat2Z_inj_succ -> Z_of_nat [] ; + Nat2Z_inj_succ -> Pos2Z_inj_succ [] ; + _well_founded_induction -> _well_founded_induction_type [] ; + QArith_base_Qinv_pos -> QArith_base_Qinv [] ; + QArith_base_Qinv_pos -> QArith_base_Q_Setoid [] ; + Nat_Private_OrderTac_Tac_not_gt_le -> Nat_Private_OrderTac_IsTotal_lt_total [] ; + Nat_Private_OrderTac_Tac_not_gt_le -> Nat_Private_OrderTac_IsTotal_le_lteq [] ; + QArith_base_Qpower_comp -> QArith_base_Qpower [] ; + QArith_base_Qpower_comp -> QArith_base_Qinv_comp [] ; + QArith_base_Qpower_comp -> QArith_base_Qpower_positive_comp [] ; + Nat_lt_wf -> Morphisms_Prop_all_iff_morphism [] ; + Nat_lt_wf -> Nat_Private_OrderTac_Tac_le_lt_trans [] ; + Nat_lt_wf -> Morphisms_Prop_Acc_pt_morphism [] ; + Nat_lt_wf -> _well_founded [] ; + Nat_lt_wf -> Nat_lt_lt_succ_r [] ; + Nat_lt_wf -> Nat_Rlt_wd [] ; + Qpower_Qinv_power -> QArith_base_Qpower [] ; + Qpower_Qinv_power -> QArith_base_Qinv_comp [] ; + Qpower_Qinv_power -> Qpower_Qinv_power_positive [] ; + Qpower_Qinv_power_positive -> QArith_base_Qpower_positive [] ; + Qpower_Qinv_power_positive -> QArith_base_Q_Setoid [] ; + Qpower_Qinv_power_positive -> QArith_base_Qmult_comp [] ; + Qpower_Qinv_power_positive -> QArith_base_Qinv_mult_distr [] ; + Morphisms_Prop_Acc_pt_morphism -> Morphisms_subrelation_proper [] ; + Morphisms_Prop_Acc_pt_morphism -> Morphisms_reflexive_reflexive_proxy [] ; + Morphisms_Prop_Acc_pt_morphism -> Morphisms_subrelation_refl [] ; + Morphisms_Prop_Acc_pt_morphism -> Morphisms_Reflexive_partial_app_morphism [] ; + Morphisms_Prop_Acc_pt_morphism -> Morphisms_reflexive_proper_proxy [] ; + Morphisms_Prop_Acc_pt_morphism -> RelationClasses_Equivalence_Reflexive [] ; + Morphisms_Prop_Acc_pt_morphism -> Morphisms_subrelation_respectful [] ; + Morphisms_Prop_Acc_pt_morphism -> _tt [] ; + Morphisms_Prop_Acc_pt_morphism -> RelationClasses_Equivalence_Symmetric [] ; + Morphisms_Prop_Acc_pt_morphism -> Morphisms_iff_impl_subrelation [] ; + Morphisms_Prop_Acc_pt_morphism -> RelationClasses_symmetry [] ; + Morphisms_Prop_Acc_pt_morphism -> _Acc_intro [] ; + Morphisms_Prop_Acc_pt_morphism -> _Acc_inv [] ; + Morphisms_Prop_Acc_pt_morphism -> Morphisms_proper_sym_impl_iff [] ; + _well_founded -> _Acc [] ; + Z2N_id -> Z_le [] ; + Z2N_id -> _Zneg [] ; + Z2N_id -> _eq_refl [] ; + Z2N_id -> Z_of_N [] ; + Z2N_id -> Z_to_N [] ; + Nat_lt_lt_succ_r -> Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Nat_lt_lt_succ_r -> Nat_Private_OrderTac_Tac_lt_trans [] ; + Nat_lt_lt_succ_r -> Nat_Private_OrderTac_Tac_not_gt_le [] ; + _Z_N_nat -> _Z0 [] ; + _Z_N_nat -> _eq [] ; + _Z_N_nat -> _Zpos [] ; + _Z_N_nat -> _Zneg [] ; + _Z_N_nat -> Z_to_nat [] ; + _Z_N_nat -> _eq_refl [] ; + _Z_N_nat -> N_to_nat [] ; + _Z_N_nat -> Z_to_N [] ; + ConstructiveCauchyReals_seq -> ConstructiveCauchyReals_CReal [] ; + Nat_Rlt_wd -> Nat_le_wd [] ; + Nat_Rlt_wd -> Morphisms_Prop_and_iff_morphism [] ; + _inbetween -> _IZR [] ; + _inbetween -> _Rdiv [] ; + _inbetween -> _Rcompare [] ; + _inbetween -> SpecFloat_loc_Exact [] ; + _inbetween -> SpecFloat_loc_Inexact [] ; + _Float -> _radix [] ; + Morphisms_Prop_and_iff_morphism -> Morphisms_Proper [] ; + Morphisms_Prop_and_iff_morphism -> Morphisms_Prop_and_iff_morphism_obligation_1 [] ; + _Rcompare -> _total_order_T [] ; + Morphisms_Prop_and_iff_morphism_obligation_1 -> _iff [] ; + Morphisms_Prop_and_iff_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_Prop_and_iff_morphism_obligation_1 -> _and_ind [] ; + Morphisms_Prop_and_iff_morphism_obligation_1 -> _conj [] ; + _Rplus -> _R [] ; + _Rplus -> _Rrepr [] ; + _Rplus -> _Rabst [] ; + SpecFloat_loc_Exact -> _comparison [] ; + _Acc_inv -> _Acc [] ; + SpecFloat_loc_Inexact -> _comparison [] ; + Morphisms_proper_sym_impl_iff -> Basics_impl [] ; + Morphisms_proper_sym_impl_iff -> _iff [] ; + Morphisms_proper_sym_impl_iff -> Morphisms_Proper [] ; + Morphisms_proper_sym_impl_iff -> Morphisms_respectful [] ; + Morphisms_proper_sym_impl_iff -> RelationClasses_Symmetric [] ; + Morphisms_proper_sym_impl_iff -> _conj [] ; + _well_founded_induction_type -> _well_founded [] ; + _well_founded_induction_type -> _Acc_rect [] ; + ConstructiveCauchyReals_CReal_plus -> ConstructiveCauchyReals_mkCReal [] ; + ConstructiveCauchyReals_CReal_plus -> ConstructiveCauchyReals_CReal_plus_bound [] ; + ConstructiveCauchyReals_CReal_plus -> ConstructiveCauchyReals_CReal_plus_cauchy [] ; + _Rabst -> ClassicalDedekindReals_DRealAbstr [] ; + _Acc_rect -> _Acc [] ; + Nat_le_preorder -> RelationClasses_PreOrder [] ; + Nat_le_preorder -> Nat_le_trans [] ; + Nat_le_preorder -> RelationClasses_Build_PreOrder [] ; + ClassicalDedekindReals_DRealAbstr -> ClassicalDedekindReals_DReal [] ; + ClassicalDedekindReals_DRealAbstr -> ClassicalDedekindReals_DRealAbstr_aux [] ; + QArith_base_Qlt_le_dec -> QArith_base_Qlt [] ; + QArith_base_Qlt_le_dec -> QArith_base_Qle [] ; + QArith_base_Qlt_le_dec -> _Z_lt_le_dec [] ; + RelationClasses_PreOrder_Reflexive -> RelationClasses_PreOrder [] ; + Nat_le_le_succ_r -> Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Nat_le_le_succ_r -> Nat_Private_OrderTac_Tac_lt_trans [] ; + Nat_le_le_succ_r -> Nat_Private_OrderTac_Tac_not_gt_le [] ; + ClassicalDedekindReals_DRealAbstr_aux -> ClassicalDedekindReals_isLowerCut [] ; + ClassicalDedekindReals_DRealAbstr_aux -> QArith_base_Qplus_le_r [] ; + ClassicalDedekindReals_DRealAbstr_aux -> ClassicalDedekindReals_sig_forall_dec [] ; + ClassicalDedekindReals_DRealAbstr_aux -> Qfield_Qfield_field_lemma2 [] ; + ClassicalDedekindReals_DRealAbstr_aux -> ConstructiveRcomplete_Rfloor [] ; + ClassicalDedekindReals_DRealAbstr_aux -> CRelationClasses_Equivalence_Symmetric [] ; + ClassicalDedekindReals_DRealAbstr_aux -> CRelationClasses_symmetry [] ; + ClassicalDedekindReals_DRealAbstr_aux -> QArith_base_Qinv_minus_distr [] ; + ClassicalDedekindReals_DRealAbstr_aux -> ClassicalDedekindReals_Qpower_2_neg_le_one [] ; + Nat_le_succ_r -> RelationClasses_reflexivity [] ; + Nat_le_succ_r -> Nat_lt_eq_cases [] ; + Nat_le_succ_r -> Nat_lt_succ_r [] ; + ConstructiveCauchyReals_CReal_red_seq -> ConstructiveCauchyReals_mkCReal [] ; + ConstructiveCauchyReals_CReal_red_seq -> _eq_refl [] ; + ConstructiveCauchyReals_CReal_red_seq -> ConstructiveCauchyReals_seq [] ; + CMorphisms_reflexive_proper_proxy -> CRelationClasses_Reflexive [] ; + CMorphisms_reflexive_proper_proxy -> CMorphisms_ProperProxy [] ; + RelationClasses_PreOrder -> RelationClasses_Reflexive [] ; + RelationClasses_PreOrder -> RelationClasses_Transitive [] ; + Qfield_Qfield_field_lemma2 -> QArith_base_Qplus_comp [] ; + Qfield_Qfield_field_lemma2 -> Qfield_Qpower_theory [] ; + Qfield_Qfield_field_lemma2 -> _get_sign_None_th [] ; + Qfield_Qfield_field_lemma2 -> _triv_div_th [] ; + Qfield_Qfield_field_lemma2 -> QArith_base_Qopp_comp [] ; + Qfield_Qfield_field_lemma2 -> Qfield_Qsft [] ; + Qfield_Qfield_field_lemma2 -> QArith_base_Qmult_comp [] ; + Qfield_Qfield_field_lemma2 -> QArith_base_Qeq_bool_eq [] ; + Qfield_Qfield_field_lemma2 -> QArith_base_Qinv_comp [] ; + Qfield_Qfield_field_lemma2 -> _F2AF [] ; + Qfield_Qfield_field_lemma2 -> _Field_rw_pow_correct [] ; + CMorphisms_subrelation_respectful -> CMorphisms_respectful [] ; + CMorphisms_subrelation_respectful -> CRelationClasses_subrelation [] ; + Nat_le_trans -> Nat_lt_trans [] ; + RelationClasses_Build_PreOrder -> RelationClasses_Reflexive [] ; + RelationClasses_Build_PreOrder -> RelationClasses_Transitive [] ; + ConstructiveCauchyReals_inject_Q -> ConstructiveCauchyReals_CReal [] ; + ConstructiveCauchyReals_inject_Q -> ConstructiveCauchyReals_mkCReal [] ; + ConstructiveCauchyReals_inject_Q -> ConstructiveCauchyReals_inject_Q_cauchy [] ; + ConstructiveCauchyReals_inject_Q -> QExtra_Qbound_ltabs_ZExp2_spec [] ; + CMorphisms_subrelation_proper -> Init_Unconvertible [] ; + CMorphisms_subrelation_proper -> CMorphisms_Proper [] ; + CMorphisms_subrelation_proper -> CRelationClasses_subrelation [] ; + Nat_mul_lt_mono_neg_r -> Nat_mul_comm [] ; + Nat_mul_lt_mono_neg_r -> Nat_mul_lt_mono_neg_l [] ; + Nat_mul_lt_mono_neg_l -> Nat_mul_0_l [] ; + Nat_mul_lt_mono_neg_l -> Nat_order_induction_0 [] ; + Nat_mul_lt_mono_neg_l -> Nat_mul_lt_pred [] ; + Nat_mul_lt_mono_neg_l -> Nat_le_lt_add_lt [] ; + ConstructiveCauchyReals_CRealLt_asym -> QArith_base_Qplus_lt_l [] ; + ConstructiveCauchyReals_CRealLt_asym -> QArith_base_Qlt_trans [] ; + ConstructiveCauchyReals_CRealLt_asym -> ConstructiveCauchyReals_CRealLe [] ; + ConstructiveCauchyReals_CRealLt_asym -> ConstructiveCauchyReals_CRealLt_above [] ; + ConstructiveCauchyReals_CRealLt_asym -> ConstructiveCauchyReals_CRealLt_above_same [] ; + Nat_lt_succ_l -> Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Nat_lt_succ_l -> Nat_Private_OrderTac_Tac_lt_trans [] ; + Nat_lt_succ_l -> Nat_Private_OrderTac_Tac_not_gt_le [] ; + ConstructiveCauchyReals_inject_Q_plus -> ConstructiveCauchyReals_CReal_plus [] ; + ConstructiveCauchyReals_inject_Q_plus -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyReals_inject_Q_plus -> ConstructiveCauchyReals_inject_Q [] ; + ConstructiveCauchyReals_inject_Q_plus -> ConstructiveCauchyReals_CRealEq [] ; + Nat_order_induction_0 -> Nat_order_induction [] ; + QExtra_Qbound_ltabs_ZExp2 -> Qabs_Qabs [] ; + QExtra_Qbound_ltabs_ZExp2 -> QExtra_Qbound_lt_ZExp2 [] ; + Nat_mul_lt_pred -> Nat_mul_wd [] ; + Nat_mul_lt_pred -> Nat_mul_succ_l [] ; + Nat_mul_lt_pred -> Nat_add_assoc [] ; + Nat_mul_lt_pred -> Nat_add_lt_mono_r [] ; + ConstructiveCauchyReals_CRealLt_morph -> CRelationClasses_iffT [] ; + ConstructiveCauchyReals_CRealLt_morph -> CMorphisms_respectful [] ; + ConstructiveCauchyReals_CRealLt_morph -> ConstructiveCauchyReals_CRealEq [] ; + ConstructiveCauchyReals_CRealLt_morph -> ConstructiveCauchyReals_CRealLt_dec [] ; + ConstructiveCauchyReals_CRealLt_morph -> CMorphisms_Proper [] ; + Nat_le_lt_add_lt -> Nat_nlt_ge [] ; + Nat_le_lt_add_lt -> Nat_add_le_mono [] ; + CMorphisms_iffT_arrow_subrelation -> CRelationClasses_iffT [] ; + CMorphisms_iffT_arrow_subrelation -> CRelationClasses_arrow [] ; + CMorphisms_iffT_arrow_subrelation -> CRelationClasses_subrelation [] ; + CMorphisms_iffT_arrow_subrelation -> _prod_rect [] ; + CMorphisms_subrelation_refl -> CRelationClasses_subrelation [] ; + Nat_nlt_ge -> Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Nat_nlt_ge -> Nat_Private_OrderTac_Tac_le_lt_trans [] ; + Nat_nlt_ge -> Nat_Private_OrderTac_Tac_not_gt_le [] ; + Nat_add_le_mono -> Nat_le_trans [] ; + Nat_add_le_mono -> Nat_add_le_mono_r [] ; + ConstructiveRcomplete_Rfloor -> ConstructiveCauchyReals_inject_Q_plus [] ; + ConstructiveRcomplete_Rfloor -> ConstructiveCauchyRealsMult_CRealRing_ring_lemma2 [] ; + ConstructiveRcomplete_Rfloor -> CMorphisms_iffT_flip_arrow_subrelation [] ; + ConstructiveRcomplete_Rfloor -> ConstructiveCauchyRealsMult_CRealArchimedean [] ; + ConstructiveRcomplete_Rfloor -> ConstructiveCauchyReals_CReal_plus_morph_T [] ; + ConstructiveRcomplete_Rfloor -> ConstructiveCauchyReals_opp_inject_Q [] ; + ConstructiveRcomplete_Rfloor -> ConstructiveCauchyReals_inject_Q_morph_T [] ; + ConstructiveRcomplete_Rfloor -> ConstructiveCauchyReals_CReal_plus_lt_reg_r [] ; + CRelationClasses_iffT -> _prod [] ; + Nat_add_le_mono_l -> Nat_add_wd [] ; + Nat_add_le_mono_l -> Nat_add_succ_l [] ; + Nat_add_le_mono_l -> Nat_add_0_l [] ; + Nat_add_le_mono_l -> Nat_succ_le_mono [] ; + Nat_add_le_mono_r -> Nat_add_comm [] ; + Nat_add_le_mono_r -> Nat_add_le_mono_l [] ; + Nat_succ_le_mono -> Nat_succ_lt_mono [] ; + _display_pow_linear -> Ring_polynom_Pphi_pow [] ; + Nat_order_induction -> Nat_right_induction [] ; + Nat_order_induction -> Nat_left_induction [] ; + CMorphisms_Reflexive_partial_app_morphism -> CMorphisms_respectful [] ; + CMorphisms_Reflexive_partial_app_morphism -> CMorphisms_ProperProxy [] ; + CMorphisms_Reflexive_partial_app_morphism -> CMorphisms_Proper [] ; + Nat_left_induction -> Nat_strong_left_induction [] ; + Nat_left_induction -> Nat_eq_le_incl [] ; + _eq_rec -> _eq [] ; + Nat_strong_left_induction -> Nat_Private_OrderTac_Tac_not_ge_lt [] ; + Nat_strong_left_induction -> _well_founded_induction [] ; + Nat_strong_left_induction -> Nat_gt_wf [] ; + ConstructiveCauchyReals_inject_Q_cauchy -> ConstructiveCauchyReals_QCauchySeq [] ; + ConstructiveCauchyReals_inject_Q_cauchy -> VarMap_find [] ; + ConstructiveCauchyReals_inject_Q_cauchy -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyReals_inject_Q_cauchy -> VarMap_Empty [] ; + ConstructiveCauchyReals_inject_Q_cauchy -> VarMap_Elt [] ; + ConstructiveCauchyReals_inject_Q_cauchy -> VarMap_Branch [] ; + ConstructiveCauchyReals_inject_Q_cauchy -> Qpower_Qpower_0_lt [] ; + ConstructiveCauchyReals_inject_Q_cauchy -> Qabs_Qabs_Qlt_condition [] ; + Nat_eq_le_incl -> Nat_Private_OrderTac_Tac_lt_eq [] ; + Nat_eq_le_incl -> Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Nat_eq_le_incl -> Nat_Private_OrderTac_Tac_not_gt_le [] ; + CRelationClasses_Equivalence_Symmetric -> CRelationClasses_Equivalence [] ; + Nat_gt_wf -> Morphisms_Prop_all_iff_morphism [] ; + Nat_gt_wf -> Nat_Private_OrderTac_Tac_le_lt_trans [] ; + Nat_gt_wf -> Morphisms_Prop_Acc_pt_morphism [] ; + Nat_gt_wf -> _well_founded [] ; + Nat_gt_wf -> Nat_lt_succ_l [] ; + Nat_gt_wf -> Nat_Rgt_wd [] ; + QExtra_Qbound_ltabs_ZExp2_spec -> QExtra_Qbound_lt_ZExp2_spec [] ; + QExtra_Qbound_ltabs_ZExp2_spec -> Qabs_Qabs_case [] ; + QExtra_Qbound_ltabs_ZExp2_spec -> QExtra_Qbound_ltabs_ZExp2 [] ; + CRelationClasses_symmetry -> CRelationClasses_Symmetric [] ; + Nat_Rgt_wd -> Nat_le_wd [] ; + Nat_Rgt_wd -> Morphisms_Prop_and_iff_morphism [] ; + Init_Nat_mul -> _O [] ; + Init_Nat_mul -> Init_Nat_add [] ; + ConstructiveCauchyReals_CRealLe_not_lt -> _exist [] ; + ConstructiveCauchyReals_CRealLe_not_lt -> VarMap_find [] ; + ConstructiveCauchyReals_CRealLe_not_lt -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyReals_CRealLe_not_lt -> VarMap_Elt [] ; + ConstructiveCauchyReals_CRealLe_not_lt -> VarMap_Branch [] ; + ConstructiveCauchyReals_CRealLe_not_lt -> QArith_base_Qlt_le_dec [] ; + ConstructiveCauchyReals_CRealLe_not_lt -> ConstructiveCauchyReals_CRealLe [] ; + PeanoNat_Nat_mul_wd_obligation_1 -> Morphisms_respectful [] ; + PeanoNat_Nat_mul_wd_obligation_1 -> _eq_ind_r [] ; + PeanoNat_Nat_mul_wd_obligation_1 -> Init_Nat_mul [] ; + QArith_base_Qinv_minus_distr -> QArith_base_Qopp [] ; + QArith_base_Qinv_minus_distr -> QArith_base_Qplus [] ; + QArith_base_Qinv_minus_distr -> _ring_subst_niter [] ; + QArith_base_Qinv_minus_distr -> QArith_base_Qeq [] ; + QArith_base_Qinv_minus_distr -> Pos2Z_inj_mul [] ; + QArith_base_Qinv_minus_distr -> _Zr_ring_lemma1 [] ; + CMorphisms_respectful -> CRelationClasses_crelation [] ; + RelationClasses_eq_equivalence -> RelationClasses_Equivalence [] ; + RelationClasses_eq_equivalence -> RelationClasses_Build_Equivalence [] ; + RelationClasses_eq_equivalence -> RelationClasses_eq_Reflexive [] ; + RelationClasses_eq_equivalence -> RelationClasses_eq_Transitive [] ; + RelationClasses_eq_equivalence -> RelationClasses_eq_Symmetric [] ; + RelationClasses_eq_Reflexive -> _eq [] ; + RelationClasses_eq_Reflexive -> _eq_refl [] ; + RelationClasses_eq_Reflexive -> RelationClasses_Reflexive [] ; + CRelationClasses_Equivalence_Reflexive -> CRelationClasses_Equivalence [] ; + RelationClasses_eq_Transitive -> RelationClasses_Transitive [] ; + RelationClasses_eq_Transitive -> _eq_trans [] ; + ConstructiveCauchyReals_CRealEq -> _and [] ; + ConstructiveCauchyReals_CRealEq -> ConstructiveCauchyReals_CRealLe [] ; + RelationClasses_eq_Symmetric -> RelationClasses_Symmetric [] ; + RelationClasses_eq_Symmetric -> _eq_sym [] ; + ConstructiveCauchyReals_CRealLe -> ConstructiveCauchyReals_CRealLt [] ; + Nat_two_succ -> _eq [] ; + Nat_two_succ -> _O [] ; + Nat_two_succ -> _S [] ; + Nat_two_succ -> _nat [] ; + Nat_two_succ -> _eq_refl [] ; + ConstructiveCauchyReals_CRealLt -> _sig [] ; + ConstructiveCauchyReals_CRealLt -> ConstructiveCauchyReals_seq [] ; + Nat_one_succ -> _eq [] ; + Nat_one_succ -> _O [] ; + Nat_one_succ -> _S [] ; + Nat_one_succ -> _nat [] ; + Nat_one_succ -> _eq_refl [] ; + QArith_base_Qminus_comp -> QArith_base_Qminus [] ; + QArith_base_Qminus_comp -> QArith_base_Qplus_comp [] ; + QArith_base_Qminus_comp -> QArith_base_Q_Setoid [] ; + QArith_base_Qminus_comp -> QArith_base_Qopp_comp [] ; + Nat_neq_succ_0 -> Morphisms_PER_morphism [] ; + Nat_neq_succ_0 -> Morphisms_iff_impl_subrelation [] ; + Nat_neq_succ_0 -> Nat_succ_wd [] ; + Nat_neq_succ_0 -> Nat_neq_succ_diag_l [] ; + Nat_neq_succ_0 -> Nat_pred_succ [] ; + Nat_neq_succ_0 -> Nat_pred_wd [] ; + Nat_neq_succ_0 -> Nat_pred_0 [] ; + ConstructiveCauchyReals_CRealEq_relT -> ConstructiveCauchyReals_CRealEq_sym [] ; + ConstructiveCauchyReals_CRealEq_relT -> ConstructiveCauchyReals_CRealEq_trans [] ; + ConstructiveCauchyReals_CRealEq_relT -> ConstructiveCauchyReals_CRealEq_refl [] ; + ConstructiveCauchyReals_CRealEq_relT -> CRelationClasses_Equivalence [] ; + ConstructiveCauchyReals_CRealEq_relT -> CRelationClasses_Build_Equivalence [] ; + Nat_pred_0 -> _eq [] ; + Nat_pred_0 -> _O [] ; + Nat_pred_0 -> Nat_pred [] ; + Nat_pred_0 -> _eq_refl [] ; + ClassicalDedekindReals_Qpower_2_neg_le_one -> Qminmax_Q_Proper_instance_0 [] ; + ClassicalDedekindReals_Qpower_2_neg_le_one -> VarMap_find [] ; + ClassicalDedekindReals_Qpower_2_neg_le_one -> QMicromega_QTautoChecker_sound [] ; + ClassicalDedekindReals_Qpower_2_neg_le_one -> VarMap_Elt [] ; + ClassicalDedekindReals_Qpower_2_neg_le_one -> Z_sub_1_r [] ; + ClassicalDedekindReals_Qpower_2_neg_le_one -> Qpower_Qpower_minus_pos [] ; + ClassicalDedekindReals_Qpower_2_neg_le_one -> Nat2Z_inj_succ [] ; + Nat_lt_0_succ -> Nat_induction [] ; + Nat_case_analysis -> Nat_induction [] ; + ConstructiveCauchyReals_CRealEq_sym -> _False_ind [] ; + ConstructiveCauchyReals_CRealEq_sym -> _conj [] ; + ConstructiveCauchyReals_CRealEq_sym -> ConstructiveCauchyReals_CRealEq [] ; + Nat_induction -> Nat_le_0_l [] ; + Nat_induction -> Nat_right_induction [] ; + ConstructiveCauchyReals_CRealEq_trans -> ConstructiveCauchyReals_CRealEq [] ; + ConstructiveCauchyReals_CRealEq_trans -> ConstructiveCauchyReals_CRealLt_dec [] ; + Ring_polynom_Pphi_pow -> Ring_polynom_Pphi_avoid [] ; + ConstructiveCauchyReals_CRealEq_refl -> ConstructiveCauchyReals_CRealEq [] ; + ConstructiveCauchyReals_CRealEq_refl -> ConstructiveCauchyReals_CRealLe_refl [] ; + CRelationClasses_Equivalence -> CRelationClasses_Reflexive [] ; + CRelationClasses_Equivalence -> CRelationClasses_Transitive [] ; + CRelationClasses_Equivalence -> CRelationClasses_Symmetric [] ; + Qfield_Qfield_ring_lemma2 -> QArith_base_Qplus_comp [] ; + Qfield_Qfield_ring_lemma2 -> Setoid_Build_Setoid_Theory [] ; + Qfield_Qfield_ring_lemma2 -> Qfield_Qpower_theory [] ; + Qfield_Qfield_ring_lemma2 -> _get_sign_None_th [] ; + Qfield_Qfield_ring_lemma2 -> _triv_div_th [] ; + Qfield_Qfield_ring_lemma2 -> QArith_base_Qopp_comp [] ; + Qfield_Qfield_ring_lemma2 -> Qfield_Qsft [] ; + Qfield_Qfield_ring_lemma2 -> QArith_base_Qmult_comp [] ; + Qfield_Qfield_ring_lemma2 -> Morphisms_proper_prf [] ; + Qfield_Qfield_ring_lemma2 -> QArith_base_Qeq_bool_eq [] ; + Qfield_Qfield_ring_lemma2 -> _F_R [] ; + CRelationClasses_Build_Equivalence -> CRelationClasses_Reflexive [] ; + CRelationClasses_Build_Equivalence -> CRelationClasses_Transitive [] ; + CRelationClasses_Build_Equivalence -> CRelationClasses_Symmetric [] ; + QArith_base_Qplus_comp -> QArith_base_Qplus [] ; + QArith_base_Qplus_comp -> _ring_subst_niter [] ; + QArith_base_Qplus_comp -> QArith_base_Qeq [] ; + QArith_base_Qplus_comp -> Pos2Z_inj_mul [] ; + QArith_base_Qplus_comp -> _Zr_ring_lemma1 [] ; + QArith_base_Qplus_comp -> _Zr_ring_lemma2 [] ; + CRelationClasses_Reflexive -> CRelationClasses_crelation [] ; + QArith_base_Qplus_lt_l -> QArith_base_Qplus_comp [] ; + QArith_base_Qplus_lt_l -> QArith_base_Qlt_compat [] ; + QArith_base_Qplus_lt_l -> QArith_base_Qle_refl [] ; + QArith_base_Qplus_lt_l -> QArith_base_Qplus_assoc [] ; + QArith_base_Qplus_lt_l -> QArith_base_Qplus_0_r [] ; + QArith_base_Qplus_lt_l -> QArith_base_Qplus_opp_r [] ; + QArith_base_Qplus_lt_l -> QArith_base_Qplus_lt_le_compat [] ; + ClassicalDedekindReals_lowerCutAbove -> ClassicalDedekindReals_isLowerCut [] ; + ClassicalDedekindReals_lowerCutAbove -> QArith_base_Qlt_le_weak [] ; + ClassicalDedekindReals_lowerCutAbove -> _positive_nat_Z [] ; + ClassicalDedekindReals_lowerCutAbove -> QArith_base_Qarchimedean [] ; + ClassicalDedekindReals_lowerCutAbove -> _False_rec [] ; + ClassicalDedekindReals_lowerCutAbove -> ClassicalDedekindReals_sig_forall_dec [] ; + ClassicalDedekindReals_lowerCutAbove -> _left [] ; + ClassicalDedekindReals_lowerCutAbove -> _right [] ; + CRelationClasses_Transitive -> CRelationClasses_crelation [] ; + ClassicalDedekindReals_lowerCutBelow -> ClassicalDedekindReals_isLowerCut [] ; + ClassicalDedekindReals_lowerCutBelow -> Qfield_Qfield_ring_lemma2 [] ; + ClassicalDedekindReals_lowerCutBelow -> QArith_base_Qplus_lt_l [] ; + ClassicalDedekindReals_lowerCutBelow -> _positive_nat_Z [] ; + ClassicalDedekindReals_lowerCutBelow -> QArith_base_Qarchimedean [] ; + ClassicalDedekindReals_lowerCutBelow -> Qminmax_Q_Proper_instance_0 [] ; + ClassicalDedekindReals_lowerCutBelow -> _False_rec [] ; + ClassicalDedekindReals_lowerCutBelow -> ClassicalDedekindReals_sig_forall_dec [] ; + ClassicalDedekindReals_lowerCutBelow -> _left [] ; + ClassicalDedekindReals_lowerCutBelow -> _right [] ; + SetoidTactics_default_relation -> SetoidTactics_DefaultRelation [] ; + CRelationClasses_Symmetric -> CRelationClasses_crelation [] ; + ClassicalDedekindReals_DRealQlim_rec -> _proj1_sig [] ; + ClassicalDedekindReals_DRealQlim_rec -> Nat_add_comm [] ; + ClassicalDedekindReals_DRealQlim_rec -> ClassicalDedekindReals_lowerCutBelow [] ; + ClassicalDedekindReals_DRealQlim_rec -> QArith_base_Qplus_le_r [] ; + ClassicalDedekindReals_DRealQlim_rec -> Nat2Z_inj_add [] ; + ClassicalDedekindReals_DRealQlim_rec -> QArith_base_Qinv_plus_distr [] ; + ConstructiveCauchyReals_CRealLe_refl -> ConstructiveCauchyReals_CRealLt_asym [] ; + Z_of_N -> _Z [] ; + Z_of_N -> _Z0 [] ; + Z_of_N -> _Zpos [] ; + Z_of_N -> _N [] ; + ConstructiveCauchyReals_CRealLt_dec -> Qpower_Qpower_le_compat_l [] ; + ConstructiveCauchyReals_CRealLt_dec -> Qpower_Qpower_minus_pos [] ; + ConstructiveCauchyReals_CRealLt_dec -> QArith_base_Qlt_le_dec [] ; + ConstructiveCauchyReals_CRealLt_dec -> ConstructiveCauchyReals_CRealLt [] ; + ConstructiveCauchyReals_CRealLt_dec -> _sum [] ; + ConstructiveCauchyReals_CRealLt_dec -> ConstructiveCauchyReals_cauchy [] ; + ConstructiveCauchyReals_CRealLt_dec -> QExtra_QarchimedeanExp2_Z [] ; + ConstructiveCauchyReals_CRealLt_dec -> Qabs_Qabs_Qlt_condition [] ; + ConstructiveCauchyReals_CRealLt_dec -> Z_min_spec [] ; + ConstructiveCauchyReals_CRealLt_dec -> QArith_base_Qinv_lt_contravar [] ; + ConstructiveCauchyReals_CRealLt_dec -> _inl [] ; + ConstructiveCauchyReals_CRealLt_dec -> _inr [] ; + _get_sign_None -> _option [] ; + _get_sign_None -> _None [] ; + Qminmax_Q_OT_lt_compat -> QOrderedType_Q_as_OT_lt_compat [] ; + ConstructiveCauchyReals_cauchy -> ConstructiveCauchyReals_seq [] ; + Nat2Z_inj_mul -> _nat_N_Z [] ; + Nat2Z_inj_mul -> N2Z_inj_mul [] ; + Nat2Z_inj_mul -> Nnat_Nat2N_inj_mul [] ; + QExtra_QarchimedeanExp2_Z -> _sig [] ; + QExtra_QarchimedeanExp2_Z -> _exist [] ; + QExtra_QarchimedeanExp2_Z -> QExtra_Qbound_lt_ZExp2_spec [] ; + Z_min -> Z_compare [] ; + Qminmax_Q_OT_eq_equiv -> QOrderedType_Q_as_OT_eq_equiv [] ; + Pos_succ_of_nat -> _not [] ; + Pos_succ_of_nat -> Pos_of_nat_succ [] ; + Qabs_Qabs_Qlt_condition -> QArith_base_Qle_lt_trans [] ; + Qabs_Qabs_Qlt_condition -> QArith_base_Qlt_compat [] ; + Qabs_Qabs_Qlt_condition -> Qabs_Qle_Qabs [] ; + Qabs_Qabs_Qlt_condition -> Qfield_Qopp_opp [] ; + Qabs_Qabs_Qlt_condition -> QArith_base_Qopp_lt_compat [] ; + Qabs_Qabs_Qlt_condition -> Qabs_Qabs_opp [] ; + _ring_subst_niter -> Init_Nat_mul [] ; + Z_min_spec -> Z_lt_total [] ; + Z_min_spec -> Z_le_lteq [] ; + Z_min_spec -> Z_min_l [] ; + Z_min_spec -> Z_min_r [] ; + QArith_base_Qinv_lt_contravar -> QArith_base_Qlt_irrefl [] ; + QArith_base_Qinv_lt_contravar -> QArith_base_Qmult_1_l [] ; + QArith_base_Qinv_lt_contravar -> QArith_base_Qlt_shift_div_l [] ; + QArith_base_Qinv_lt_contravar -> QArith_base_Qinv_involutive [] ; + QArith_base_Qinv_lt_contravar -> QArith_base_Qlt_shift_div_r [] ; + QArith_base_Qinv_lt_contravar -> QArith_base_Qmult_lt_l [] ; + Ring_polynom_PEeval -> Ring_polynom_PExpr [] ; + Ring_polynom_PEeval -> BinList_nth [] ; + Pos_to_nat -> _O [] ; + Pos_to_nat -> Init_Nat_add [] ; + Pos_to_nat -> Pos_iter_op [] ; + QArith_base_Qlt_le_weak -> QArith_base_Qlt [] ; + QArith_base_Qlt_le_weak -> QArith_base_Qle [] ; + QArith_base_Qlt_le_weak -> Z_lt_le_incl [] ; + _positive_nat_Z -> Z_of_nat [] ; + _positive_nat_Z -> SuccNat2Pos_inv [] ; + QArith_base_Qlt_shift_div_r -> QArith_base_Qle_comp [] ; + QArith_base_Qlt_shift_div_r -> QArith_base_Qlt_not_eq [] ; + QArith_base_Qlt_shift_div_r -> QArith_base_Qnot_le_lt [] ; + QArith_base_Qlt_shift_div_r -> QArith_base_Qnot_eq_sym [] ; + QArith_base_Qlt_shift_div_r -> QArith_base_Qinv_lt_0_compat [] ; + QArith_base_Qlt_shift_div_r -> QArith_base_Qmult_lt_0_le_reg_r [] ; + QArith_base_Qlt_shift_div_r -> QArith_base_Qlt_not_le [] ; + QArith_base_Qlt_shift_div_r -> QArith_base_Qdiv_mult_l [] ; + Z_of_nat -> _Z [] ; + Z_of_nat -> _Z0 [] ; + Z_of_nat -> _Zpos [] ; + Z_of_nat -> PosDef_Pos_of_succ_nat [] ; + QArith_base_Qmult_lt_l -> QArith_base_Qlt_compat [] ; + QArith_base_Qmult_lt_l -> QArith_base_Qmult_comm [] ; + QArith_base_Qmult_lt_l -> QArith_base_Qmult_lt_r [] ; + SetoidTactics_equivalence_default -> RelationClasses_Equivalence [] ; + SetoidTactics_equivalence_default -> SetoidTactics_DefaultRelation [] ; + SetoidTactics_equivalence_default -> SetoidTactics_Build_DefaultRelation [] ; + QArith_base_Qmult_lt_r -> QArith_base_Qlt [] ; + QArith_base_Qmult_lt_r -> QArith_base_Qmult [] ; + QArith_base_Qmult_lt_r -> Z_mul_1_r [] ; + QArith_base_Qmult_lt_r -> Pos2Z_inj_mul [] ; + QArith_base_Qmult_lt_r -> Z_mul_shuffle1 [] ; + QArith_base_Qmult_lt_r -> Z_mul_pos_pos [] ; + PosDef_Pos_of_succ_nat -> PosDef_Pos_succ [] ; + PosDef_Pos_of_succ_nat -> _nat [] ; + Z_min_l -> Z_le [] ; + Z_min_l -> Z_compare_spec [] ; + Z_min_l -> Z_min [] ; + _triv_div -> _prod [] ; + _triv_div -> _bool [] ; + _triv_div -> _pair [] ; + Z_min_r -> Z_le [] ; + Z_min_r -> Z_compare_spec [] ; + Z_min_r -> Z_min [] ; + Qabs_Qle_Qabs -> QArith_base_Qle_refl [] ; + Qabs_Qle_Qabs -> QArith_base_Qle_trans [] ; + Qabs_Qle_Qabs -> Qabs_Qabs_case [] ; + Qabs_Qle_Qabs -> QArith_base_Qopp_le_compat [] ; + QArith_base_Qeq -> _eq [] ; + QArith_base_Qeq -> Z_mul [] ; + QArith_base_Qeq -> QArith_base_Qden [] ; + QArith_base_Qeq -> QArith_base_Qnum [] ; + Qfield_Qopp_opp -> Qfield_Qfield_ring_lemma1 [] ; + QArith_base_Qarchimedean -> QArith_base_Qlt [] ; + QArith_base_Qarchimedean -> QArith_base_Qmake [] ; + QArith_base_Qarchimedean -> _sig [] ; + QArith_base_Qarchimedean -> _exist [] ; + QArith_base_Qarchimedean -> Z_mul_1_r [] ; + QArith_base_Qarchimedean -> Z_lt_le_trans [] ; + QArith_base_Qarchimedean -> Pos_le_1_l [] ; + QArith_base_Qarchimedean -> Pos2Z_pos_le_pos [] ; + QArith_base_Qarchimedean -> Pos2Z_inj_mul [] ; + QArith_base_Qarchimedean -> Z_mul_le_mono_nonneg [] ; + Ring_polynom_norm_subst -> Ring_polynom_PNSubstL [] ; + Ring_polynom_norm_subst -> Ring_polynom_norm_aux [] ; + QArith_base_Qopp_lt_compat -> QArith_base_Qlt [] ; + QArith_base_Qopp_lt_compat -> QArith_base_Qopp [] ; + QArith_base_Qopp_lt_compat -> Z_opp_lt_mono [] ; + QArith_base_Qopp_lt_compat -> Z_mul_opp_l [] ; + Qabs_Qabs_opp -> Qfield_Qfield_ring_lemma2 [] ; + Qabs_Qabs_opp -> QArith_base_Qle_comp [] ; + Qabs_Qabs_opp -> QArith_base_Qle_antisym [] ; + Qabs_Qabs_opp -> Qfield_Qfield_ring_lemma1 [] ; + Qabs_Qabs_opp -> QArith_base_Qle_minus_iff [] ; + Qabs_Qabs_opp -> Qabs_Qabs_case [] ; + Qminmax_Q_Proper_instance_0 -> Qminmax_Q_Private_Tac_eq_le [] ; + Qminmax_Q_Proper_instance_0 -> Qminmax_Q_Private_Tac_eq_lt [] ; + Qminmax_Q_Proper_instance_0 -> Qminmax_Q_Private_Tac_le_eq [] ; + Qminmax_Q_Proper_instance_0 -> Qminmax_Q_Private_Tac_lt_eq [] ; + Qminmax_Q_Proper_instance_0 -> Qminmax_Q_Private_Tac_le_lt_trans [] ; + Qminmax_Q_Proper_instance_0 -> Qminmax_Q_Private_Tac_lt_irrefl [] ; + Qminmax_Q_Proper_instance_0 -> Qminmax_Q_Private_Tac_eq_sym [] ; + Qminmax_Q_Proper_instance_0 -> Qminmax_Q_Private_Tac_not_gt_le [] ; + QArith_base_Qopp_le_compat -> QArith_base_Qopp [] ; + QArith_base_Qopp_le_compat -> QArith_base_Qle [] ; + QArith_base_Qopp_le_compat -> Z_mul_opp_l [] ; + QArith_base_Qopp_le_compat -> Z_opp_le_mono [] ; + QArith_base_Qeq_bool -> Z_mul [] ; + QArith_base_Qeq_bool -> QArith_base_Qden [] ; + QArith_base_Qeq_bool -> QArith_base_Qnum [] ; + QArith_base_Qeq_bool -> Z_eqb [] ; + Z_mul_1_r -> Z_mul_succ_r [] ; + Z_mul_1_r -> Z_mul_0_r [] ; + Z_mul_1_r -> Z_one_succ [] ; + CMorphisms_ProperProxy -> CRelationClasses_crelation [] ; + CMorphisms_Proper -> CRelationClasses_crelation [] ; + Ring_polynom_mk_monpol_list -> _O [] ; + Ring_polynom_mk_monpol_list -> Ring_polynom_norm_subst [] ; + Ring_polynom_mk_monpol_list -> _nil [] ; + Ring_polynom_mk_monpol_list -> _cons [] ; + Ring_polynom_mk_monpol_list -> Ring_polynom_mon_of_pol [] ; + Ring_polynom_Pphi_dev -> Ring_polynom_Pphi_avoid [] ; + Ring_polynom_Pphi_dev -> Ring_polynom_mkpow [] ; + Ring_polynom_Pphi_dev -> Ring_polynom_mkopp_pow [] ; + Z_mul_comm -> Z_mul_succ_r [] ; + Z_mul_comm -> Z_mul_0_r [] ; + ConstructiveCauchyRealsMult_CRealRing_ring_lemma2 -> ConstructiveCauchyRealsMult_CReal_isRing [] ; + ConstructiveCauchyRealsMult_CRealRing_ring_lemma2 -> ConstructiveCauchyRealsMult_CReal_mult_morph_Proper [] ; + ConstructiveCauchyRealsMult_CRealRing_ring_lemma2 -> ConstructiveCauchyRealsMult_CReal_opp_morph_Proper [] ; + ConstructiveCauchyRealsMult_CRealRing_ring_lemma2 -> Ring_polynom_ring_rw_correct [] ; + Ring_polynom_Mon -> _positive [] ; + ConstructiveCauchyReals_CReal_minus -> ConstructiveCauchyReals_CReal_plus [] ; + ConstructiveCauchyReals_CReal_minus -> ConstructiveCauchyReals_CReal_opp [] ; + Ring_polynom_Pol -> _positive [] ; + CMorphisms_iffT_flip_arrow_subrelation -> CRelationClasses_iffT [] ; + CMorphisms_iffT_flip_arrow_subrelation -> CRelationClasses_arrow [] ; + CMorphisms_iffT_flip_arrow_subrelation -> CRelationClasses_flip [] ; + CMorphisms_iffT_flip_arrow_subrelation -> CRelationClasses_subrelation [] ; + CMorphisms_iffT_flip_arrow_subrelation -> _prod_rect [] ; + Ring_polynom_PExpr -> _N [] ; + ConstructiveCauchyReals_inject_Z -> ConstructiveCauchyReals_inject_Q [] ; + Ring_polynom_Pc -> _positive [] ; + ConstructiveCauchyReals_CReal_opp -> ConstructiveCauchyReals_mkCReal [] ; + ConstructiveCauchyReals_CReal_opp -> ConstructiveCauchyReals_CReal_opp_bound [] ; + ConstructiveCauchyReals_CReal_opp -> ConstructiveCauchyReals_CReal_opp_cauchy [] ; + Ring_polynom_Pinj -> _positive [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> _exist [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> QArith_base_Qinv_plus_distr [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> ConstructiveCauchyReals_CReal_plus [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> ConstructiveCauchyReals_CRealLt [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> _sigT [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> ConstructiveCauchyReals_inject_Z [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> _existT [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> Qround_Qlt_floor [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> _eq_rec_r [] ; + ConstructiveCauchyRealsMult_CRealArchimedean -> Qround_Qfloor_le [] ; + Ring_polynom_PX -> _positive [] ; + ConstructiveCauchyReals_CReal_plus_morph_T -> CMorphisms_respectful [] ; + ConstructiveCauchyReals_CReal_plus_morph_T -> CMorphisms_Proper [] ; + ConstructiveCauchyReals_CReal_plus_morph_T -> ConstructiveCauchyReals_CReal_plus_proper_r [] ; + Ring_polynom_PEX -> _N [] ; + ConstructiveCauchyReals_opp_inject_Q -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyReals_opp_inject_Q -> ConstructiveCauchyReals_inject_Q [] ; + ConstructiveCauchyReals_opp_inject_Q -> ConstructiveCauchyReals_CRealEq [] ; + ConstructiveCauchyReals_opp_inject_Q -> ConstructiveCauchyReals_CReal_opp [] ; + Ring_polynom_PEadd -> _N [] ; + ConstructiveCauchyRealsMult_CReal_mult -> ConstructiveCauchyReals_mkCReal [] ; + ConstructiveCauchyRealsMult_CReal_mult -> ConstructiveCauchyRealsMult_CReal_mult_bound [] ; + ConstructiveCauchyRealsMult_CReal_mult -> ConstructiveCauchyRealsMult_CReal_mult_cauchy [] ; + Ring_polynom_PEsub -> _N [] ; + ConstructiveCauchyReals_CReal_plus_comm -> ConstructiveCauchyReals_CReal_plus [] ; + ConstructiveCauchyReals_CReal_plus_comm -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyReals_CReal_plus_comm -> ConstructiveCauchyReals_CRealEq_diff [] ; + ConstructiveCauchyReals_inject_Q_morph_T -> ConstructiveCauchyReals_inject_Q [] ; + ConstructiveCauchyReals_inject_Q_morph_T -> CMorphisms_respectful [] ; + ConstructiveCauchyReals_inject_Q_morph_T -> ConstructiveCauchyReals_CRealEq [] ; + ConstructiveCauchyReals_inject_Q_morph_T -> QArith_base_Qminus_comp [] ; + ConstructiveCauchyReals_inject_Q_morph_T -> CMorphisms_Proper [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> CMorphisms_reflexive_proper_proxy [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> CMorphisms_subrelation_respectful [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> CMorphisms_subrelation_proper [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> ConstructiveCauchyReals_CRealLt_morph [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> CMorphisms_iffT_arrow_subrelation [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> CMorphisms_subrelation_refl [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> CMorphisms_Reflexive_partial_app_morphism [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> CRelationClasses_Equivalence_Reflexive [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> ConstructiveCauchyReals_CRealEq_relT [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> ConstructiveCauchyReals_CReal_plus_comm [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_r -> ConstructiveCauchyReals_CReal_plus_lt_reg_l [] ; + _N -> _positive [] ; + Z_eq_equiv -> _Z [] ; + Z_eq_equiv -> RelationClasses_eq_equivalence [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_l -> _exist [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_l -> ConstructiveCauchyReals_CReal_plus [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_l -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyReals_CReal_plus_lt_reg_l -> ConstructiveCauchyReals_CRealLt [] ; + Z_mul_wd -> Z_mul [] ; + Z_mul_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Z_mul_wd -> RelationClasses_eq_Reflexive [] ; + Z_mul_wd -> Morphisms_reflexive_proper [] ; + Z_mul_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_mul_wd -> Z_eq [] ; + ConstructiveCauchyReals_CReal_plus_bound -> VarMap_find [] ; + ConstructiveCauchyReals_CReal_plus_bound -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyReals_CReal_plus_bound -> VarMap_Empty [] ; + ConstructiveCauchyReals_CReal_plus_bound -> VarMap_Elt [] ; + ConstructiveCauchyReals_CReal_plus_bound -> VarMap_Branch [] ; + ConstructiveCauchyReals_CReal_plus_bound -> ZMicromega_ZTautoChecker_sound [] ; + ConstructiveCauchyReals_CReal_plus_bound -> Qpower_Qpower_le_compat_l [] ; + ConstructiveCauchyReals_CReal_plus_bound -> Qabs_Qabs_Qlt_condition [] ; + ConstructiveCauchyReals_CReal_plus_bound -> ConstructiveCauchyReals_CReal_plus_scale [] ; + ConstructiveCauchyReals_CReal_plus_bound -> Qreduction_Qred_correct [] ; + ConstructiveCauchyReals_CReal_plus_bound -> ConstructiveCauchyReals_CReal_plus_seq [] ; + ConstructiveCauchyReals_CReal_plus_bound -> ConstructiveCauchyReals_bound [] ; + Z_mul_succ_l -> Z_succ [] ; + Z_mul_succ_l -> Z_Private_BootStrap_mul_1_l [] ; + Z_mul_succ_l -> Z_Private_BootStrap_mul_add_distr_r [] ; + ConstructiveCauchyReals_CReal_plus_scale -> Z_max [] ; + ConstructiveCauchyReals_CReal_plus_scale -> ConstructiveCauchyReals_scale [] ; + Z_mul_succ_r -> Z_mul_wd [] ; + Z_mul_succ_r -> Z_mul_succ_l [] ; + Z_mul_succ_r -> Z_add_cancel_r [] ; + Z_mul_succ_r -> Z_mul_0_l [] ; + Z_mul_succ_r -> Z_add_assoc [] ; + Qreduction_Qred_correct -> _ring_subst_niter [] ; + Qreduction_Qred_correct -> QArith_base_Qeq [] ; + Qreduction_Qred_correct -> _Zr_ring_lemma1 [] ; + Qreduction_Qred_correct -> Z_gcd_nonneg [] ; + Qreduction_Qred_correct -> Z_ggcd_correct_divisors [] ; + Qreduction_Qred_correct -> Z_ggcd_gcd [] ; + Qreduction_Qred_correct -> Z_le_neq [] ; + Qreduction_Qred_correct -> Qreduction_Qred [] ; + Qreduction_Qred_correct -> Z2Pos_id [] ; + Qreduction_Qred_correct -> Z_mul_pos_cancel_l [] ; + Z_succ -> Z_add [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> VarMap_find [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> VarMap_Empty [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> VarMap_Elt [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> VarMap_Branch [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> ZMicromega_ZTautoChecker_sound [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> Qabs_Qabs_wd_Proper [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> Qpower_Qpower_minus_pos [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> QArith_base_Qminus_comp [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> ConstructiveCauchyReals_cauchy [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> Qabs_Qabs_Qlt_condition [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> Qreduction_Qred_correct [] ; + ConstructiveCauchyReals_CReal_plus_cauchy -> ConstructiveCauchyReals_CReal_plus_seq [] ; + Z_bi_induction -> Z_eq [] ; + Z_bi_induction -> Z_succ_pred [] ; + Z_bi_induction -> Z_peano_ind [] ; + Qreduction_Qred -> QArith_base_Q [] ; + Qreduction_Qred -> QArith_base_Qmake [] ; + Qreduction_Qred -> _snd [] ; + Qreduction_Qred -> Z_ggcd [] ; + Qreduction_Qred -> Z_to_pos [] ; + Z_to_pos -> _Z [] ; + Z_to_pos -> _xH [] ; + Z_add_cancel_r -> Z_add_comm [] ; + Z_add_cancel_r -> Z_add_cancel_l [] ; + Z_mul_0_l -> _eq [] ; + Z_mul_0_l -> Z_mul [] ; + Z_mul_0_l -> _eq_refl [] ; + ConstructiveCauchyReals_CReal_plus_seq -> Z_sub [] ; + ConstructiveCauchyReals_CReal_plus_seq -> ConstructiveCauchyReals_seq [] ; + ConstructiveCauchyReals_CReal_plus_seq -> Qreduction_Qred [] ; + Z_mul_0_r -> Z_mul_wd [] ; + Z_mul_0_r -> Z_mul_succ_l [] ; + Z_mul_0_r -> Z_mul_0_l [] ; + Z_mul_0_r -> Z_add_0_r [] ; + Z2Pos_id -> _Z0 [] ; + Z2Pos_id -> _Zpos [] ; + Z2Pos_id -> _Zneg [] ; + Z2Pos_id -> Z_lt [] ; + Z2Pos_id -> _False_ind [] ; + Z2Pos_id -> _eq_ind [] ; + Z2Pos_id -> _True [] ; + Z2Pos_id -> _eq_refl [] ; + Z2Pos_id -> _I [] ; + Z2Pos_id -> Z_to_pos [] ; + Z_mul_pos_cancel_l -> Z_mul_0_r [] ; + Z_mul_pos_cancel_l -> Z_mul_lt_mono_pos_l [] ; + Z_add_0_r -> Z_bi_induction [] ; + Z_add_0_r -> Z_add_wd [] ; + Z_add_0_r -> Z_succ_inj_wd [] ; + Z_add_0_r -> Z_add_succ_l [] ; + Z_add_0_r -> Z_add_0_l [] ; + ConstructiveCauchyReals_scale -> ConstructiveCauchyReals_CReal [] ; + Z_add_wd -> Z_add [] ; + Z_add_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Z_add_wd -> RelationClasses_eq_Reflexive [] ; + Z_add_wd -> Morphisms_reflexive_proper [] ; + Z_add_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_add_wd -> Z_eq [] ; + Z_succ_inj_wd -> Z_succ_wd [] ; + Z_succ_inj_wd -> Z_succ_inj [] ; + ConstructiveCauchyReals_bound -> ConstructiveCauchyReals_seq [] ; + ConstructiveCauchyReals_bound -> ConstructiveCauchyReals_scale [] ; + Z_add_succ_l -> Z_succ [] ; + Z_add_succ_l -> Z_Private_BootStrap_add_assoc [] ; + ConstructiveCauchyReals_CRealEq_diff -> ConstructiveCauchyReals_CRealLe_not_lt [] ; + ConstructiveCauchyReals_CRealEq_diff -> ConstructiveCauchyReals_CRealEq [] ; + ConstructiveCauchyReals_CRealEq_diff -> Qabs_Qabs_Qle_condition [] ; + Z_add_0_l -> _eq [] ; + Z_add_0_l -> Z_add [] ; + Z_add_0_l -> _eq_refl [] ; + Qabs_Qabs_Qle_condition -> Qabs_Qle_Qabs [] ; + Qabs_Qabs_Qle_condition -> Qfield_Qopp_opp [] ; + Qabs_Qabs_Qle_condition -> Qabs_Qabs_opp [] ; + Z_Private_BootStrap_add_assoc -> Z_Private_BootStrap_add_assoc_pos [] ; + ConstructiveCauchyRealsMult_CReal_mult_seq -> Z_sub [] ; + ConstructiveCauchyRealsMult_CReal_mult_seq -> ConstructiveCauchyReals_seq [] ; + ConstructiveCauchyRealsMult_CReal_mult_seq -> ConstructiveCauchyReals_scale [] ; + Z_Private_BootStrap_add_comm -> Z_add [] ; + Z_Private_BootStrap_add_comm -> Pos_add_comm [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> VarMap_find [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> VarMap_Empty [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> VarMap_Elt [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> VarMap_Branch [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> Qpower_Qpower_plus [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> ConstructiveCauchyReals_bound [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> ConstructiveCauchyRealsMult_CReal_mult_seq [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> ConstructiveCauchyRealsMult_CReal_mult_scale [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> Qabs_Qabs_nonneg [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> Qabs_Qabs_Qmult [] ; + ConstructiveCauchyRealsMult_CReal_mult_bound -> QArith_base_Qmult_lt_compat_nonneg [] ; + Pos_add_comm -> _eq_ind_r [] ; + Pos_add_comm -> PosDef_Pos_add_carry [] ; + Pos_add_comm -> Pos_add_carry_spec [] ; + ConstructiveCauchyRealsMult_CReal_mult_scale -> ConstructiveCauchyReals_scale [] ; + _positive_ind -> _positive [] ; + _positive_ind -> _xO [] ; + _positive_ind -> _xH [] ; + _positive_ind -> _xI [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> QArith_base_Qle_lt_trans [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> QArith_base_Qplus_lt_le_compat [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> VarMap_find [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> VarMap_Empty [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> VarMap_Elt [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> VarMap_Branch [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> ZMicromega_ZTautoChecker_sound [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> Qpower_Qpower_0_lt [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> Qpower_Qpower_plus [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> Qabs_Qabs_triangle [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> Qabs_Qabs_wd_Proper [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> QArith_base_Qmult_le_compat_r [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> ConstructiveCauchyReals_cauchy [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> QArith_base_Qmult_lt_l [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> ConstructiveCauchyReals_bound [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> ConstructiveCauchyRealsMult_CReal_mult_seq [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> Qabs_Qabs_nonneg [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> Qpower_Qpower_0_r [] ; + ConstructiveCauchyRealsMult_CReal_mult_cauchy -> Qabs_Qabs_Qmult [] ; + PosDef_Pos_add_carry -> PosDef_Pos_succ [] ; + Qabs_Qabs_nonneg -> Qabs_Qabs_case [] ; + Qabs_Qabs_nonneg -> QArith_base_Qopp_le_compat [] ; + Pos_add_carry_spec -> Pos_add [] ; + Pos_add_carry_spec -> _f_equal [] ; + Pos_add_carry_spec -> _eq_trans [] ; + Pos_add_carry_spec -> _positive_ind [] ; + Pos_add_carry_spec -> Pos_add_carry [] ; + Qpower_Qpower_0_r -> QArith_base_Qpower [] ; + Qpower_Qpower_0_r -> QArith_base_Q_Setoid [] ; + Pos_add_carry -> Pos_succ [] ; + Qabs_Qabs_Qmult -> Qabs_Qabs [] ; + Qabs_Qabs_Qmult -> QArith_base_Qmult [] ; + Qabs_Qabs_Qmult -> QArith_base_Q_Setoid [] ; + Qabs_Qabs_Qmult -> Z_abs_mul [] ; + Z_Private_BootStrap_opp_inj -> Z_opp [] ; + Z_Private_BootStrap_opp_inj -> _False_ind [] ; + Z_Private_BootStrap_opp_inj -> _eq_ind [] ; + Z_Private_BootStrap_opp_inj -> _True [] ; + Z_Private_BootStrap_opp_inj -> _I [] ; + Z_Private_BootStrap_opp_inj -> _f_equal [] ; + Z_Private_BootStrap_opp_inj -> _eq_trans [] ; + QArith_base_Qmult_lt_compat_nonneg -> QArith_base_Qlt [] ; + QArith_base_Qmult_lt_compat_nonneg -> QArith_base_Qmult [] ; + QArith_base_Qmult_lt_compat_nonneg -> QArith_base_Qle [] ; + QArith_base_Qmult_lt_compat_nonneg -> _ring_subst_niter [] ; + QArith_base_Qmult_lt_compat_nonneg -> Pos2Z_inj_mul [] ; + QArith_base_Qmult_lt_compat_nonneg -> Z_mul_le_mono_nonneg [] ; + QArith_base_Qmult_lt_compat_nonneg -> _Zr_ring_lemma1 [] ; + QArith_base_Qmult_lt_compat_nonneg -> Pos2Z_is_nonneg [] ; + QArith_base_Qmult_lt_compat_nonneg -> RelationClasses_impl_Reflexive [] ; + QArith_base_Qmult_lt_compat_nonneg -> RelationClasses_inverse_impl_rewrite_relation [] ; + QArith_base_Qmult_lt_compat_nonneg -> RelationClasses_flip_Reflexive [] ; + RelationClasses_impl_Reflexive -> RelationClasses_Reflexive [] ; + RelationClasses_impl_Reflexive -> RelationClasses_impl_Reflexive_obligation_1 [] ; + Z_Private_BootStrap_add_assoc_pos -> Z_Private_BootStrap_add_comm [] ; + Z_Private_BootStrap_add_assoc_pos -> Z_Private_BootStrap_opp_inj [] ; + Z_Private_BootStrap_add_assoc_pos -> Z_Private_BootStrap_opp_add_distr [] ; + Z_Private_BootStrap_add_assoc_pos -> Z_Private_BootStrap_pos_sub_add [] ; + Z_Private_BootStrap_add_assoc_pos -> Z_Private_BootStrap_add_0_r [] ; + Z_Private_BootStrap_opp_add_distr -> Z_add [] ; + Z_Private_BootStrap_opp_add_distr -> Z_pos_sub_opp [] ; + RelationClasses_inverse_impl_rewrite_relation -> Basics_flip [] ; + RelationClasses_inverse_impl_rewrite_relation -> Basics_impl [] ; + RelationClasses_inverse_impl_rewrite_relation -> RelationClasses_RewriteRelation [] ; + RelationClasses_inverse_impl_rewrite_relation -> RelationClasses_Build_RewriteRelation [] ; + Z_pos_sub_opp -> Z_pos_sub [] ; + Z_pos_sub_opp -> Z_opp [] ; + Z_pos_sub_opp -> _eq_ind [] ; + Z_pos_sub_opp -> _eq_refl [] ; + Z_pos_sub_opp -> _positive_ind [] ; + RelationClasses_flip_Reflexive -> Basics_flip [] ; + RelationClasses_flip_Reflexive -> RelationClasses_Reflexive [] ; + RelationClasses_impl_Reflexive_obligation_1 -> Basics_impl [] ; + Pos_add_assoc -> Pos_add_1_l [] ; + Pos_add_assoc -> Pos_add_succ_l [] ; + Z_Private_BootStrap_pos_sub_add -> Z_add [] ; + Z_Private_BootStrap_pos_sub_add -> RelationClasses_eq_equivalence [] ; + Z_Private_BootStrap_pos_sub_add -> Pos_lt_gt [] ; + Z_Private_BootStrap_pos_sub_add -> Pos_add_sub_assoc [] ; + Z_Private_BootStrap_pos_sub_add -> PosDef_Pos_sub [] ; + Z_Private_BootStrap_pos_sub_add -> Pos_sub_add_distr [] ; + Z_Private_BootStrap_pos_sub_add -> RelationClasses_equivalence_rewrite_relation [] ; + Z_Private_BootStrap_pos_sub_add -> Morphisms_rewrite_relation_eq_dom [] ; + Z_Private_BootStrap_pos_sub_add -> Pos_add_sub [] ; + Z_Private_BootStrap_pos_sub_add -> Morphisms_reflexive_proper [] ; + Z_Private_BootStrap_pos_sub_add -> Pos_sub_sub_distr [] ; + Z_Private_BootStrap_pos_sub_add -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_Private_BootStrap_pos_sub_add -> Z_pos_sub_spec [] ; + ConstructiveCauchyReals_CReal_plus_proper_r -> ConstructiveCauchyReals_CRealEq_trans [] ; + ConstructiveCauchyReals_CReal_plus_proper_r -> ConstructiveCauchyReals_CReal_plus_comm [] ; + ConstructiveCauchyReals_CReal_plus_proper_r -> ConstructiveCauchyReals_CReal_plus_lt_reg_l [] ; + Z_Private_BootStrap_add_0_r -> _eq [] ; + Z_Private_BootStrap_add_0_r -> Z_add [] ; + Z_Private_BootStrap_add_0_r -> _eq_refl [] ; + Qround_Qlt_floor -> QArith_base_Qlt [] ; + Qround_Qlt_floor -> _ring_subst_niter [] ; + Qround_Qlt_floor -> _Zr_ring_lemma1 [] ; + Qround_Qlt_floor -> _Zr_ring_lemma2 [] ; + Qround_Qlt_floor -> Z_mod_pos_bound [] ; + Qround_Qlt_floor -> QArith_base_inject_Z [] ; + Qround_Qlt_floor -> Qround_Qfloor [] ; + Qround_Qlt_floor -> Z_lt_add_lt_sub_r [] ; + Qround_Qlt_floor -> _Z_div_mod_eq_full [] ; + Pos_lt_gt -> Pos_gt_lt_iff [] ; + QArith_base_inject_Z -> _xH [] ; + QArith_base_inject_Z -> QArith_base_Q [] ; + QArith_base_inject_Z -> QArith_base_Qmake [] ; + _eq_rec_r -> _eq_sym [] ; + _eq_rec_r -> _eq_rec [] ; + Pos_add_compare_mono_r -> Pos_add_compare_mono_l [] ; + Pos_add_sub_assoc -> Pos_lt_add_r [] ; + Pos_add_sub_assoc -> Pos_sub_add [] ; + Qround_Qfloor_le -> QArith_base_Qle [] ; + Qround_Qfloor_le -> _ring_subst_niter [] ; + Qround_Qfloor_le -> _Zr_ring_lemma1 [] ; + Qround_Qfloor_le -> Z_mul_div_le [] ; + Qround_Qfloor_le -> QArith_base_inject_Z [] ; + Qround_Qfloor_le -> Qround_Qfloor [] ; + PosDef_Pos_sub -> PosDef_Pos_sub_mask [] ; + Qround_Qfloor -> QArith_base_Q [] ; + Qround_Qfloor -> Z_div [] ; + Pos_sub_add_distr -> Pos_lt_add_r [] ; + Pos_sub_add_distr -> Pos_sub_add [] ; + Pos_sub_add_distr -> Pos_add_lt_mono_r [] ; + Z_lt_add_lt_sub_r -> Z_add_simpl_r [] ; + Z_lt_add_lt_sub_r -> Z_sub_lt_mono_r [] ; + Pos_lt_add_r -> Pos_lt_trans [] ; + Pos_lt_add_r -> Pos_add_lt_mono_l [] ; + Pos_lt_add_r -> Pos_lt_succ_diag_r [] ; + _Z_div_mod_eq_full -> Z_eq_dec [] ; + _Z_div_mod_eq_full -> Z_div_mod [] ; + Z_sub_lt_mono_r -> Z_add_lt_mono_r [] ; + Z_sub_lt_mono_r -> Z_add_opp_r [] ; + RelationClasses_equivalence_rewrite_relation -> RelationClasses_Equivalence [] ; + RelationClasses_equivalence_rewrite_relation -> RelationClasses_RewriteRelation [] ; + RelationClasses_equivalence_rewrite_relation -> RelationClasses_Build_RewriteRelation [] ; + Pos_lt_trans -> Morphisms_subrelation_proper [] ; + Pos_lt_trans -> Morphisms_reflexive_reflexive_proxy [] ; + Pos_lt_trans -> Morphisms_subrelation_refl [] ; + Pos_lt_trans -> Morphisms_Reflexive_partial_app_morphism [] ; + Pos_lt_trans -> Morphisms_iff_flip_impl_subrelation [] ; + Pos_lt_trans -> Morphisms_reflexive_proper_proxy [] ; + Pos_lt_trans -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + Pos_lt_trans -> Morphisms_subrelation_respectful [] ; + Pos_lt_trans -> _tt [] ; + Pos_lt_trans -> Morphisms_impl_pars [] ; + Pos_lt_trans -> Pos_lt_iff_add [] ; + ConstructiveCauchyReals_CReal_opp_bound -> VarMap_find [] ; + ConstructiveCauchyReals_CReal_opp_bound -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyReals_CReal_opp_bound -> VarMap_Empty [] ; + ConstructiveCauchyReals_CReal_opp_bound -> VarMap_Elt [] ; + ConstructiveCauchyReals_CReal_opp_bound -> VarMap_Branch [] ; + ConstructiveCauchyReals_CReal_opp_bound -> Qabs_Qabs_Qlt_condition [] ; + ConstructiveCauchyReals_CReal_opp_bound -> ConstructiveCauchyReals_bound [] ; + ConstructiveCauchyReals_CReal_opp_bound -> ConstructiveCauchyReals_CReal_opp_scale [] ; + ConstructiveCauchyReals_CReal_opp_bound -> ConstructiveCauchyReals_CReal_opp_seq [] ; + Pos_sub_add -> Pos_sub [] ; + Pos_sub_add -> Pos_sub_mask_pos [] ; + ConstructiveCauchyReals_CReal_opp_scale -> ConstructiveCauchyReals_scale [] ; + Morphisms_rewrite_relation_eq_dom -> _eq [] ; + Morphisms_rewrite_relation_eq_dom -> Morphisms_respectful [] ; + Morphisms_rewrite_relation_eq_dom -> RelationClasses_RewriteRelation [] ; + Morphisms_rewrite_relation_eq_dom -> RelationClasses_Build_RewriteRelation [] ; + ConstructiveCauchyReals_CReal_opp_cauchy -> VarMap_find [] ; + ConstructiveCauchyReals_CReal_opp_cauchy -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyReals_CReal_opp_cauchy -> VarMap_Empty [] ; + ConstructiveCauchyReals_CReal_opp_cauchy -> VarMap_Elt [] ; + ConstructiveCauchyReals_CReal_opp_cauchy -> VarMap_Branch [] ; + ConstructiveCauchyReals_CReal_opp_cauchy -> ZMicromega_ZTautoChecker_sound [] ; + ConstructiveCauchyReals_CReal_opp_cauchy -> ConstructiveCauchyReals_cauchy [] ; + ConstructiveCauchyReals_CReal_opp_cauchy -> Qabs_Qabs_Qlt_condition [] ; + ConstructiveCauchyReals_CReal_opp_cauchy -> ConstructiveCauchyReals_CReal_opp_seq [] ; + Pos_add_sub -> Pos_lt_add_r [] ; + Pos_add_sub -> Pos_sub_add [] ; + ConstructiveCauchyReals_CReal_opp_seq -> ConstructiveCauchyReals_seq [] ; + CRelationClasses_subrelation -> CRelationClasses_crelation [] ; + Pos_add_lt_mono_r -> _iff_refl [] ; + Pos_add_lt_mono_r -> Pos_add_compare_mono_r [] ; + Pos_add_lt_mono_r -> Pos_lt [] ; + Morphisms_reflexive_proper -> Morphisms_Proper [] ; + Morphisms_reflexive_proper -> Morphisms_ReflexiveProxy [] ; + _prod_rect -> _prod [] ; + _prod_rect -> _pair [] ; + Pos_compare_spec -> Morphisms_iff_impl_subrelation [] ; + Pos_compare_spec -> _CompareSpec [] ; + Pos_compare_spec -> Pos_compare_eq_iff [] ; + Pos_compare_spec -> Pos_compare_lt_iff [] ; + Pos_compare_spec -> Pos_compare_antisym [] ; + Pos_compare_spec -> _CompOpp_iff [] ; + Pos_compare_spec -> _CompEq [] ; + Pos_compare_spec -> _CompLt [] ; + Pos_compare_spec -> _CompGt [] ; + ConstructiveCauchyReals_CRealEq_rel_Symmetric -> RelationClasses_Symmetric [] ; + ConstructiveCauchyReals_CRealEq_rel_Symmetric -> ConstructiveCauchyReals_CRealEq_sym [] ; + Pos_compare -> _Eq [] ; + Pos_compare -> Pos_compare_cont [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyReals_CRealEq_refl [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyReals_CReal_minus [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyReals_CReal_plus_proper_r [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyReals_CRealEq_rel_Symmetric [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyReals_CRealEq_rel_Transitive [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyReals_CReal_plus_opp_r [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyRealsMult_CReal_mult_comm [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyReals_CReal_plus_assoc [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyReals_CReal_plus_0_l [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyRealsMult_CReal_mult_1_l [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyReals_CReal_plus_proper_l [] ; + ConstructiveCauchyRealsMult_CReal_isRing -> ConstructiveCauchyRealsMult_CReal_mult_assoc [] ; + Pos_sub_sub_distr -> Pos_sub_add [] ; + Pos_sub_sub_distr -> Pos_add_lt_mono_r [] ; + ConstructiveCauchyReals_CRealEq_rel_Reflexive -> ConstructiveCauchyReals_CRealEq_refl [] ; + Morphisms_reflexive_eq_dom_reflexive -> Morphisms_respectful [] ; + Morphisms_reflexive_eq_dom_reflexive -> RelationClasses_Reflexive [] ; + Morphisms_reflexive_eq_dom_reflexive -> _eq_ind_r [] ; + ConstructiveCauchyReals_CReal_plus_morph_Proper -> ConstructiveCauchyReals_CReal_plus_proper_r [] ; + Z_pos_sub_spec -> Z_pos_sub [] ; + Z_pos_sub_spec -> Pos_compare_spec [] ; + Z_pos_sub_spec -> Pos_sub_mask_diag [] ; + Z_pos_sub_spec -> Pos_compare_xI_xI [] ; + Z_pos_sub_spec -> Pos_compare_xO_xO [] ; + Z_pos_sub_spec -> Pos_sub_xI_xI [] ; + Z_pos_sub_spec -> Pos_sub_xI_xO [] ; + Z_pos_sub_spec -> Pos_sub_xO_xI [] ; + Z_pos_sub_spec -> Pos_sub_xO_xO [] ; + ConstructiveCauchyRealsMult_CReal_mult_morph_Proper -> ConstructiveCauchyRealsMult_CReal_isRingExt [] ; + Pos_gt -> _eq [] ; + Pos_gt -> Pos_compare [] ; + ConstructiveCauchyReals_CRealEq_rel_Transitive -> ConstructiveCauchyReals_CRealEq_trans [] ; + Pos_lt -> _eq [] ; + Pos_lt -> Pos_compare [] ; + ConstructiveCauchyRealsMult_CReal_opp_morph_Proper -> ConstructiveCauchyRealsMult_CReal_isRingExt [] ; + _CompareSpec -> _Eq [] ; + _CompareSpec -> _Lt [] ; + _CompareSpec -> _Gt [] ; + Ring_polynom_ring_rw_correct -> Ring_polynom_norm_subst_ok [] ; + Ring_polynom_ring_rw_correct -> Ring_polynom_Pphi_dev_ok [] ; + RelationClasses_RewriteRelation -> Relation_Definitions_relation [] ; + Ring_polynom_Pphi_dev_ok -> Ring_polynom_Pphi_avoid_ok [] ; + Ring_polynom_Pphi_dev_ok -> Ring_polynom_Pphi_dev [] ; + Ring_polynom_Pphi_dev_ok -> Ring_polynom_mkopp_pow_ok [] ; + Ring_polynom_Pphi_dev_ok -> Ring_polynom_mkpow_ok [] ; + Pos_sub -> Pos_sub_mask [] ; + Ring_polynom_mkmult_pow -> _positive [] ; + Pos_sub_mask_diag -> Pos_sub_mask_nul_iff [] ; + Ring_polynom_mkmult_pow_ok -> _pow_pos [] ; + Ring_polynom_mkmult_pow_ok -> Morphisms_reflexive_reflexive_proxy [] ; + Ring_polynom_mkmult_pow_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Ring_polynom_mkmult_pow_ok -> Morphisms_eq_proper_proxy [] ; + Ring_polynom_mkmult_pow_ok -> RelationClasses_Equivalence_PER [] ; + Ring_polynom_mkmult_pow_ok -> Morphisms_reflexive_proper_proxy [] ; + Ring_polynom_mkmult_pow_ok -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Ring_polynom_mkmult_pow_ok -> _positive_ind [] ; + Ring_polynom_mkmult_pow_ok -> Ring_polynom_rmul_ext_Proper [] ; + Ring_polynom_mkmult_pow_ok -> Setoid_Seq_refl [] ; + Ring_polynom_mkmult_pow_ok -> _ARmul_assoc [] ; + Ring_polynom_mkmult_pow_ok -> Ring_polynom_mkmult_pow [] ; + Pos_sub_mask -> Pos_succ_double_mask [] ; + Pos_sub_mask -> Pos_double_mask [] ; + Pos_sub_mask -> Pos_double_pred_mask [] ; + Ring_polynom_mkpow -> Pos_pred_double [] ; + Ring_polynom_mkpow -> Ring_polynom_mkmult_pow [] ; + Pos_pred_double -> _positive [] ; + Pos_pred_double -> _xO [] ; + Pos_pred_double -> _xH [] ; + Pos_pred_double -> _xI [] ; + Ring_polynom_mkopp_pow -> Pos_pred_double [] ; + Ring_polynom_mkopp_pow -> Ring_polynom_mkmult_pow [] ; + Ring_polynom_mkopp_pow_ok -> Pos_succ_pred_double [] ; + Ring_polynom_mkopp_pow_ok -> Ring_polynom_ropp_ext_Proper [] ; + Ring_polynom_mkopp_pow_ok -> Ring_polynom_pow_pos_add [] ; + Ring_polynom_mkopp_pow_ok -> _ARopp_mul_l [] ; + Ring_polynom_mkopp_pow_ok -> Ring_polynom_mkmult_pow_ok [] ; + Ring_polynom_mkopp_pow_ok -> Ring_polynom_mkopp_pow [] ; + Pos_compare_xI_xI -> _eq [] ; + Pos_compare_xI_xI -> _xI [] ; + Pos_compare_xI_xI -> _eq_refl [] ; + Pos_compare_xI_xI -> Pos_compare [] ; + Ring_polynom_mkpow_ok -> Pos_succ_pred_double [] ; + Ring_polynom_mkpow_ok -> Ring_polynom_pow_pos_add [] ; + Ring_polynom_mkpow_ok -> Ring_polynom_mkmult_pow_ok [] ; + Ring_polynom_mkpow_ok -> Ring_polynom_mkpow [] ; + Pos_compare_xI_xO -> Pos_compare_cont_spec [] ; + Pos_compare_xO_xI -> Pos_compare_cont_spec [] ; + ConstructiveCauchyRealsMult_CReal_isRingExt -> ConstructiveCauchyReals_CReal_plus_morph [] ; + ConstructiveCauchyRealsMult_CReal_isRingExt -> ConstructiveCauchyRealsMult_CReal_mult_proper_l [] ; + ConstructiveCauchyRealsMult_CReal_isRingExt -> ConstructiveCauchyRealsMult_CReal_mult_comm [] ; + Pos_compare_xO_xO -> _eq [] ; + Pos_compare_xO_xO -> _xO [] ; + Pos_compare_xO_xO -> _eq_refl [] ; + Pos_compare_xO_xO -> Pos_compare [] ; + ConstructiveCauchyReals_CReal_plus_morph -> ConstructiveCauchyReals_CReal_plus_morph_Proper [] ; + Pos_succ_double_mask -> _xH [] ; + Pos_succ_double_mask -> _xI [] ; + Pos_succ_double_mask -> Pos_mask [] ; + Pos_succ_double_mask -> Pos_IsPos [] ; + Pos_succ_double_mask -> Pos_IsNeg [] ; + ConstructiveCauchyReals_CReal_plus_opp_r -> ConstructiveCauchyReals_CReal_plus [] ; + ConstructiveCauchyReals_CReal_plus_opp_r -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyReals_CReal_plus_opp_r -> ConstructiveCauchyReals_inject_Q [] ; + ConstructiveCauchyReals_CReal_plus_opp_r -> ConstructiveCauchyReals_CReal_opp [] ; + ConstructiveCauchyReals_CReal_plus_opp_r -> ConstructiveCauchyReals_CRealEq_diff [] ; + Pos_sub_xI_xI -> Pos_sub [] ; + Pos_sub_xI_xI -> Pos_sub_mask_pos [] ; + ConstructiveCauchyReals_CReal_plus_eq_reg_l -> ConstructiveCauchyReals_CRealEq [] ; + ConstructiveCauchyReals_CReal_plus_eq_reg_l -> ConstructiveCauchyReals_CReal_plus_lt_compat_l [] ; + Pos_sub_xI_xO -> Pos_sub [] ; + Pos_sub_xI_xO -> Pos_sub_mask_pos [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_l -> ConstructiveCauchyReals_CRealEq_rel_Reflexive [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_l -> ConstructiveCauchyReals_CReal_plus_morph_Proper [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_l -> ConstructiveCauchyReals_CReal_plus_opp_l [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_l -> ConstructiveCauchyRealsMult_CReal_opp_mult_distr_r [] ; + Pos_sub_xO_xI -> Pos_sub [] ; + Pos_sub_xO_xI -> Pos_sub_mask_carry_spec [] ; + ConstructiveCauchyRealsMult_CReal_mult_comm -> Qfield_Qfield_ring_lemma2 [] ; + ConstructiveCauchyRealsMult_CReal_mult_comm -> QArith_base_Qlt_not_le [] ; + ConstructiveCauchyRealsMult_CReal_mult_comm -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyRealsMult_CReal_mult_comm -> ConstructiveCauchyReals_CRealEq [] ; + ConstructiveCauchyRealsMult_CReal_mult_comm -> ConstructiveCauchyRealsMult_CReal_mult [] ; + Pos_sub_xO_xO -> Pos_sub [] ; + Pos_sub_xO_xO -> Pos_sub_mask_pos [] ; + ConstructiveCauchyReals_CReal_plus_opp_l -> ConstructiveCauchyReals_CReal_plus_comm [] ; + ConstructiveCauchyReals_CReal_plus_opp_l -> ConstructiveCauchyReals_CRealEq_rel_Transitive [] ; + ConstructiveCauchyReals_CReal_plus_opp_l -> ConstructiveCauchyReals_CReal_plus_opp_r [] ; + Pos_switch_Eq -> _comparison [] ; + Pos_switch_Eq -> _Lt [] ; + Pos_switch_Eq -> _Gt [] ; + ConstructiveCauchyReals_CRealEq_rel -> ConstructiveCauchyReals_CRealEq_sym [] ; + ConstructiveCauchyReals_CRealEq_rel -> ConstructiveCauchyReals_CRealEq_trans [] ; + ConstructiveCauchyReals_CRealEq_rel -> ConstructiveCauchyReals_CRealEq_refl [] ; + Pos_mask -> _positive [] ; + ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l -> ConstructiveCauchyReals_CReal_plus [] ; + ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l -> ConstructiveCauchyRealsMult_CReal_mult [] ; + ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l -> ConstructiveCauchyReals_CRealEq_diff [] ; + ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l -> QArith_base_Qmult_le_compat_nonneg [] ; + ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l -> ConstructiveCauchyRealsMult_Weaken_Qle_QpowerAddExp [] ; + ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l -> Z_max_comm [] ; + ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l -> ConstructiveCauchyRealsMult_CReal_red_scale [] ; + Pos_IsNul -> _positive [] ; + ConstructiveCauchyRealsMult_CReal_opp_mult_distr_r -> ConstructiveCauchyReals_CRealEq_rel_Symmetric [] ; + ConstructiveCauchyRealsMult_CReal_opp_mult_distr_r -> ConstructiveCauchyReals_CRealEq_rel_Transitive [] ; + ConstructiveCauchyRealsMult_CReal_opp_mult_distr_r -> ConstructiveCauchyReals_CReal_plus_opp_r [] ; + ConstructiveCauchyRealsMult_CReal_opp_mult_distr_r -> ConstructiveCauchyReals_CReal_plus_eq_reg_l [] ; + ConstructiveCauchyRealsMult_CReal_opp_mult_distr_r -> ConstructiveCauchyReals_CRealEq_rel [] ; + ConstructiveCauchyRealsMult_CReal_opp_mult_distr_r -> ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l [] ; + ConstructiveCauchyRealsMult_CReal_opp_mult_distr_r -> ConstructiveCauchyRealsMult_CReal_mult_proper_0_l [] ; + Pos_sub_mask_pos -> Pos_sub_mask_pos_ [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_0_l -> Qpower_Qpower_minus_pos [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_0_l -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_0_l -> ConstructiveCauchyReals_inject_Q [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_0_l -> ConstructiveCauchyRealsMult_CReal_mult [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_0_l -> ConstructiveCauchyReals_CRealEq_diff [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_0_l -> QArith_base_Qmult_le_compat_nonneg [] ; + ConstructiveCauchyRealsMult_CReal_mult_proper_0_l -> ConstructiveCauchyRealsMult_Weaken_Qle_QpowerFac [] ; + Pos_double_mask -> _xO [] ; + Pos_double_mask -> Pos_mask [] ; + Pos_double_mask -> Pos_IsNul [] ; + Pos_double_mask -> Pos_IsPos [] ; + Pos_double_mask -> Pos_IsNeg [] ; + QArith_base_Qmult_le_compat_nonneg -> QArith_base_Qmult [] ; + QArith_base_Qmult_le_compat_nonneg -> QArith_base_Qle [] ; + QArith_base_Qmult_le_compat_nonneg -> _ring_subst_niter [] ; + QArith_base_Qmult_le_compat_nonneg -> Pos2Z_inj_mul [] ; + QArith_base_Qmult_le_compat_nonneg -> Z_mul_le_mono_nonneg [] ; + QArith_base_Qmult_le_compat_nonneg -> _Zr_ring_lemma1 [] ; + QArith_base_Qmult_le_compat_nonneg -> Pos2Z_is_nonneg [] ; + QArith_base_Qmult_le_compat_nonneg -> RelationClasses_PreOrder_Transitive [] ; + QArith_base_Qmult_le_compat_nonneg -> Z_Proper_instance_0 [] ; + Pos_IsPos -> _positive [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerFac -> VarMap_find [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerFac -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerFac -> VarMap_Empty [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerFac -> VarMap_Elt [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerFac -> VarMap_Branch [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerFac -> Qpower_Qpower_0_le [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerFac -> QArith_base_Qmult_le_compat_r [] ; + Pos_IsNeg -> _positive [] ; + RelationClasses_PreOrder_Transitive -> RelationClasses_PreOrder [] ; + Pos_sub_mask_pos_ -> Morphisms_subrelation_proper [] ; + Pos_sub_mask_pos_ -> Morphisms_reflexive_reflexive_proxy [] ; + Pos_sub_mask_pos_ -> Morphisms_subrelation_refl [] ; + Pos_sub_mask_pos_ -> Morphisms_iff_flip_impl_subrelation [] ; + Pos_sub_mask_pos_ -> Morphisms_reflexive_proper_proxy [] ; + Pos_sub_mask_pos_ -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + Pos_sub_mask_pos_ -> Morphisms_subrelation_respectful [] ; + Pos_sub_mask_pos_ -> _tt [] ; + Pos_sub_mask_pos_ -> Pos_lt_iff_add [] ; + Pos_sub_mask_pos_ -> Pos_sub_mask_pos_iff [] ; + Z_Proper_instance_0 -> Z_Private_Tac_eq_le [] ; + Z_Proper_instance_0 -> Z_Private_Tac_eq_lt [] ; + Z_Proper_instance_0 -> Z_Private_Tac_le_eq [] ; + Z_Proper_instance_0 -> Z_Private_Tac_lt_eq [] ; + Z_Proper_instance_0 -> Z_Private_Tac_le_lt_trans [] ; + Z_Proper_instance_0 -> Z_Private_Tac_lt_irrefl [] ; + Z_Proper_instance_0 -> Z_Private_Tac_eq_sym [] ; + Z_Proper_instance_0 -> Z_Private_Tac_not_gt_le [] ; + Pos_lt_iff_add -> RelationClasses_Equivalence_PER [] ; + Pos_lt_iff_add -> RelationClasses_iff_equivalence [] ; + Pos_lt_iff_add -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Pos_lt_iff_add -> Pos_lt [] ; + Pos_lt_iff_add -> Pos_compare_sub_mask [] ; + Pos_lt_iff_add -> Pos_sub_mask_neg_iff [] ; + Z_Private_Tac_eq_le -> Z_Private_Tac_trans [] ; + Pos_sub_mask_pos_iff -> Pos_sub_mask_add_diag_l [] ; + Pos_sub_mask_pos_iff -> Pos_sub_mask_add [] ; + Z_Private_Tac_eq_lt -> Z_Private_Tac_trans [] ; + Pos_sub_mask_add_diag_l -> Pos_sub_mask_spec [] ; + Pos_sub_mask_add_diag_l -> Pos_add_cancel_l [] ; + Z_Private_Tac_le_eq -> Z_Private_Tac_trans [] ; + Pos_sub_mask_add -> _False_ind [] ; + Pos_sub_mask_add -> _True [] ; + Pos_sub_mask_add -> _I [] ; + Pos_sub_mask_add -> Pos_sub_mask_spec [] ; + Pos_sub_mask_add -> PosDef_Pos_IsNul [] ; + Pos_sub_mask_add -> PosDef_Pos_IsNeg [] ; + Z_Private_Tac_lt_eq -> Z_Private_Tac_trans [] ; + Pos_sub_mask_spec -> Pos_SubMaskSpec [] ; + Pos_sub_mask_spec -> Pos_add_xI_pred_double [] ; + Pos_sub_mask_spec -> Pos_sub_mask_carry_spec [] ; + Pos_sub_mask_spec -> Pos_SubIsNul [] ; + Pos_sub_mask_spec -> Pos_SubIsPos [] ; + Pos_sub_mask_spec -> Pos_SubIsNeg [] ; + Z_Private_Tac_le_lt_trans -> Z_Private_Tac_trans [] ; + Pos_SubMaskSpec -> _eq [] ; + Pos_SubMaskSpec -> Pos_add [] ; + Pos_SubMaskSpec -> Pos_IsNul [] ; + Pos_SubMaskSpec -> Pos_IsPos [] ; + Pos_SubMaskSpec -> Pos_IsNeg [] ; + Z_Private_Tac_lt_irrefl -> RelationClasses_StrictOrder_Irreflexive [] ; + Z_Private_Tac_lt_irrefl -> Z_lt_strorder [] ; + PosDef_Pos_IsNul -> _positive [] ; + Z_Private_Tac_eq_sym -> RelationClasses_Equivalence_Symmetric [] ; + Z_Private_Tac_eq_sym -> RelationClasses_symmetry [] ; + Z_Private_Tac_eq_sym -> Z_eq_equiv [] ; + PosDef_Pos_IsNeg -> _positive [] ; + Z_Private_Tac_not_gt_le -> Z_lt_total [] ; + Z_Private_Tac_not_gt_le -> Z_le_lteq [] ; + Z_Private_Tac_trans -> OrdersTac_OEQ [] ; + Z_Private_Tac_trans -> RelationClasses_StrictOrder_Transitive [] ; + Z_Private_Tac_trans -> OrdersTac_trans_ord [] ; + Z_Private_Tac_trans -> Z_le_lteq [] ; + Z_Private_Tac_trans -> Z_lt_strorder [] ; + Z_Private_Tac_trans -> Z_lt_compat [] ; + Z_Private_Tac_trans -> Z_Private_Tac_interp_ord [] ; + Pos_add_xI_pred_double -> Pos_add_assoc [] ; + Pos_add_xI_pred_double -> Pos_succ_pred_double [] ; + Pos_sub_mask_carry_spec -> _eq_ind_r [] ; + Pos_sub_mask_carry_spec -> _positive_ind [] ; + Pos_sub_mask_carry_spec -> Pos_sub_mask [] ; + Pos_sub_mask_carry_spec -> Pos_pred_mask [] ; + Pos_sub_mask_carry_spec -> Pos_sub_mask_carry [] ; + Z_Private_Tac_interp_ord -> Z_le [] ; + Z_Private_Tac_interp_ord -> Z_lt [] ; + Z_Private_Tac_interp_ord -> OrdersTac_ord [] ; + Pos_succ_pred_double -> Pos_succ [] ; + Pos_succ_pred_double -> _f_equal [] ; + Pos_succ_pred_double -> _eq_trans [] ; + Pos_succ_pred_double -> _positive_ind [] ; + Pos_succ_pred_double -> Pos_pred_double [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerAddExp -> VarMap_find [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerAddExp -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerAddExp -> VarMap_Empty [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerAddExp -> VarMap_Elt [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerAddExp -> VarMap_Branch [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerAddExp -> ZMicromega_ZTautoChecker_sound [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerAddExp -> Qpower_Qpower_le_compat_l [] ; + Z_max_comm -> Z_max_spec [] ; + Z_max_comm -> Z_Private_Tac_le_lt_trans [] ; + Z_max_comm -> Z_Private_Tac_lt_irrefl [] ; + Z_max_comm -> Z_Private_Tac_not_gt_le [] ; + Z_max_comm -> Z_Private_Tac_lt_trans [] ; + Pos_add_succ_r -> _eq_ind_r [] ; + Pos_add_succ_r -> PosDef_Pos_add_carry [] ; + Pos_add_succ_r -> Pos_add_carry_spec [] ; + Pos_add_succ_r -> Pos_add_1_r [] ; + Pos_add_1_l -> _eq [] ; + Pos_add_1_l -> Pos_add [] ; + Pos_add_1_l -> _eq_refl [] ; + ConstructiveCauchyRealsMult_CReal_red_scale -> ConstructiveCauchyReals_mkCReal [] ; + ConstructiveCauchyRealsMult_CReal_red_scale -> _eq_refl [] ; + ConstructiveCauchyRealsMult_CReal_red_scale -> ConstructiveCauchyReals_scale [] ; + Z_Private_Tac_lt_trans -> Z_Private_Tac_trans [] ; + Pos_add_1_r -> _eq [] ; + Pos_add_1_r -> Pos_add [] ; + Pos_add_1_r -> _eq_refl [] ; + Pos_pred_mask -> Pos_mask [] ; + Pos_pred_mask -> Pos_IsNul [] ; + Pos_pred_mask -> Pos_IsPos [] ; + Pos_pred_mask -> Pos_IsNeg [] ; + Pos_pred_mask -> Pos_pred [] ; + ConstructiveCauchyReals_CReal_plus_lt_compat_l -> ConstructiveCauchyReals_CReal_plus [] ; + ConstructiveCauchyReals_CReal_plus_lt_compat_l -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyReals_CReal_plus_lt_compat_l -> ConstructiveCauchyReals_CRealLt_above [] ; + Pos_sub_mask_carry -> Pos_succ_double_mask [] ; + Pos_sub_mask_carry -> Pos_double_mask [] ; + Pos_sub_mask_carry -> Pos_double_pred_mask [] ; + ConstructiveCauchyReals_CRealLt_above -> ConstructiveCauchyReals_CRealLt [] ; + ConstructiveCauchyReals_CRealLt_above -> ConstructiveCauchyReals_CRealLt_aboveSig_ [] ; + Pos_SubIsNul -> _eq [] ; + Pos_SubIsNul -> Pos_add [] ; + Pos_SubIsNul -> Pos_IsNul [] ; + Pos_SubIsNul -> Pos_IsPos [] ; + Pos_SubIsNul -> Pos_IsNeg [] ; + ConstructiveCauchyReals_CRealLt_aboveSig_ -> Qpower_Qpower_le_compat_l [] ; + ConstructiveCauchyReals_CRealLt_aboveSig_ -> Qpower_Qpower_minus_pos [] ; + ConstructiveCauchyReals_CRealLt_aboveSig_ -> ConstructiveCauchyReals_CRealLt_aboveSig [] ; + ConstructiveCauchyReals_CRealLt_aboveSig_ -> Z_le_min_l [] ; + Pos_SubIsPos -> _eq [] ; + Pos_SubIsPos -> Pos_add [] ; + Pos_SubIsPos -> Pos_IsNul [] ; + Pos_SubIsPos -> Pos_IsPos [] ; + Pos_SubIsPos -> Pos_IsNeg [] ; + ConstructiveCauchyReals_CRealLt_aboveSig -> ConstructiveCauchyReals_cauchy [] ; + ConstructiveCauchyReals_CRealLt_aboveSig -> QExtra_QarchimedeanExp2_Z [] ; + ConstructiveCauchyReals_CRealLt_aboveSig -> Qabs_Qabs_Qlt_condition [] ; + ConstructiveCauchyReals_CRealLt_aboveSig -> QArith_base_Qinv_lt_contravar [] ; + Pos_SubIsNeg -> _eq [] ; + Pos_SubIsNeg -> Pos_add [] ; + Pos_SubIsNeg -> Pos_IsNul [] ; + Pos_SubIsNeg -> Pos_IsPos [] ; + Pos_SubIsNeg -> Pos_IsNeg [] ; + Z_le_min_l -> Z_min_spec [] ; + Z_le_min_l -> Z_Private_Tac_lt_eq [] ; + Z_le_min_l -> Z_Private_Tac_le_lt_trans [] ; + Z_le_min_l -> Z_Private_Tac_lt_irrefl [] ; + Z_le_min_l -> Z_Private_Tac_not_gt_le [] ; + Pos_double_pred_mask -> Pos_pred_double [] ; + Pos_double_pred_mask -> Pos_mask [] ; + Pos_double_pred_mask -> Pos_IsNul [] ; + Pos_double_pred_mask -> Pos_IsPos [] ; + ConstructiveCauchyReals_CReal_plus_assoc -> ConstructiveCauchyReals_CReal_plus [] ; + ConstructiveCauchyReals_CReal_plus_assoc -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyReals_CReal_plus_assoc -> ConstructiveCauchyReals_CRealEq_diff [] ; + Pos_pred -> Pos_pred_double [] ; + ConstructiveCauchyReals_CReal_plus_0_l -> ConstructiveCauchyReals_CReal_plus [] ; + ConstructiveCauchyReals_CReal_plus_0_l -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyReals_CReal_plus_0_l -> ConstructiveCauchyReals_inject_Q [] ; + ConstructiveCauchyReals_CReal_plus_0_l -> ConstructiveCauchyReals_CRealEq_diff [] ; + Pos_add_no_neutral -> Pos_add [] ; + Pos_add_no_neutral -> _not [] ; + Pos_add_no_neutral -> _False_ind [] ; + Pos_add_no_neutral -> _eq_ind [] ; + Pos_add_no_neutral -> _True [] ; + Pos_add_no_neutral -> _I [] ; + Pos_add_no_neutral -> _f_equal [] ; + Pos_add_no_neutral -> _positive_ind [] ; + ConstructiveCauchyRealsMult_CReal_mult_1_l -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyRealsMult_CReal_mult_1_l -> ConstructiveCauchyReals_inject_Q [] ; + ConstructiveCauchyRealsMult_CReal_mult_1_l -> ConstructiveCauchyRealsMult_CReal_mult [] ; + ConstructiveCauchyRealsMult_CReal_mult_1_l -> ConstructiveCauchyReals_CRealEq_diff [] ; + ConstructiveCauchyRealsMult_CReal_mult_1_l -> ConstructiveCauchyRealsMult_CReal_red_scale [] ; + Pos_add_cancel_l -> _iff [] ; + Pos_add_cancel_l -> _conj [] ; + Pos_add_cancel_l -> Pos_add_reg_l [] ; + ConstructiveCauchyReals_CReal_plus_proper_l -> ConstructiveCauchyReals_CRealEq [] ; + ConstructiveCauchyReals_CReal_plus_proper_l -> ConstructiveCauchyReals_CReal_plus_lt_reg_l [] ; + Pos_add_reg_l -> Pos_add_comm [] ; + Pos_add_reg_l -> Pos_add_reg_r [] ; + ConstructiveCauchyRealsMult_CReal_mult_assoc -> QArith_base_Qpower_comp [] ; + ConstructiveCauchyRealsMult_CReal_mult_assoc -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyRealsMult_CReal_mult_assoc -> QArith_base_Qminus_comp [] ; + ConstructiveCauchyRealsMult_CReal_mult_assoc -> ConstructiveCauchyRealsMult_CReal_mult [] ; + ConstructiveCauchyRealsMult_CReal_mult_assoc -> ConstructiveCauchyReals_CRealEq_diff [] ; + ConstructiveCauchyRealsMult_CReal_mult_assoc -> QArith_base_Qmult_le_compat_nonneg [] ; + ConstructiveCauchyRealsMult_CReal_mult_assoc -> ConstructiveCauchyRealsMult_CReal_red_scale [] ; + ConstructiveCauchyRealsMult_CReal_mult_assoc -> ConstructiveCauchyRealsMult_Weaken_Qle_QpowerRemSubExp [] ; + Pos_add_reg_r -> Pos_add_succ_r [] ; + Pos_add_reg_r -> Pos_add_no_neutral [] ; + Pos_add_reg_r -> Pos_add_carry_add [] ; + Pos_add_reg_r -> _not_eq_sym [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerRemSubExp -> VarMap_find [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerRemSubExp -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerRemSubExp -> VarMap_Empty [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerRemSubExp -> VarMap_Elt [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerRemSubExp -> VarMap_Branch [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerRemSubExp -> ZMicromega_ZTautoChecker_sound [] ; + ConstructiveCauchyRealsMult_Weaken_Qle_QpowerRemSubExp -> Qpower_Qpower_le_compat_l [] ; + Pos_succ_inj -> _eq_sym [] ; + Pos_succ_inj -> _f_equal [] ; + Pos_succ_inj -> _eq_trans [] ; + Pos_succ_inj -> _positive_ind [] ; + Pos_succ_inj -> Pos_succ_not_1 [] ; + ConstructiveCauchyReals_CRealLt_above_same -> VarMap_find [] ; + ConstructiveCauchyReals_CRealLt_above_same -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyReals_CRealLt_above_same -> VarMap_Empty [] ; + ConstructiveCauchyReals_CRealLt_above_same -> VarMap_Elt [] ; + ConstructiveCauchyReals_CRealLt_above_same -> VarMap_Branch [] ; + ConstructiveCauchyReals_CRealLt_above_same -> ZMicromega_ZTautoChecker_sound [] ; + ConstructiveCauchyReals_CRealLt_above_same -> ConstructiveCauchyReals_cauchy [] ; + ConstructiveCauchyReals_CRealLt_above_same -> Qabs_Qabs_Qlt_condition [] ; + Pos_add_carry_add -> Pos_add_carry_spec [] ; + Pos_add_carry_add -> Pos_succ_inj [] ; + _Field_rw_pow_correct -> Ring_polynom_ring_rw_pow_correct [] ; + _Field_rw_pow_correct -> _Fnorm_FEeval_PEeval [] ; + _Field_rw_pow_correct -> _display_pow_linear [] ; + _not_eq_sym -> _eq [] ; + _not_eq_sym -> _not [] ; + _not_eq_sym -> _eq_refl [] ; + _Z_lt_le_dec -> _Z_lt_ge_dec [] ; + _Z_lt_le_dec -> Z_ge_le [] ; + _Z_lt_le_dec -> _sumbool_rec [] ; + _total_order_T -> _Rquot1 [] ; + _total_order_T -> ConstructiveCauchyReals_CRealLtForget [] ; + _total_order_T -> _Rlt_def [] ; + _total_order_T -> ConstructiveCauchyReals_CRealLt_lpo_dec [] ; + Pos_succ_not_1 -> Pos_succ [] ; + Pos_succ_not_1 -> _not [] ; + Pos_succ_not_1 -> _False_ind [] ; + Pos_succ_not_1 -> _eq_ind [] ; + Pos_succ_not_1 -> _True [] ; + Pos_succ_not_1 -> _eq_refl [] ; + Pos_succ_not_1 -> _I [] ; + Pos_mask2cmp -> _comparison [] ; + Pos_mask2cmp -> _Eq [] ; + Pos_mask2cmp -> _Lt [] ; + Pos_mask2cmp -> _Gt [] ; + Pos_mask2cmp -> Pos_mask [] ; + _Rquot1 -> ClassicalDedekindReals_DRealQuot1 [] ; + Pos_compare_sub_mask -> Pos_compare_xI_xO [] ; + Pos_compare_sub_mask -> Pos_compare_xO_xI [] ; + Pos_compare_sub_mask -> Pos_sub_mask_carry_spec [] ; + Pos_compare_sub_mask -> Pos_mask2cmp [] ; + ConstructiveCauchyReals_CRealLtForget -> ConstructiveCauchyReals_CRealLtProp [] ; + ConstructiveCauchyReals_CRealLtForget -> _ex_intro [] ; + ConstructiveCauchyReals_CRealLtForget -> ConstructiveCauchyReals_CRealLt [] ; + Pos_sub_mask_neg_iff -> _iff [] ; + Pos_sub_mask_neg_iff -> _conj [] ; + Pos_sub_mask_neg_iff -> _ex [] ; + Pos_sub_mask_neg_iff -> _ex_intro [] ; + Pos_sub_mask_neg_iff -> Pos_sub_mask_add_diag_r [] ; + _Rlt_def -> _Rlt [] ; + Pos_sub_mask_add_diag_r -> Pos_sub_mask_spec [] ; + Pos_sub_mask_add_diag_r -> Pos_add_no_neutral [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> _exist [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> VarMap_find [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> QMicromega_QTautoChecker_sound [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> VarMap_Elt [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> VarMap_Branch [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> QArith_base_Qlt_le_dec [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> ConstructiveCauchyReals_CRealLt [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> _sum [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> _inl [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> _inr [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> QArith_base_Qle_not_lt [] ; + ConstructiveCauchyReals_CRealLt_lpo_dec -> ConstructiveExtra_Z_inj_nat_id [] ; + Pos_compare_cont_spec -> _eq_ind_r [] ; + Pos_compare_cont_spec -> _positive_ind [] ; + Pos_compare_cont_spec -> Pos_compare [] ; + Pos_compare_cont_spec -> Pos_switch_Eq [] ; + QArith_base_Qle_not_lt -> QArith_base_Qlt [] ; + QArith_base_Qle_not_lt -> QArith_base_Qle [] ; + QArith_base_Qle_not_lt -> Z_le_ngt [] ; + Pos_compare_cont -> _positive [] ; + Pos_compare_cont -> _comparison [] ; + Pos_compare_cont -> _Lt [] ; + Pos_compare_cont -> _Gt [] ; + ConstructiveExtra_Z_inj_nat -> _Z [] ; + ConstructiveExtra_Z_inj_nat -> Pos_to_nat [] ; + ConstructiveExtra_Z_inj_nat -> Pos_pred_double [] ; + Pos_sub_mask_nul_iff -> _False_ind [] ; + Pos_sub_mask_nul_iff -> _True [] ; + Pos_sub_mask_nul_iff -> _I [] ; + Pos_sub_mask_nul_iff -> _iff [] ; + Pos_sub_mask_nul_iff -> _conj [] ; + Pos_sub_mask_nul_iff -> Pos_sub_mask_spec [] ; + ConstructiveExtra_Z_inj_nat_id -> Nat_neq_0_lt_0 [] ; + ConstructiveExtra_Z_inj_nat_id -> Pos2Nat_id [] ; + ConstructiveExtra_Z_inj_nat_id -> Pos_pred_double_succ [] ; + ConstructiveExtra_Z_inj_nat_id -> ConstructiveExtra_Z_inj_nat [] ; + ConstructiveExtra_Z_inj_nat_id -> ConstructiveExtra_Z_inj_nat_rev [] ; + ConstructiveExtra_Z_inj_nat_id -> Pos2Nat_is_pos [] ; + ConstructiveExtra_Z_inj_nat_id -> Pos_xI_succ_xO [] ; + ConstructiveExtra_Z_inj_nat_id -> ConstructiveExtra_Pos_pred_double_inj [] ; + Pos_compare_eq_iff -> RelationClasses_Equivalence_PER [] ; + Pos_compare_eq_iff -> RelationClasses_iff_equivalence [] ; + Pos_compare_eq_iff -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Pos_compare_eq_iff -> Pos_compare_sub_mask [] ; + Pos_compare_eq_iff -> Pos_sub_mask_nul_iff [] ; + ConstructiveExtra_Z_inj_nat_rev -> _Z [] ; + ConstructiveExtra_Z_inj_nat_rev -> _Z0 [] ; + ConstructiveExtra_Z_inj_nat_rev -> _Zpos [] ; + ConstructiveExtra_Z_inj_nat_rev -> _Zneg [] ; + ConstructiveExtra_Z_inj_nat_rev -> Pos_of_nat [] ; + Pos2Nat_is_pos -> Nat_lt_0_succ [] ; + Pos2Nat_is_pos -> Pos2Nat_is_succ [] ; + Pos_compare_lt_iff -> RelationClasses_reflexivity [] ; + Pos_compare_lt_iff -> RelationClasses_iff_Reflexive [] ; + Pos_compare_lt_iff -> Pos_lt [] ; + Pos_xI_succ_xO -> _eq [] ; + Pos_xI_succ_xO -> Pos_succ [] ; + Pos_xI_succ_xO -> _eq_refl [] ; + Pos_compare_antisym -> _eq_ind_r [] ; + Pos_compare_antisym -> Pos_compare [] ; + Pos_compare_antisym -> Pos_compare_cont_antisym [] ; + ConstructiveExtra_Pos_pred_double_inj -> _eq_ind_r [] ; + ConstructiveExtra_Pos_pred_double_inj -> Pos_succ_pred_double [] ; + _CompOpp_iff -> _iff [] ; + _CompOpp_iff -> _conj [] ; + _CompOpp_iff -> _eq_ind_r [] ; + _CompOpp_iff -> _CompOpp_involutive [] ; + _CompOpp_iff -> _CompOpp_inj [] ; + _CompEq -> _Eq [] ; + _CompEq -> _Lt [] ; + _CompEq -> _Gt [] ; + Z_le_ngt -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_le_ngt -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_le_ngt -> Z_Private_OrderTac_Tac_not_gt_le [] ; + _CompLt -> _Eq [] ; + _CompLt -> _Lt [] ; + _CompLt -> _Gt [] ; + ClassicalDedekindReals_DRealQuot1 -> ConstructiveCauchyReals_CRealEq [] ; + ClassicalDedekindReals_DRealQuot1 -> ConstructiveCauchyReals_CReal_le_lt_trans [] ; + ClassicalDedekindReals_DRealQuot1 -> ClassicalDedekindReals_DRealReprQ [] ; + ClassicalDedekindReals_DRealQuot1 -> ClassicalDedekindReals_DRealReprQup [] ; + ClassicalDedekindReals_DRealQuot1 -> ClassicalDedekindReals_Rle_antisym [] ; + _CompGt -> _Eq [] ; + _CompGt -> _Lt [] ; + _CompGt -> _Gt [] ; + ConstructiveCauchyReals_CReal_le_lt_trans -> ConstructiveCauchyReals_CRealLe [] ; + ConstructiveCauchyReals_CReal_le_lt_trans -> ConstructiveCauchyReals_linear_order_T [] ; + ClassicalDedekindReals_DRealReprQ -> ClassicalDedekindReals_DRealRepr [] ; + ClassicalDedekindReals_DRealReprQ -> ConstructiveCauchyReals_CReal_red_seq [] ; + ClassicalDedekindReals_DRealReprQ -> ConstructiveCauchyReals_inject_Q [] ; + ClassicalDedekindReals_DRealReprQ -> ConstructiveCauchyReals_CRealLt [] ; + ClassicalDedekindReals_DRealReprQ -> ClassicalDedekindReals_DRealOpen [] ; + ClassicalDedekindReals_DRealReprQ -> QExtra_QarchimedeanLowExp2_Z [] ; + _CompOpp_involutive -> _eq [] ; + _CompOpp_involutive -> _CompOpp [] ; + _CompOpp_involutive -> _eq_refl [] ; + ClassicalDedekindReals_DRealReprQup -> ClassicalDedekindReals_DRealRepr [] ; + ClassicalDedekindReals_DRealReprQup -> ConstructiveCauchyReals_CReal_red_seq [] ; + ClassicalDedekindReals_DRealReprQup -> ConstructiveCauchyReals_inject_Q [] ; + ClassicalDedekindReals_DRealReprQup -> ConstructiveCauchyReals_CRealLe [] ; + _CompOpp_inj -> _CompOpp [] ; + _CompOpp_inj -> _False_ind [] ; + _CompOpp_inj -> _eq_ind [] ; + _CompOpp_inj -> _True [] ; + _CompOpp_inj -> _I [] ; + _CompOpp_inj -> _eq_sym [] ; + Pos_compare_cont_antisym -> _eq [] ; + Pos_compare_cont_antisym -> _CompOpp [] ; + Pos_compare_cont_antisym -> _eq_refl [] ; + Pos_compare_cont_antisym -> _positive_ind [] ; + Pos_compare_cont_antisym -> Pos_compare_cont [] ; + ClassicalDedekindReals_Rle -> ClassicalDedekindReals_DReal [] ; + ClassicalDedekindReals_Rle -> _proj1_sig [] ; + RelationClasses_Build_RewriteRelation -> Relation_Definitions_relation [] ; + ClassicalDedekindReals_Rle_antisym -> _exist [] ; + ClassicalDedekindReals_Rle_antisym -> ClassicalDedekindReals_Rle [] ; + ClassicalDedekindReals_Rle_antisym -> ClassicalDedekindReals_isLowerCut_hprop [] ; + Pos_peano_ind -> Pos_peano_rect [] ; + ClassicalDedekindReals_isLowerCut_hprop -> ClassicalDedekindReals_isLowerCut [] ; + ClassicalDedekindReals_isLowerCut_hprop -> _True [] ; + ClassicalDedekindReals_isLowerCut_hprop -> _I [] ; + ClassicalDedekindReals_isLowerCut_hprop -> _or_introl [] ; + ClassicalDedekindReals_isLowerCut_hprop -> _or_intror [] ; + ClassicalDedekindReals_isLowerCut_hprop -> HLevels_forall_hprop [] ; + ClassicalDedekindReals_isLowerCut_hprop -> Eqdep_dec_eq_proofs_unicity_on [] ; + ClassicalDedekindReals_isLowerCut_hprop -> HLevels_impl_hprop [] ; + ClassicalDedekindReals_isLowerCut_hprop -> HLevels_not_hprop [] ; + ClassicalDedekindReals_isLowerCut_hprop -> HLevelsBase_and_hprop [] ; + FunctionalExtensionality_functional_extensionality -> FunctionalExtensionality_functional_extensionality_dep [] ; + Pos_add_lt_mono_l -> _iff_refl [] ; + Pos_add_lt_mono_l -> Pos_lt [] ; + Pos_add_lt_mono_l -> Pos_add_compare_mono_l [] ; + Pos_lt_succ_diag_r -> Morphisms_iff_flip_impl_subrelation [] ; + Pos_lt_succ_diag_r -> Pos_lt_iff_add [] ; + FunctionalExtensionality_functional_extensionality_dep -> _eq [] ; + HLevels_forall_hprop -> FunctionalExtensionality_functional_extensionality_dep [] ; + HLevels_forall_hprop -> HLevelsBase_IsHProp [] ; + Pos_add_compare_mono_l -> Pos_add_1_l [] ; + Pos_add_compare_mono_l -> Pos_peano_ind [] ; + Pos_add_compare_mono_l -> Pos_add_succ_l [] ; + Pos_add_compare_mono_l -> Pos_compare_succ_succ [] ; + Eqdep_dec_eq_proofs_unicity_on -> Eqdep_dec_nu_constant [] ; + Eqdep_dec_eq_proofs_unicity_on -> Eqdep_dec_nu_left_inv_on [] ; + Pos_add_succ_l -> Pos_add_comm [] ; + Pos_add_succ_l -> Pos_add_succ_r [] ; + HLevels_impl_hprop -> FunctionalExtensionality_functional_extensionality [] ; + HLevels_impl_hprop -> HLevelsBase_IsHProp [] ; + Pos_compare_succ_succ -> Pos_compare_succ_l [] ; + HLevels_not_hprop -> _False_ind [] ; + HLevels_not_hprop -> FunctionalExtensionality_functional_extensionality [] ; + HLevels_not_hprop -> HLevelsBase_IsHProp [] ; + Pos_compare_succ_l -> Pos_compare_antisym [] ; + Pos_compare_succ_l -> Pos_compare_succ_r [] ; + Pos_compare_succ_r -> Pos_succ [] ; + Pos_compare_succ_r -> Pos_compare_xI_xI [] ; + Pos_compare_succ_r -> Pos_compare_xI_xO [] ; + Pos_compare_succ_r -> Pos_compare_xO_xI [] ; + Pos_compare_succ_r -> Pos_compare_xO_xO [] ; + HLevelsBase_and_hprop -> _and [] ; + HLevelsBase_and_hprop -> _eq_ind [] ; + HLevelsBase_and_hprop -> _eq_refl [] ; + HLevelsBase_and_hprop -> _conj [] ; + HLevelsBase_and_hprop -> HLevelsBase_IsHProp [] ; + Pos_peano_rect -> Pos_succ [] ; + HLevelsBase_IsHProp -> _eq [] ; + PosDef_Pos_sub_mask -> PosDef_Pos_double_pred_mask [] ; + PosDef_Pos_sub_mask -> PosDef_Pos_double_mask [] ; + PosDef_Pos_sub_mask -> PosDef_Pos_succ_double_mask [] ; + Eqdep_dec_nu_constant -> _eq [] ; + Eqdep_dec_nu_constant -> _not [] ; + Eqdep_dec_nu_constant -> _or [] ; + Eqdep_dec_nu_constant -> _False_ind [] ; + Eqdep_dec_nu_constant -> _eq_refl [] ; + PosDef_Pos_mask -> _positive [] ; + Eqdep_dec_nu_left_inv_on -> _not [] ; + Eqdep_dec_nu_left_inv_on -> _or [] ; + Eqdep_dec_nu_left_inv_on -> _False_ind [] ; + Eqdep_dec_nu_left_inv_on -> Eqdep_dec_trans_sym_eq [] ; + Eqdep_dec_trans_sym_eq -> _eq_ind [] ; + Eqdep_dec_trans_sym_eq -> _eq_refl [] ; + PosDef_Pos_double_pred_mask -> PosDef_Pos_pred_double [] ; + PosDef_Pos_double_pred_mask -> PosDef_Pos_IsNul [] ; + PosDef_Pos_double_pred_mask -> PosDef_Pos_mask [] ; + PosDef_Pos_double_pred_mask -> PosDef_Pos_IsPos [] ; + PosDef_Pos_double_mask -> _xO [] ; + PosDef_Pos_double_mask -> PosDef_Pos_IsNul [] ; + PosDef_Pos_double_mask -> PosDef_Pos_IsNeg [] ; + PosDef_Pos_double_mask -> PosDef_Pos_mask [] ; + PosDef_Pos_double_mask -> PosDef_Pos_IsPos [] ; + ClassicalDedekindReals_DRealOpen -> ClassicalDedekindReals_DRealQlim [] ; + ClassicalDedekindReals_DRealOpen -> QArith_base_Qle_trans [] ; + ClassicalDedekindReals_DRealOpen -> QArith_base_Qnot_le_lt [] ; + ClassicalDedekindReals_DRealOpen -> QArith_base_Qmult_0_r [] ; + ClassicalDedekindReals_DRealOpen -> QArith_base_Qinv_lt_0_compat [] ; + ClassicalDedekindReals_DRealOpen -> QArith_base_Qlt_not_le [] ; + ClassicalDedekindReals_DRealOpen -> QArith_base_Qmult_1_r [] ; + ClassicalDedekindReals_DRealOpen -> QArith_base_Qmult_le_l [] ; + ClassicalDedekindReals_DRealOpen -> QArith_base_Qlt_le_dec [] ; + ClassicalDedekindReals_DRealOpen -> QArith_base_Qmult_lt_l [] ; + ClassicalDedekindReals_DRealOpen -> Pos2Nat_inj_le [] ; + ClassicalDedekindReals_DRealOpen -> ClassicalDedekindReals_lowerUpper [] ; + ClassicalDedekindReals_DRealOpen -> QArith_base_Qlt_minus_iff [] ; + PosDef_Pos_succ_double_mask -> _xH [] ; + PosDef_Pos_succ_double_mask -> _xI [] ; + PosDef_Pos_succ_double_mask -> PosDef_Pos_IsNeg [] ; + PosDef_Pos_succ_double_mask -> PosDef_Pos_mask [] ; + PosDef_Pos_succ_double_mask -> PosDef_Pos_IsPos [] ; + QExtra_QarchimedeanLowExp2_Z -> _sig [] ; + QExtra_QarchimedeanLowExp2_Z -> _exist [] ; + QExtra_QarchimedeanLowExp2_Z -> QExtra_Qlowbound_lt_ZExp2_spec [] ; + PosDef_Pos_IsPos -> _positive [] ; + QExtra_Qlowbound_lt_ZExp2_spec -> QExtra_Qbound_ltabs_ZExp2_spec [] ; + QExtra_Qlowbound_lt_ZExp2_spec -> QArith_base_Qinv_lt_contravar [] ; + QExtra_Qlowbound_lt_ZExp2_spec -> Qabs_Qabs_pos [] ; + QExtra_Qlowbound_lt_ZExp2_spec -> QExtra_Qlowbound_ltabs_ZExp2_inv [] ; + Pos_gt_lt_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Pos_gt_lt_iff -> RelationClasses_reflexivity [] ; + Pos_gt_lt_iff -> Morphisms_eq_proper_proxy [] ; + Pos_gt_lt_iff -> RelationClasses_iff_Transitive [] ; + Pos_gt_lt_iff -> RelationClasses_iff_Reflexive [] ; + Pos_gt_lt_iff -> Pos_gt [] ; + Pos_gt_lt_iff -> Pos_lt [] ; + Pos_gt_lt_iff -> Pos_compare_antisym [] ; + Pos_gt_lt_iff -> _CompOpp_iff [] ; + QExtra_Qlowbound_ltabs_ZExp2 -> Z_add [] ; + QExtra_Qlowbound_ltabs_ZExp2 -> QExtra_Qbound_ltabs_ZExp2 [] ; + Z_succ_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Z_succ_wd -> RelationClasses_eq_Reflexive [] ; + Z_succ_wd -> Z_succ [] ; + Z_succ_wd -> Morphisms_reflexive_proper [] ; + Z_succ_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_succ_wd -> Z_eq [] ; + Qabs_Qabs_pos -> QArith_base_Q_Setoid [] ; + Qabs_Qabs_pos -> QArith_base_Qopp_comp [] ; + Qabs_Qabs_pos -> QArith_base_Qle_antisym [] ; + Qabs_Qabs_pos -> Qabs_Qabs_case [] ; + Z_succ_inj -> Morphisms_PER_morphism [] ; + Z_succ_inj -> Morphisms_trans_co_impl_morphism [] ; + Z_succ_inj -> Z_eq_equiv [] ; + Z_succ_inj -> Z_pred_succ [] ; + Z_succ_inj -> Z_pred_wd [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> QArith_base_Qlt [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> QArith_base_Qinv [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> VarMap_find [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> VarMap_Empty [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> VarMap_Elt [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> VarMap_Branch [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> ZifyClasses_mkapp2 [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> Pos2Z_inj_succ [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> Pos2Z_pos_is_pos [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> ZifyClasses_inj [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> ZifyClasses_mkrel [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> ZMicromega_ZTautoChecker_sound [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> ZifyClasses_rew_iff_rev [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> ZifyClasses_mkapp [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> QExtra_Qlowbound_ltabs_ZExp2 [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> ZifyInst_Inj_Z_Z [] ; + QExtra_Qlowbound_ltabs_ZExp2_inv -> Pos2Z_add_pos_neg [] ; + Z_pred -> Z_add [] ; + ZifyInst_Inj_Z_Z -> _Z [] ; + ZifyInst_Inj_Z_Z -> _True [] ; + ZifyInst_Inj_Z_Z -> _I [] ; + ZifyInst_Inj_Z_Z -> ZifyClasses_InjTyp [] ; + ZifyInst_Inj_Z_Z -> ZifyClasses_mkinj [] ; + Z_pred_succ -> Z_succ [] ; + Z_pred_succ -> Z_Private_BootStrap_add_assoc [] ; + Z_pred_succ -> Z_pred [] ; + Z_pred_succ -> Z_Private_BootStrap_add_opp_diag_r [] ; + Pos2Z_add_pos_neg -> _eq [] ; + Pos2Z_add_pos_neg -> Z_add [] ; + Pos2Z_add_pos_neg -> _eq_refl [] ; + Z_pred_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Z_pred_wd -> RelationClasses_eq_Reflexive [] ; + Z_pred_wd -> Morphisms_reflexive_proper [] ; + Z_pred_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_pred_wd -> Z_pred [] ; + Z_pred_wd -> Z_eq [] ; + Pos2Nat_inj_le -> Pos2Nat_inj_compare [] ; + ClassicalDedekindReals_lowerUpper -> ClassicalDedekindReals_isLowerCut [] ; + ClassicalDedekindReals_lowerUpper -> _False_ind [] ; + ClassicalDedekindReals_lowerUpper -> _eq_ind [] ; + ClassicalDedekindReals_lowerUpper -> _True [] ; + ClassicalDedekindReals_lowerUpper -> _eq_refl [] ; + ClassicalDedekindReals_lowerUpper -> _I [] ; + Z_eq -> _Z [] ; + Z_eq -> _eq [] ; + Z_Private_BootStrap_add_opp_diag_r -> Z_add [] ; + Z_Private_BootStrap_add_opp_diag_r -> Z_opp [] ; + Z_Private_BootStrap_add_opp_diag_r -> Z_pos_sub_diag [] ; + QArith_base_Qlt_minus_iff -> QArith_base_Qlt [] ; + QArith_base_Qlt_minus_iff -> QArith_base_Qopp [] ; + QArith_base_Qlt_minus_iff -> QArith_base_Qplus [] ; + QArith_base_Qlt_minus_iff -> Z_mul_1_r [] ; + QArith_base_Qlt_minus_iff -> Z_mul_opp_l [] ; + QArith_base_Qlt_minus_iff -> Z_lt_sub_lt_add_r [] ; + Z_pos_sub_diag -> Z_pos_sub_spec [] ; + Z_pos_sub_diag -> Pos_compare_refl [] ; + Z_lt_sub_lt_add_r -> Z_add_lt_mono_r [] ; + Z_lt_sub_lt_add_r -> Z_sub_simpl_r [] ; + Pos2Nat_inj_compare -> Pos_compare_succ_succ [] ; + Pos2Nat_inj_compare -> Pos2Nat_is_pos [] ; + Pos2Nat_inj_compare -> Pos_lt_1_succ [] ; + Pos2Nat_inj_compare -> Pos_succ_pred_or [] ; + Pos2Nat_inj_compare -> Nat_compare_succ [] ; + Pos2Nat_inj_compare -> Pos2Nat_inj_1 [] ; + Pos2Nat_inj_compare -> Nat_compare_gt_iff [] ; + Pos_compare_refl -> RelationClasses_reflexivity [] ; + Pos_compare_refl -> RelationClasses_Equivalence_Reflexive [] ; + Pos_compare_refl -> Pos_compare_eq_iff [] ; + Pos_compare_refl -> Pos_eq_equiv [] ; + Pos_lt_1_succ -> Pos_le_1_l [] ; + Pos_lt_1_succ -> Pos_lt_succ_r [] ; + Pos_eq_equiv -> _positive [] ; + Pos_eq_equiv -> RelationClasses_eq_equivalence [] ; + Pos_succ_pred_or -> _or [] ; + Pos_succ_pred_or -> _or_introl [] ; + Pos_succ_pred_or -> _or_intror [] ; + Pos_succ_pred_or -> Pos_succ_pred_double [] ; + Pos_succ_pred_or -> Pos_pred [] ; + Z_add_comm -> Z_add_0_r [] ; + Z_add_comm -> Z_add_succ_r [] ; + Nat_compare_succ -> _eq [] ; + Nat_compare_succ -> _S [] ; + Nat_compare_succ -> _eq_refl [] ; + Nat_compare_succ -> Nat_compare [] ; + Z_add_cancel_l -> Morphisms_per_partial_app_morphism [] ; + Z_add_cancel_l -> Z_bi_induction [] ; + Z_add_cancel_l -> Z_add_wd [] ; + Z_add_cancel_l -> Z_succ_inj_wd [] ; + Z_add_cancel_l -> Z_add_succ_l [] ; + Z_add_cancel_l -> Z_add_0_l [] ; + Pos2Nat_inj_1 -> _eq [] ; + Pos2Nat_inj_1 -> _xH [] ; + Pos2Nat_inj_1 -> _eq_refl [] ; + Pos2Nat_inj_1 -> Pos_to_nat [] ; + Z_add_succ_r -> Morphisms_per_partial_app_morphism [] ; + Z_add_succ_r -> Z_bi_induction [] ; + Z_add_succ_r -> Z_add_wd [] ; + Z_add_succ_r -> Z_succ_inj_wd [] ; + Z_add_succ_r -> Z_add_succ_l [] ; + Z_add_succ_r -> Z_add_0_l [] ; + Z_succ_pred -> Z_succ [] ; + Z_succ_pred -> Z_Private_BootStrap_add_assoc [] ; + Z_succ_pred -> Z_pred [] ; + Z_succ_pred -> Z_Private_BootStrap_add_opp_diag_r [] ; + Nat_compare_gt_iff -> RelationClasses_reflexivity [] ; + Nat_compare_gt_iff -> RelationClasses_Equivalence_PER [] ; + Nat_compare_gt_iff -> RelationClasses_iff_equivalence [] ; + Nat_compare_gt_iff -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_compare_gt_iff -> Nat_compare_lt_iff [] ; + Nat_compare_gt_iff -> _CompOpp_iff [] ; + Nat_compare_gt_iff -> Nat_compare_antisym [] ; + Z_peano_ind -> _eq_ind [] ; + Z_peano_ind -> Z_succ [] ; + Z_peano_ind -> Pos_add_1_r [] ; + Z_peano_ind -> Pos_peano_ind [] ; + Z_peano_ind -> Z_pred [] ; + Nat_compare_antisym -> _eq [] ; + Nat_compare_antisym -> _CompOpp [] ; + Nat_compare_antisym -> _eq_refl [] ; + Nat_compare_antisym -> Nat_compare [] ; + Nat_compare_antisym -> _nat_ind [] ; + ConstructiveCauchyReals_linear_order_T -> ConstructiveCauchyReals_CRealLt_dec [] ; + Z_add_assoc -> Morphisms_per_partial_app_morphism [] ; + Z_add_assoc -> Z_bi_induction [] ; + Z_add_assoc -> Z_add_wd [] ; + Z_add_assoc -> Z_succ_inj_wd [] ; + Z_add_assoc -> Z_add_succ_l [] ; + Z_add_assoc -> Z_add_0_l [] ; + Z_Private_BootStrap_mul_1_l -> _eq [] ; + Z_Private_BootStrap_mul_1_l -> Z_mul [] ; + Z_Private_BootStrap_mul_1_l -> _eq_refl [] ; + _mag -> _mag_prop [] ; + Z_Private_BootStrap_mul_add_distr_r -> Z_Private_BootStrap_opp_inj [] ; + Z_Private_BootStrap_mul_add_distr_r -> Z_Private_BootStrap_opp_add_distr [] ; + Z_Private_BootStrap_mul_add_distr_r -> Z_Private_BootStrap_mul_0_r [] ; + Z_Private_BootStrap_mul_add_distr_r -> Z_Private_BootStrap_mul_opp_r [] ; + Z_Private_BootStrap_mul_add_distr_r -> Z_Private_BootStrap_mul_add_distr_pos [] ; + _mag_val -> _mag_prop [] ; + _mag_prop -> _bpow [] ; + _mag_prop -> _Rabs [] ; + Z_Private_BootStrap_mul_0_r -> _eq [] ; + Z_Private_BootStrap_mul_0_r -> Z_mul [] ; + Z_Private_BootStrap_mul_0_r -> _eq_refl [] ; + Z_Private_BootStrap_mul_opp_r -> _eq [] ; + Z_Private_BootStrap_mul_opp_r -> Z_mul [] ; + Z_Private_BootStrap_mul_opp_r -> Z_opp [] ; + Z_Private_BootStrap_mul_opp_r -> _eq_refl [] ; + _Rle -> _Rlt [] ; + Z_Private_BootStrap_mul_add_distr_pos -> Z_mul [] ; + Z_Private_BootStrap_mul_add_distr_pos -> Z_add [] ; + Z_Private_BootStrap_mul_add_distr_pos -> Z_pos_sub_spec [] ; + Z_Private_BootStrap_mul_add_distr_pos -> Pos_mul_add_distr_r [] ; + Z_Private_BootStrap_mul_add_distr_pos -> Pos_mul_sub_distr_r [] ; + Z_Private_BootStrap_mul_add_distr_pos -> Pos_mul_compare_mono_r [] ; + _bpow -> _IZR [] ; + _bpow -> RinvImpl_Rinv [] ; + _bpow -> _radix_val [] ; + Pos_mul_add_distr_r -> Pos_mul_comm [] ; + Pos_mul_add_distr_r -> Pos_mul_add_distr_l [] ; + _Rabs -> _Rcase_abs [] ; + Pos_mul_sub_distr_r -> Pos_mul_comm [] ; + Pos_mul_sub_distr_r -> Pos_mul_sub_distr_l [] ; + _Rge -> _Rgt [] ; + Pos_mul_compare_mono_r -> Pos_mul_comm [] ; + Pos_mul_compare_mono_r -> Pos_mul_compare_mono_l [] ; + _Rcase_abs -> _IZR [] ; + _Rcase_abs -> _Rle_ge [] ; + _Rcase_abs -> _Rnot_le_lt [] ; + _Rcase_abs -> _Rle_dec [] ; + Pos_mul_comm -> Pos_mul_1_r [] ; + Pos_mul_comm -> Pos_mul_xI_r [] ; + Pos_mul_comm -> Pos_mul_xO_r [] ; + _Ropp -> _R [] ; + _Ropp -> _Rrepr [] ; + _Ropp -> _Rabst [] ; + Pos_mul_compare_mono_l -> Pos_mul [] ; + Pos_mul_compare_mono_l -> Pos_lt_gt [] ; + Pos_mul_compare_mono_l -> Pos_compare_spec [] ; + Pos_mul_compare_mono_l -> Pos_compare_refl [] ; + Pos_mul_compare_mono_l -> Pos_gt_lt [] ; + Pos_mul_compare_mono_l -> Pos_add_lt_mono [] ; + _Rle_ge -> _Rle [] ; + _Rle_ge -> _Rge [] ; + Pos_gt_lt -> Pos_gt_lt_iff [] ; + _Rnot_le_lt -> _Rle [] ; + _Rnot_le_lt -> _Rtotal_order [] ; + Pos_add_lt_mono -> Pos_lt_trans [] ; + Pos_add_lt_mono -> Pos_add_lt_mono_r [] ; + Pos_add_lt_mono -> Pos_add_lt_mono_l [] ; + _Rle_dec -> _Rlt_not_le [] ; + _Rle_dec -> _Rnot_lt_le [] ; + _Rle_dec -> _Rlt_dec [] ; + Pos_mul_1_r -> Pos_mul [] ; + Pos_mul_1_r -> _f_equal [] ; + Pos_mul_1_r -> _eq_trans [] ; + Pos_mul_1_r -> _positive_ind [] ; + _Rlt_not_le -> _Rle [] ; + _Rlt_not_le -> _Rlt_not_eq [] ; + Pos_mul_xI_r -> Pos_mul [] ; + Pos_mul_xI_r -> Pos_add_assoc [] ; + _Rnot_lt_le -> _Rle [] ; + _Rnot_lt_le -> _Rtotal_order [] ; + Pos_mul_xO_r -> Pos_mul [] ; + Pos_mul_xO_r -> PosDef_Pos_add [] ; + Pos_mul_xO_r -> _f_equal [] ; + Pos_mul_xO_r -> _eq_trans [] ; + Pos_mul_xO_r -> _positive_ind [] ; + _Rlt_dec -> _total_order_T [] ; + _Rlt_dec -> _Rge_not_lt [] ; + Pos_mul_sub_distr_l -> Pos_sub_add [] ; + Pos_mul_sub_distr_l -> Pos_mul_add_distr_l [] ; + Pos_mul_sub_distr_l -> Pos_mul_lt_mono_l [] ; + _Rgt -> _Rlt [] ; + Pos_mul_add_distr_l -> Pos_mul [] ; + Pos_mul_add_distr_l -> Pos_add_assoc [] ; + _Rge_not_lt -> _Rge_le [] ; + _Rge_not_lt -> _Rle_not_lt [] ; + Pos_mul_lt_mono_l -> Pos_mul_compare_mono_l [] ; + _Rge_le -> _Rle [] ; + _Rge_le -> _Rge [] ; + Ring_polynom_mon_of_pol -> _prod [] ; + Ring_polynom_mon_of_pol -> _option [] ; + Ring_polynom_mon_of_pol -> _pair [] ; + Ring_polynom_mon_of_pol -> Ring_polynom_P0 [] ; + Ring_polynom_mon_of_pol -> Ring_polynom_Peq [] ; + Ring_polynom_mon_of_pol -> Ring_polynom_mkVmon [] ; + Ring_polynom_mon_of_pol -> _Some [] ; + Ring_polynom_mon_of_pol -> _None [] ; + _Rle_not_lt -> _Rle [] ; + _Rle_not_lt -> _Rlt_not_eq [] ; + _Rlt_not_eq -> RelationClasses_impl_Reflexive [] ; + _Rlt_not_eq -> RelationClasses_inverse_impl_rewrite_relation [] ; + _Rlt_not_eq -> RelationClasses_flip_Reflexive [] ; + _Rlt_not_eq -> _Rlt_irrefl [] ; + _Rlt_asym -> ConstructiveCauchyReals_CRealLt_asym [] ; + _Rlt_asym -> _Rlt_def [] ; + _Rlt_asym -> ConstructiveCauchyReals_CRealLtEpsilon [] ; + Ring_polynom_P0 -> Ring_polynom_Pol [] ; + Ring_polynom_P0 -> Ring_polynom_Pc [] ; + ConstructiveCauchyReals_CRealLtEpsilon -> ConstructiveCauchyReals_CRealLtProp [] ; + ConstructiveCauchyReals_CRealLtEpsilon -> QArith_base_Qlt_le_dec [] ; + ConstructiveCauchyReals_CRealLtEpsilon -> ConstructiveCauchyReals_CRealLt [] ; + ConstructiveCauchyReals_CRealLtEpsilon -> QArith_base_Qle_not_lt [] ; + ConstructiveCauchyReals_CRealLtEpsilon -> ConstructiveExtra_constructive_indefinite_ground_description_Z [] ; + ConstructiveExtra_constructive_indefinite_ground_description_Z -> ConstructiveExtra_Z_inj_nat_id [] ; + ConstructiveExtra_constructive_indefinite_ground_description_Z -> ConstructiveEpsilon_constructive_indefinite_ground_description [] ; + Ring_polynom_Peq -> _bool [] ; + Ring_polynom_Peq -> _false [] ; + Ring_polynom_Peq -> Ring_polynom_Pol [] ; + Ring_polynom_Peq -> Pos_compare [] ; + Ring_polynom_mkVmon -> Pos_add [] ; + Ring_polynom_mkVmon -> Ring_polynom_zmon_pred [] ; + Ring_polynom_mkVmon -> Ring_polynom_vmon [] ; + ConstructiveEpsilon_constructive_indefinite_ground_description -> _eq_ind_r [] ; + ConstructiveEpsilon_constructive_indefinite_ground_description -> _ex_intro [] ; + ConstructiveEpsilon_constructive_indefinite_ground_description -> ConstructiveEpsilon_P__decidable [] ; + ConstructiveEpsilon_constructive_indefinite_ground_description -> ConstructiveEpsilon_constructive_indefinite_ground_description_nat [] ; + Ring_polynom_mkZmon -> Ring_polynom_Mon [] ; + Ring_polynom_mkZmon -> Ring_polynom_mon0 [] ; + Ring_polynom_mkZmon -> Ring_polynom_zmon [] ; + ConstructiveEpsilon_P_ -> _nat [] ; + Ring_polynom_mon0 -> _positive [] ; + ConstructiveEpsilon_P__decidable -> _not [] ; + ConstructiveEpsilon_P__decidable -> _sumbool [] ; + ConstructiveEpsilon_P__decidable -> ConstructiveEpsilon_P_ [] ; + ConstructiveEpsilon_constructive_indefinite_ground_description_nat -> ConstructiveEpsilon_rel_ls_post [] ; + ConstructiveEpsilon_constructive_indefinite_ground_description_nat -> ConstructiveEpsilon_linear_search_from_0_conform [] ; + ConstructiveEpsilon_rel_ls_post -> ConstructiveEpsilon_rel_ls_ind [] ; + Ring_polynom_zmon -> _positive [] ; + ConstructiveEpsilon_linear_search_from_0_conform -> _ex [] ; + ConstructiveEpsilon_linear_search_from_0_conform -> ConstructiveEpsilon_linear_search_conform [] ; + ConstructiveEpsilon_linear_search_from_0_conform -> ConstructiveEpsilon_O_witness [] ; + ConstructiveEpsilon_linear_search_from_0_conform -> ConstructiveEpsilon_stop [] ; + ConstructiveEpsilon_rel_ls -> _not [] ; + ConstructiveEpsilon_rel_ls -> _S [] ; + ConstructiveEpsilon_rel_ls -> _nat [] ; + Ring_polynom_zmon_pred -> Pos_pred [] ; + Ring_polynom_zmon_pred -> Ring_polynom_mkZmon [] ; + Ring_polynom_vmon -> _positive [] ; + ConstructiveEpsilon_linear_search_conform -> _sig [] ; + ConstructiveEpsilon_linear_search_conform -> _exist [] ; + ConstructiveEpsilon_linear_search_conform -> _sumbool [] ; + ConstructiveEpsilon_linear_search_conform -> ConstructiveEpsilon_rel_ls [] ; + ConstructiveEpsilon_linear_search_conform -> ConstructiveEpsilon_inv_before_witness [] ; + ConstructiveEpsilon_linear_search_conform -> ConstructiveEpsilon_Rstop [] ; + ConstructiveEpsilon_linear_search_conform -> ConstructiveEpsilon_Rnext [] ; + Z_one_succ -> _eq [] ; + Z_one_succ -> _eq_refl [] ; + Z_one_succ -> Z_succ [] ; + ConstructiveEpsilon_O_witness -> _O [] ; + ConstructiveEpsilon_O_witness -> ConstructiveEpsilon_before_witness [] ; + ConstructiveEpsilon_O_witness -> ConstructiveEpsilon_next [] ; + ConstructiveEpsilon_before_witness -> _S [] ; + ConstructiveEpsilon_before_witness -> _nat [] ; + Z_eqb -> _Z [] ; + Z_eqb -> PosDef_Pos_eqb [] ; + ConstructiveEpsilon_stop -> _S [] ; + ConstructiveEpsilon_stop -> _nat [] ; + PosDef_Pos_eqb -> _positive [] ; + PosDef_Pos_eqb -> _bool [] ; + PosDef_Pos_eqb -> _true [] ; + PosDef_Pos_eqb -> _false [] ; + ConstructiveEpsilon_next -> _S [] ; + ConstructiveEpsilon_next -> _nat [] ; + Qminmax_Q_Private_Tac_eq_le -> Qminmax_Q_Private_Tac_trans [] ; + ConstructiveEpsilon_inv_before_witness -> _not [] ; + ConstructiveEpsilon_inv_before_witness -> ConstructiveEpsilon_before_witness [] ; + Qminmax_Q_Private_Tac_eq_lt -> Qminmax_Q_Private_Tac_trans [] ; + ConstructiveEpsilon_Rstop -> _not [] ; + ConstructiveEpsilon_Rstop -> _S [] ; + ConstructiveEpsilon_Rstop -> _nat [] ; + Qminmax_Q_Private_Tac_le_eq -> Qminmax_Q_Private_Tac_trans [] ; + ConstructiveEpsilon_Rnext -> _not [] ; + ConstructiveEpsilon_Rnext -> _S [] ; + ConstructiveEpsilon_Rnext -> _nat [] ; + Qminmax_Q_Private_Tac_lt_eq -> Qminmax_Q_Private_Tac_trans [] ; + ConstructiveEpsilon_rel_ls_ind -> ConstructiveEpsilon_rel_ls [] ; + Qminmax_Q_Private_Tac_le_lt_trans -> Qminmax_Q_Private_Tac_trans [] ; + Qminmax_Q_Private_Tac_lt_irrefl -> Qminmax_Q_OT_lt_strorder [] ; + _Rlt_irrefl -> _Rlt_asym [] ; + Qminmax_Q_Private_Tac_eq_sym -> Qminmax_Q_OT_eq_equiv [] ; + _Rtotal_order -> _total_order_T [] ; + _Rtotal_order -> _Rgt [] ; + Qminmax_Q_Private_Tac_not_gt_le -> Morphisms_iff_flip_impl_subrelation [] ; + Qminmax_Q_Private_Tac_not_gt_le -> Qminmax_Q_OT_lt_total [] ; + Qminmax_Q_Private_Tac_not_gt_le -> Qminmax_Q_OT_le_lteq [] ; + RinvImpl_Rinv -> _Req_appart_dec [] ; + RinvImpl_Rinv -> _Rrepr_appart_0 [] ; + RinvImpl_Rinv -> ConstructiveCauchyRealsMult_CReal_inv [] ; + _radix_val -> _radix [] ; + Qminmax_Q_OT_lt_total -> _or [] ; + Qminmax_Q_OT_lt_total -> _or_introl [] ; + Qminmax_Q_OT_lt_total -> _or_intror [] ; + Qminmax_Q_OT_lt_total -> Qminmax_Q_OT_compare_spec [] ; + Qminmax_Q_OT_le_lteq -> QOrderedType_Q_as_OT_le_lteq [] ; + _Req_appart_dec -> _total_order_T [] ; + QOrderedType_Q_as_OT_le_lteq -> QArith_base_Qle_lteq [] ; + _Rrepr_appart_0 -> _Rlt_def [] ; + _Rrepr_appart_0 -> ConstructiveCauchyReals_CReal_appart [] ; + _Rrepr_appart_0 -> _Rquot2 [] ; + _Rrepr_appart_0 -> ConstructiveCauchyReals_CRealLtProp_morph_Proper [] ; + _Rrepr_appart_0 -> ConstructiveRcomplete_CRealLtDisjunctEpsilon [] ; + _Rrepr_appart_0 -> _R0_def [] ; + QArith_base_Qle_lteq -> Morphisms_reflexive_reflexive_proxy [] ; + QArith_base_Qle_lteq -> Morphisms_Reflexive_partial_app_morphism [] ; + QArith_base_Qle_lteq -> Morphisms_reflexive_proper_proxy [] ; + QArith_base_Qle_lteq -> Morphisms_Prop_or_iff_morphism [] ; + QArith_base_Qle_lteq -> QArith_base_Qeq_alt [] ; + QArith_base_Qle_lteq -> QArith_base_Qle_alt [] ; + QArith_base_Qle_lteq -> QArith_base_Qlt_alt [] ; + ConstructiveCauchyRealsMult_CReal_inv -> ConstructiveCauchyReals_CReal_appart [] ; + ConstructiveCauchyRealsMult_CReal_inv -> ConstructiveCauchyRealsMult_CReal_inv_pos [] ; + ConstructiveCauchyRealsMult_CReal_inv -> ConstructiveCauchyRealsMult_CReal_neg_lt_pos [] ; + _R0 -> _R [] ; + _R0 -> _Rabst [] ; + QArith_base_Qeq_alt -> QArith_base_Qeq [] ; + QArith_base_Qeq_alt -> QArith_base_Qcompare [] ; + QArith_base_Qeq_alt -> Z_compare_eq_iff [] ; + QArith_base_Qle_alt -> QArith_base_Qle [] ; + QArith_base_Qle_alt -> RelationClasses_reflexivity [] ; + QArith_base_Qle_alt -> RelationClasses_iff_Reflexive [] ; + QArith_base_Qle_alt -> QArith_base_Qcompare [] ; + ConstructiveCauchyReals_CReal_appart -> ConstructiveCauchyReals_CRealLt [] ; + ConstructiveCauchyReals_CReal_appart -> _sum [] ; + QArith_base_Qlt_alt -> QArith_base_Qlt [] ; + QArith_base_Qlt_alt -> RelationClasses_reflexivity [] ; + QArith_base_Qlt_alt -> RelationClasses_iff_Reflexive [] ; + QArith_base_Qlt_alt -> QArith_base_Qcompare [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos -> ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos -> ConstructiveCauchyRealsMult_CReal_inv_pos_bound [] ; + QArith_base_Qcompare -> Z_compare [] ; + QArith_base_Qcompare -> Z_mul [] ; + QArith_base_Qcompare -> QArith_base_Qden [] ; + QArith_base_Qcompare -> QArith_base_Qnum [] ; + ConstructiveCauchyRealsMult_CReal_neg_lt_pos -> _exist [] ; + ConstructiveCauchyRealsMult_CReal_neg_lt_pos -> ConstructiveCauchyReals_inject_Q [] ; + ConstructiveCauchyRealsMult_CReal_neg_lt_pos -> ConstructiveCauchyReals_CRealLt [] ; + ConstructiveCauchyRealsMult_CReal_neg_lt_pos -> ConstructiveCauchyReals_CReal_opp [] ; + ConstructiveCauchyRealsMult_CReal_neg_lt_pos -> ConstructiveCauchyRealsMult_CReal_neg_lt_pos_subproof [] ; + Z_compare_eq_iff -> _Z0 [] ; + Z_compare_eq_iff -> _Zpos [] ; + Z_compare_eq_iff -> Z_compare [] ; + Z_compare_eq_iff -> _Zneg [] ; + Z_compare_eq_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Z_compare_eq_iff -> Morphisms_eq_proper_proxy [] ; + Z_compare_eq_iff -> Pos_compare_eq_iff [] ; + Z_compare_eq_iff -> _CompOpp_iff [] ; + ConstructiveCauchyRealsMult_CReal_neg_lt_pos_subproof -> QArith_base_Qlt_compat [] ; + ConstructiveCauchyRealsMult_CReal_neg_lt_pos_subproof -> QArith_base_Qplus_0_r [] ; + ConstructiveCauchyRealsMult_CReal_neg_lt_pos_subproof -> QArith_base_Qplus_0_l [] ; + ConstructiveCauchyRealsMult_CReal_neg_lt_pos_subproof -> ConstructiveCauchyReals_seq [] ; + Qminmax_Q_OT_compare_spec -> QOrderedType_Q_as_OT_compare_spec [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> Qabs_Qabs_wd_Proper [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> QArith_base_Qpower_comp [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> Z_min_spec [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> QArith_base_Qlt_shift_div_r [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> Qabs_Qabs_nonneg [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> Qabs_Qabs_Qmult [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> QArith_base_Qmult_lt_compat_nonneg [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> ConstructiveCauchyRealsMult_CReal_inv_pos_seq [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> ConstructiveCauchyRealsMult_CRealLowerBoundSpec [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> Qabs_Qabs_Qinv [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> QArith_base_Qle_shift_div_l [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy -> Qabs_Qabs_gt [] ; + QOrderedType_Q_as_OT_compare_spec -> QArith_base_Qcompare_spec [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_seq -> ConstructiveCauchyRealsMult_CReal_inv_pos_cm [] ; + QArith_base_Qcompare_spec -> QArith_base_Qlt [] ; + QArith_base_Qcompare_spec -> QArith_base_Qeq [] ; + QArith_base_Qcompare_spec -> QArith_base_Qcompare [] ; + QArith_base_Qcompare_spec -> Z_compare_spec [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_bound -> Z_min_spec [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_bound -> QArith_base_Qinv_lt_contravar [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_bound -> Qabs_Qabs_pos [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_bound -> ConstructiveCauchyRealsMult_CReal_inv_pos_seq [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_bound -> ConstructiveCauchyRealsMult_CReal_inv_pos_scale [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_bound -> ConstructiveCauchyRealsMult_CRealLowerBoundSpec [] ; + Z_compare_spec -> Morphisms_iff_impl_subrelation [] ; + Z_compare_spec -> _CompareSpec [] ; + Z_compare_spec -> _CompEq [] ; + Z_compare_spec -> _CompLt [] ; + Z_compare_spec -> _CompGt [] ; + Z_compare_spec -> Z_compare_eq_iff [] ; + Z_compare_spec -> Z_compare_antisym [] ; + Z_compare_spec -> Z_compare_lt_iff [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_scale -> ConstructiveCauchyRealsMult_CRealLowerBound [] ; + Z_compare_antisym -> _Z0 [] ; + Z_compare_antisym -> _Zpos [] ; + Z_compare_antisym -> Z_compare [] ; + Z_compare_antisym -> _Zneg [] ; + Z_compare_antisym -> Pos_compare_antisym [] ; + ConstructiveCauchyRealsMult_CRealLowerBound -> _proj1_sig [] ; + ConstructiveCauchyRealsMult_CRealLowerBound -> ConstructiveCauchyReals_inject_Q [] ; + ConstructiveCauchyRealsMult_CRealLowerBound -> ConstructiveCauchyReals_CRealLt [] ; + Z_compare_lt_iff -> Z_lt [] ; + Z_compare_lt_iff -> RelationClasses_reflexivity [] ; + Z_compare_lt_iff -> RelationClasses_iff_Reflexive [] ; + ConstructiveCauchyRealsMult_CRealLowerBoundSpec -> _exist [] ; + ConstructiveCauchyRealsMult_CRealLowerBoundSpec -> ConstructiveCauchyReals_CReal_red_seq [] ; + ConstructiveCauchyRealsMult_CRealLowerBoundSpec -> ConstructiveCauchyReals_cauchy [] ; + ConstructiveCauchyRealsMult_CRealLowerBoundSpec -> ConstructiveCauchyRealsMult_CRealLowerBound [] ; + Qminmax_Q_OT_lt_strorder -> QOrderedType_Q_as_OT_lt_strorder [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cm -> Z_min [] ; + ConstructiveCauchyRealsMult_CReal_inv_pos_cm -> ConstructiveCauchyRealsMult_CRealLowerBound [] ; + QOrderedType_Q_as_OT_lt_strorder -> QArith_base_Qlt_trans [] ; + QOrderedType_Q_as_OT_lt_strorder -> QArith_base_Qlt_irrefl [] ; + Qabs_Qabs_Qinv -> Qabs_Qabs [] ; + Qabs_Qabs_Qinv -> QArith_base_Qinv [] ; + Qabs_Qabs_Qinv -> QArith_base_Qeq_refl [] ; + QArith_base_Qlt_trans -> QArith_base_Qlt_le_weak [] ; + QArith_base_Qlt_trans -> QArith_base_Qle_lt_trans [] ; + QArith_base_Qle_shift_div_l -> QArith_base_Qle_comp [] ; + QArith_base_Qle_shift_div_l -> QArith_base_Qlt_not_eq [] ; + QArith_base_Qle_shift_div_l -> QArith_base_Qnot_eq_sym [] ; + QArith_base_Qle_shift_div_l -> QArith_base_Qmult_lt_0_le_reg_r [] ; + QArith_base_Qle_shift_div_l -> QArith_base_Qmult_div_r [] ; + QArith_base_Qlt_irrefl -> QArith_base_Qlt [] ; + QArith_base_Qlt_irrefl -> Z_lt_irrefl [] ; + Qabs_Qabs_gt -> Qabs_Qabs_case [] ; + Qabs_Qabs_gt -> QArith_base_Qlt_le_trans [] ; + Qabs_Qabs_gt -> QArith_base_Qopp_le_compat [] ; + Z_lt_irrefl -> Morphisms_subrelation_proper [] ; + Z_lt_irrefl -> Morphisms_subrelation_refl [] ; + Z_lt_irrefl -> Morphisms_iff_flip_impl_subrelation [] ; + Z_lt_irrefl -> Morphisms_subrelation_respectful [] ; + Z_lt_irrefl -> _tt [] ; + Z_lt_irrefl -> Morphisms_Prop_not_iff_morphism [] ; + Z_lt_irrefl -> Z_compare_lt_iff [] ; + Z_lt_irrefl -> Z_compare_refl [] ; + QArith_base_Qmult_div_r -> QArith_base_Qmult_comm [] ; + QArith_base_Qmult_div_r -> QArith_base_Qdiv_mult_l [] ; + Z_compare_refl -> RelationClasses_reflexivity [] ; + Z_compare_refl -> RelationClasses_Equivalence_Reflexive [] ; + Z_compare_refl -> Z_eq_equiv [] ; + Z_compare_refl -> Z_compare_eq_iff [] ; + _Rquot2 -> ClassicalDedekindReals_DRealQuot2 [] ; + QArith_base_Qle_lt_trans -> QArith_base_Qlt [] ; + QArith_base_Qle_lt_trans -> QArith_base_Qmake [] ; + QArith_base_Qle_lt_trans -> QArith_base_Qle [] ; + QArith_base_Qle_lt_trans -> Z_mul_le_mono_pos_r [] ; + QArith_base_Qle_lt_trans -> Z_mul_lt_mono_pos_r [] ; + QArith_base_Qle_lt_trans -> Z_mul_shuffle0 [] ; + QArith_base_Qle_lt_trans -> Z_le_lt_trans [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> CMorphisms_reflexive_proper_proxy [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> CMorphisms_subrelation_respectful [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> CMorphisms_subrelation_proper [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> ConstructiveCauchyReals_CRealLt_morph [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> CMorphisms_subrelation_refl [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> CMorphisms_Reflexive_partial_app_morphism [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> CRelationClasses_Equivalence_Symmetric [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> CRelationClasses_symmetry [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> CRelationClasses_Equivalence_Reflexive [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> ConstructiveCauchyReals_CRealEq_relT [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> CMorphisms_iffT_flip_arrow_subrelation [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> ConstructiveCauchyReals_CRealLtForget [] ; + ConstructiveCauchyReals_CRealLtProp_morph_Proper -> ConstructiveCauchyReals_CRealLtEpsilon [] ; + Z_mul_le_mono_pos_r -> Z_mul_comm [] ; + Z_mul_le_mono_pos_r -> Z_mul_le_mono_pos_l [] ; + ConstructiveRcomplete_CRealLtDisjunctEpsilon -> ConstructiveCauchyReals_CRealLtProp [] ; + ConstructiveRcomplete_CRealLtDisjunctEpsilon -> QArith_base_Qlt_not_le [] ; + ConstructiveRcomplete_CRealLtDisjunctEpsilon -> QArith_base_Qlt_le_dec [] ; + ConstructiveRcomplete_CRealLtDisjunctEpsilon -> ConstructiveCauchyReals_CRealLt [] ; + ConstructiveRcomplete_CRealLtDisjunctEpsilon -> _sum [] ; + ConstructiveRcomplete_CRealLtDisjunctEpsilon -> _inl [] ; + ConstructiveRcomplete_CRealLtDisjunctEpsilon -> _inr [] ; + ConstructiveRcomplete_CRealLtDisjunctEpsilon -> QArith_base_Qle_not_lt [] ; + ConstructiveRcomplete_CRealLtDisjunctEpsilon -> ConstructiveExtra_constructive_indefinite_ground_description_Z [] ; + Z_mul_lt_mono_pos_r -> Z_mul_comm [] ; + Z_mul_lt_mono_pos_r -> Z_mul_lt_mono_pos_l [] ; + _R0_def -> _R0 [] ; + Z_mul_shuffle0 -> Z_mul_comm [] ; + Z_mul_shuffle0 -> Z_mul_assoc [] ; + ClassicalDedekindReals_DRealQuot2 -> ClassicalDedekindReals_DRealRepr [] ; + ClassicalDedekindReals_DRealQuot2 -> ClassicalDedekindReals_DRealAbstrFalse [] ; + ClassicalDedekindReals_DRealQuot2 -> _Z_ge_lt_dec [] ; + ClassicalDedekindReals_DRealQuot2 -> Nat2Z_is_nonneg [] ; + ClassicalDedekindReals_DRealQuot2 -> ClassicalDedekindReals_DRealAbstrFalse__ [] ; + Z_le_lt_trans -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_le_lt_trans -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_le_lt_trans -> Z_Private_OrderTac_Tac_not_ge_lt [] ; + ClassicalDedekindReals_DRealAbstrFalse -> _proj1_sig [] ; + ClassicalDedekindReals_DRealAbstrFalse -> ClassicalDedekindReals_DRealAbstr [] ; + Z_Private_OrderTac_Tac_le_lt_trans -> Z_Private_OrderTac_Tac_trans [] ; + _Z_ge_lt_dec -> Z_ge_le_iff [] ; + _Z_ge_lt_dec -> _sumbool_rec [] ; + _Z_ge_lt_dec -> Z_lt_nge [] ; + _Z_ge_lt_dec -> _Z_ge_dec [] ; + Z_Private_OrderTac_Tac_lt_irrefl -> RelationClasses_StrictOrder_Irreflexive [] ; + Z_Private_OrderTac_Tac_lt_irrefl -> Z_Private_OrderTac_IsTotal_lt_strorder [] ; + _Z_le_gt_dec -> Z_nle_gt [] ; + _Z_le_gt_dec -> _sumbool_rec [] ; + _Z_le_gt_dec -> Z_gt_lt_iff [] ; + _Z_le_gt_dec -> _Z_le_dec [] ; + Z_Private_OrderTac_Tac_not_ge_lt -> Z_Private_OrderTac_IsTotal_le_lteq [] ; + Z_Private_OrderTac_Tac_not_ge_lt -> Z_Private_OrderTac_IsTotal_lt_total [] ; + Z_Private_OrderTac_Tac_not_ge_lt -> Z_Private_OrderTac_IsTotal_eq_equiv [] ; + Nat2Z_is_nonneg -> _nat_ind [] ; + Nat2Z_is_nonneg -> RelationClasses_PreOrder_Reflexive [] ; + Nat2Z_is_nonneg -> Z_of_nat [] ; + Nat2Z_is_nonneg -> Z_le_preorder [] ; + Z_Private_OrderTac_IsTotal_le_lteq -> Z_le_lteq [] ; + ClassicalDedekindReals_DRealAbstrFalse__ -> _proj1_sig [] ; + ClassicalDedekindReals_DRealAbstrFalse__ -> Z2Nat_id [] ; + ClassicalDedekindReals_DRealAbstrFalse__ -> ClassicalDedekindReals_DRealAbstr [] ; + ClassicalDedekindReals_DRealAbstrFalse__ -> _Z_le_gt_dec [] ; + Z_Private_OrderTac_IsTotal_lt_total -> Z_lt_total [] ; + _Z_le_dec -> Z_le [] ; + _Z_le_dec -> _False_ind [] ; + _Z_le_dec -> _eq_ind [] ; + _Z_le_dec -> _True [] ; + _Z_le_dec -> _eq_refl [] ; + _Z_le_dec -> _I [] ; + _Z_le_dec -> _sumbool [] ; + _Z_le_dec -> _left [] ; + _Z_le_dec -> _right [] ; + Z_Private_OrderTac_IsTotal_eq_equiv -> Z_eq_equiv [] ; + _Z_ge_dec -> _False_ind [] ; + _Z_ge_dec -> _eq_ind [] ; + _Z_ge_dec -> _True [] ; + _Z_ge_dec -> _eq_refl [] ; + _Z_ge_dec -> _I [] ; + _Z_ge_dec -> _sumbool [] ; + _Z_ge_dec -> _left [] ; + _Z_ge_dec -> _right [] ; + _Z_ge_dec -> Z_ge [] ; + Z_lt_total -> Z_lt_trichotomy [] ; + _Fexp -> _float [] ; + Z_lt_trichotomy -> Z_le_gt_cases [] ; + _Fnum -> _float [] ; + Z_le_gt_cases -> Z_le_succ_l [] ; + _Rmult -> _R [] ; + _Rmult -> _Rrepr [] ; + _Rmult -> _Rabst [] ; + Z_lt_eq_cases -> Morphisms_reflexive_reflexive_proxy [] ; + Z_lt_eq_cases -> Morphisms_Reflexive_partial_app_morphism [] ; + Z_lt_eq_cases -> Morphisms_reflexive_proper_proxy [] ; + Z_lt_eq_cases -> Morphisms_Prop_or_iff_morphism [] ; + Z_lt_eq_cases -> Z_compare_eq_iff [] ; + Z_lt_eq_cases -> Z_compare_lt_iff [] ; + Z_lt_eq_cases -> Z_compare_le_iff [] ; + _Zdigits -> _Zdigits_aux [] ; + _Zdigits -> _digits2_Pnat [] ; + Z_compare_le_iff -> Z_le [] ; + Z_compare_le_iff -> RelationClasses_reflexivity [] ; + Z_compare_le_iff -> RelationClasses_iff_Reflexive [] ; + _Fdiv_core -> Z_pow [] ; + _Fdiv_core -> Z_div_eucl [] ; + _Fdiv_core -> SpecFloat_loc_Exact [] ; + _Fdiv_core -> _radix_val [] ; + _Fdiv_core -> _new_location [] ; + _new_location -> Z_even [] ; + _new_location -> _new_location_odd [] ; + _new_location -> _new_location_even [] ; + Z_lt_succ_r -> Z_le [] ; + Z_lt_succ_r -> Z_lt [] ; + Z_lt_succ_r -> Z_compare_sub [] ; + Z_lt_succ_r -> Z_sub_succ_r [] ; + Z_le_succ_l -> Morphisms_per_partial_app_morphism [] ; + Z_le_succ_l -> _or_cancel_r [] ; + Z_le_succ_l -> Z_succ_inj_wd [] ; + Z_le_succ_l -> Z_central_induction [] ; + Z_le_succ_l -> Z_le_wd [] ; + Z_le_succ_l -> Z_nle_succ_diag_l [] ; + Z_even -> _Z [] ; + Z_even -> _bool [] ; + Z_even -> _true [] ; + Z_even -> _false [] ; + _new_location_odd -> SpecFloat_location [] ; + _new_location_odd -> Z_compare [] ; + _new_location_odd -> Z_mul [] ; + _new_location_odd -> Z_add [] ; + _new_location_odd -> Z_eqb [] ; + _new_location_odd -> SpecFloat_loc_Inexact [] ; + Z_central_induction -> Z_bi_induction [] ; + _new_location_even -> SpecFloat_location [] ; + _new_location_even -> Z_compare [] ; + _new_location_even -> Z_mul [] ; + _new_location_even -> Z_eqb [] ; + _new_location_even -> SpecFloat_loc_Inexact [] ; + Z_le_refl -> RelationClasses_Equivalence_Reflexive [] ; + Z_le_refl -> Z_eq_equiv [] ; + Z_le_refl -> Z_lt_eq_cases [] ; + Z_le_wd -> RelationClasses_Equivalence_Reflexive [] ; + Z_le_wd -> Z_eq_equiv [] ; + Z_le_wd -> Z_succ_wd [] ; + Z_le_wd -> Z_lt_succ_r [] ; + Z_le_wd -> Z_lt_wd [] ; + _Zdigits_aux -> Z_mul [] ; + _Zdigits_aux -> Z_add [] ; + _Zdigits_aux -> _nat [] ; + _Zdigits_aux -> Z_ltb [] ; + _Zdigits_aux -> _radix_val [] ; + Z_lt_wd -> Z_lt [] ; + Z_lt_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Z_lt_wd -> RelationClasses_iff_Reflexive [] ; + Z_lt_wd -> Morphisms_reflexive_proper [] ; + Z_lt_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_lt_wd -> Z_eq [] ; + _digits2_Pnat -> _positive [] ; + _digits2_Pnat -> _nat [] ; + Z_nle_succ_diag_l -> Z_neq_succ_diag_l [] ; + Z_nle_succ_diag_l -> Z_nlt_succ_diag_l [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv -> _float [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv -> Z_min [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv -> _Zdigits [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv -> Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_core [] ; + Z_neq_succ_diag_l -> Z_lt_irrefl [] ; + Z_neq_succ_diag_l -> Z_lt_wd [] ; + Z_neq_succ_diag_l -> Z_lt_succ_diag_r [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_core -> Z_pow [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_core -> Z_div_eucl [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_core -> SpecFloat_loc_Exact [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_core -> _radix_val [] ; + Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_core -> _new_location [] ; + Z_nlt_succ_diag_l -> Z_lt_irrefl [] ; + Z_nlt_succ_diag_l -> Z_lt_succ_r [] ; + Z_nlt_succ_diag_l -> Z_lt_le_incl [] ; + _IPR -> _IPR_2 [] ; + Z_lt_le_incl -> Z_lt_eq_cases [] ; + _IPR_2 -> _Rplus [] ; + _IPR_2 -> _Rmult [] ; + _IPR_2 -> _R1 [] ; + Z_lt_succ_diag_r -> Z_lt_succ_r [] ; + Z_lt_succ_diag_r -> Z_le_refl [] ; + _R1 -> _R [] ; + _R1 -> _Rabst [] ; + Z_compare_sub -> Z_compare [] ; + Z_compare_sub -> Z_pos_sub_spec [] ; + Z_compare_sub -> Z_sub [] ; + Z_sub -> Z_add [] ; + Z_sub -> Z_opp [] ; + Z_sub_succ_r -> Z_succ [] ; + Z_sub_succ_r -> Z_Private_BootStrap_add_assoc [] ; + Z_sub_succ_r -> Z_pred [] ; + Z_sub_succ_r -> Z_sub [] ; + Z_le_lteq -> Z_lt_eq_cases [] ; + Z_Private_OrderTac_IsTotal_lt_strorder -> Z_lt_strorder [] ; + Z_lt_strorder -> RelationClasses_StrictOrder [] ; + Z_lt_strorder -> RelationClasses_Build_StrictOrder [] ; + Z_lt_strorder -> Z_lt_trans [] ; + Z_lt_trans -> Z_lt_asymm [] ; + Z_lt_asymm -> Z_le_succ_l [] ; + Z_Private_OrderTac_Tac_trans -> OrdersTac_OEQ [] ; + Z_Private_OrderTac_Tac_trans -> RelationClasses_StrictOrder_Transitive [] ; + Z_Private_OrderTac_Tac_trans -> OrdersTac_trans_ord [] ; + Z_Private_OrderTac_Tac_trans -> Z_Private_OrderTac_IsTotal_le_lteq [] ; + Z_Private_OrderTac_Tac_trans -> Z_Private_OrderTac_IsTotal_eq_equiv [] ; + Z_Private_OrderTac_Tac_trans -> Z_Private_OrderTac_IsTotal_lt_strorder [] ; + Z_Private_OrderTac_Tac_trans -> Z_Private_OrderTac_IsTotal_lt_compat [] ; + Z_Private_OrderTac_Tac_trans -> Z_Private_OrderTac_Tac_interp_ord [] ; + Z_Private_OrderTac_IsTotal_lt_compat -> Z_lt_compat [] ; + Z_Private_OrderTac_Tac_interp_ord -> Z_le [] ; + Z_Private_OrderTac_Tac_interp_ord -> Z_lt [] ; + Z_Private_OrderTac_Tac_interp_ord -> OrdersTac_ord [] ; + Z_lt_compat -> Z_lt_wd [] ; + Z_mul_assoc -> Z_mul_add_distr_r [] ; + Z_mul_add_distr_r -> Z_mul_wd [] ; + Z_mul_add_distr_r -> Z_mul_succ_l [] ; + Z_mul_add_distr_r -> Z_add_cancel_r [] ; + Z_mul_add_distr_r -> Z_mul_0_l [] ; + Z_mul_add_distr_r -> Z_add_assoc [] ; + Z_mul_lt_mono_pos_l -> Z_mul_wd [] ; + Z_mul_lt_mono_pos_l -> Z_mul_succ_l [] ; + Z_mul_lt_mono_pos_l -> Z_mul_0_l [] ; + Z_mul_lt_mono_pos_l -> Z_lt_ind [] ; + Z_mul_lt_mono_pos_l -> Z_add_lt_mono [] ; + Z_lt_ind -> Z_right_induction [] ; + Z_add_lt_mono -> Z_lt_trans [] ; + Z_add_lt_mono -> Z_add_lt_mono_r [] ; + Z_Private_OrderTac_Tac_lt_trans -> Z_Private_OrderTac_Tac_trans [] ; + Z_add_lt_mono_l -> Z_add_wd [] ; + Z_add_lt_mono_l -> Z_add_succ_l [] ; + Z_add_lt_mono_l -> Z_add_0_l [] ; + Z_add_lt_mono_l -> Z_succ_lt_mono [] ; + Z_add_lt_mono_r -> Z_add_comm [] ; + Z_add_lt_mono_r -> Z_add_lt_mono_l [] ; + Z_succ_lt_mono -> Z_le_succ_l [] ; + Z_right_induction -> Z_lt_exists_pred [] ; + Z_right_induction -> Z_strong_right_induction [] ; + Z_lt_exists_pred -> Morphisms_Prop_all_iff_morphism [] ; + Z_lt_exists_pred -> RelationClasses_PreOrder_Reflexive [] ; + Z_lt_exists_pred -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_lt_exists_pred -> Z_le_preorder [] ; + Z_lt_exists_pred -> Z_le_le_succ_r [] ; + Z_lt_exists_pred -> Z_le_succ_r [] ; + Z_strong_right_induction -> _well_founded_induction [] ; + Z_strong_right_induction -> Z_Private_OrderTac_Tac_not_ge_lt [] ; + Z_strong_right_induction -> Z_lt_wf [] ; + Z_Private_OrderTac_Tac_not_gt_le -> Z_Private_OrderTac_IsTotal_le_lteq [] ; + Z_Private_OrderTac_Tac_not_gt_le -> Z_Private_OrderTac_IsTotal_lt_total [] ; + Z_lt_wf -> Morphisms_Prop_all_iff_morphism [] ; + Z_lt_wf -> Morphisms_Prop_Acc_pt_morphism [] ; + Z_lt_wf -> _well_founded [] ; + Z_lt_wf -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_lt_wf -> Z_Rlt_wd [] ; + Z_lt_wf -> Z_lt_lt_succ_r [] ; + Z_Rlt_wd -> Morphisms_Prop_and_iff_morphism [] ; + Z_Rlt_wd -> Z_le_wd [] ; + Z_lt_lt_succ_r -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_lt_lt_succ_r -> Z_Private_OrderTac_Tac_lt_trans [] ; + Z_lt_lt_succ_r -> Z_Private_OrderTac_Tac_not_gt_le [] ; + Z_le_preorder -> RelationClasses_PreOrder [] ; + Z_le_preorder -> RelationClasses_Build_PreOrder [] ; + Z_le_preorder -> Z_le_trans [] ; + Z_le_le_succ_r -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_le_le_succ_r -> Z_Private_OrderTac_Tac_lt_trans [] ; + Z_le_le_succ_r -> Z_Private_OrderTac_Tac_not_gt_le [] ; + Z_le_succ_r -> Z_lt_eq_cases [] ; + Z_le_succ_r -> Z_lt_succ_r [] ; + Z_le_trans -> Z_lt_trans [] ; + Z_mul_le_mono_pos_l -> Z_mul_cancel_l [] ; + Z_mul_cancel_l -> Z_mul_lt_mono_pos_l [] ; + Z_mul_cancel_l -> Z_mul_lt_mono_neg_l [] ; + Z_mul_cancel_l -> Z_lt_gt_cases [] ; + Z_mul_cancel_l -> Z_Private_OrderTac_Tac_not_neq_eq [] ; + Z_Private_OrderTac_Tac_eq_lt -> Z_Private_OrderTac_Tac_trans [] ; + Z_Private_OrderTac_Tac_lt_eq -> Z_Private_OrderTac_Tac_trans [] ; + Z_Private_OrderTac_Tac_eq_sym -> RelationClasses_Equivalence_Symmetric [] ; + Z_Private_OrderTac_Tac_eq_sym -> RelationClasses_symmetry [] ; + Z_Private_OrderTac_Tac_eq_sym -> Z_Private_OrderTac_IsTotal_eq_equiv [] ; + Z_mul_lt_mono_neg_l -> Z_mul_0_l [] ; + Z_mul_lt_mono_neg_l -> Z_order_induction_0 [] ; + Z_mul_lt_mono_neg_l -> Z_mul_lt_pred [] ; + Z_mul_lt_mono_neg_l -> Z_le_lt_add_lt [] ; + Z_lt_gt_cases -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_lt_gt_cases -> Z_lt_trichotomy [] ; + Z_lt_gt_cases -> Z_Private_OrderTac_Tac_eq_lt [] ; + Z_lt_gt_cases -> Z_Private_OrderTac_Tac_lt_eq [] ; + Z_lt_gt_cases -> Z_Private_OrderTac_Tac_eq_sym [] ; + Z_lt_gt_cases -> Z_Private_OrderTac_Tac_eq_trans [] ; + Z_Private_OrderTac_Tac_not_neq_eq -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_Private_OrderTac_Tac_not_neq_eq -> Z_Private_OrderTac_IsTotal_lt_total [] ; + Z_Private_OrderTac_Tac_not_neq_eq -> Z_Private_OrderTac_IsTotal_eq_equiv [] ; + Z_Private_OrderTac_Tac_not_neq_eq -> Z_Private_OrderTac_IsTotal_lt_compat [] ; + Z_Private_OrderTac_Tac_eq_trans -> Z_Private_OrderTac_Tac_trans [] ; + Z_lt_succ_l -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_lt_succ_l -> Z_Private_OrderTac_Tac_lt_trans [] ; + Z_lt_succ_l -> Z_Private_OrderTac_Tac_not_gt_le [] ; + Z_order_induction_0 -> Z_order_induction [] ; + Z_mul_lt_pred -> Z_mul_wd [] ; + Z_mul_lt_pred -> Z_mul_succ_l [] ; + Z_mul_lt_pred -> Z_add_assoc [] ; + Z_mul_lt_pred -> Z_add_lt_mono_r [] ; + Z_le_lt_add_lt -> Z_nlt_ge [] ; + Z_le_lt_add_lt -> Z_add_le_mono [] ; + Z_nlt_ge -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_nlt_ge -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_nlt_ge -> Z_Private_OrderTac_Tac_not_gt_le [] ; + Z_add_le_mono -> Z_le_trans [] ; + Z_add_le_mono -> Z_add_le_mono_r [] ; + Z_add_le_mono_l -> Z_add_wd [] ; + Z_add_le_mono_l -> Z_add_succ_l [] ; + Z_add_le_mono_l -> Z_add_0_l [] ; + Z_add_le_mono_l -> Z_succ_le_mono [] ; + Z_add_le_mono_r -> Z_add_comm [] ; + Z_add_le_mono_r -> Z_add_le_mono_l [] ; + Z_succ_le_mono -> Z_succ_lt_mono [] ; + Z_order_induction -> Z_right_induction [] ; + Z_order_induction -> Z_left_induction [] ; + Z_left_induction -> Z_strong_left_induction [] ; + Z_left_induction -> Z_eq_le_incl [] ; + Z_strong_left_induction -> _well_founded_induction [] ; + Z_strong_left_induction -> Z_Private_OrderTac_Tac_not_ge_lt [] ; + Z_strong_left_induction -> Z_gt_wf [] ; + Z_eq_le_incl -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_eq_le_incl -> Z_Private_OrderTac_Tac_not_gt_le [] ; + Z_eq_le_incl -> Z_Private_OrderTac_Tac_lt_eq [] ; + Z_gt_wf -> Morphisms_Prop_all_iff_morphism [] ; + Z_gt_wf -> Morphisms_Prop_Acc_pt_morphism [] ; + Z_gt_wf -> _well_founded [] ; + Z_gt_wf -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_gt_wf -> Z_lt_succ_l [] ; + Z_gt_wf -> Z_Rgt_wd [] ; + Z_Rgt_wd -> Morphisms_Prop_and_iff_morphism [] ; + Z_Rgt_wd -> Z_le_wd [] ; + Qminmax_Q_Private_Tac_trans -> Qminmax_Q_OT_lt_compat [] ; + Qminmax_Q_Private_Tac_trans -> Qminmax_Q_OT_eq_equiv [] ; + Qminmax_Q_Private_Tac_trans -> Qminmax_Q_OT_le_lteq [] ; + Qminmax_Q_Private_Tac_trans -> Qminmax_Q_OT_lt_strorder [] ; + Qminmax_Q_Private_Tac_trans -> Qminmax_Q_Private_Tac_interp_ord [] ; + Qminmax_Q_Private_Tac_interp_ord -> QArith_base_Qlt [] ; + Qminmax_Q_Private_Tac_interp_ord -> QArith_base_Qle [] ; + Qminmax_Q_Private_Tac_interp_ord -> OrdersTac_ord [] ; + Qminmax_Q_Private_Tac_interp_ord -> QArith_base_Qeq [] ; + Ring_polynom_PNSubstL -> Ring_polynom_PSubstL [] ; + Ring_polynom_norm_aux -> Ring_polynom_PExpr [] ; + Ring_polynom_norm_aux -> Ring_polynom_Psub [] ; + Ring_polynom_norm_aux -> Ring_polynom_mk_X [] ; + Ring_polynom_norm_aux -> Ring_polynom_Ppow_N [] ; + Ring_polynom_Padd -> Ring_polynom_PaddI [] ; + Ring_polynom_Padd -> Ring_polynom_PaddX [] ; + Ring_polynom_Pmul -> Ring_polynom_Padd [] ; + Ring_polynom_Pmul -> Ring_polynom_PmulI [] ; + Ring_polynom_Popp -> Ring_polynom_Pol [] ; + Ring_polynom_Popp -> Ring_polynom_Pc [] ; + Ring_polynom_Popp -> Ring_polynom_Pinj [] ; + Ring_polynom_Popp -> Ring_polynom_PX [] ; + Ring_polynom_Psub -> Ring_polynom_PsubC [] ; + Ring_polynom_Psub -> Ring_polynom_PsubI [] ; + Ring_polynom_Psub -> Ring_polynom_PsubX [] ; + Ring_polynom_mk_X -> Ring_polynom_mkX [] ; + Ring_polynom_mk_X -> Ring_polynom_mkPinj_pred [] ; + Ring_polynom_Ppow_N -> _N [] ; + Ring_polynom_Ppow_N -> Ring_polynom_Ppow_pos [] ; + Ring_polynom_Ppow_N -> Ring_polynom_P1 [] ; + Ring_polynom_Ppow_pos -> Ring_polynom_Pmul [] ; + Ring_polynom_P1 -> Ring_polynom_Pol [] ; + Ring_polynom_P1 -> Ring_polynom_Pc [] ; + Ring_polynom_mkX -> _xH [] ; + Ring_polynom_mkX -> Ring_polynom_mkXi [] ; + Ring_polynom_mkPinj_pred -> Ring_polynom_Pol [] ; + Ring_polynom_mkPinj_pred -> Ring_polynom_Pinj [] ; + Ring_polynom_mkPinj_pred -> Pos_pred_double [] ; + Ring_polynom_mkXi -> Ring_polynom_PX [] ; + Ring_polynom_mkXi -> Ring_polynom_P0 [] ; + Ring_polynom_mkXi -> Ring_polynom_P1 [] ; + Ring_polynom_mkPX -> Ring_polynom_PX [] ; + Ring_polynom_mkPX -> Ring_polynom_P0 [] ; + Ring_polynom_mkPX -> Ring_polynom_Peq [] ; + Ring_polynom_mkPX -> Ring_polynom_mkPinj [] ; + Ring_polynom_PaddC -> Ring_polynom_Pol [] ; + Ring_polynom_PaddC -> Ring_polynom_Pc [] ; + Ring_polynom_PaddC -> Ring_polynom_Pinj [] ; + Ring_polynom_PaddC -> Ring_polynom_PX [] ; + Ring_polynom_PsubC -> Ring_polynom_Pol [] ; + Ring_polynom_PsubC -> Ring_polynom_Pc [] ; + Ring_polynom_PsubC -> Ring_polynom_Pinj [] ; + Ring_polynom_PsubC -> Ring_polynom_PX [] ; + Ring_polynom_PsubI -> Z_pos_sub [] ; + Ring_polynom_PsubI -> Pos_pred_double [] ; + Ring_polynom_PsubI -> Ring_polynom_Popp [] ; + Ring_polynom_PsubI -> Ring_polynom_PaddC [] ; + Ring_polynom_PsubI -> Ring_polynom_mkPinj [] ; + Ring_polynom_PsubX -> Z_pos_sub [] ; + Ring_polynom_PsubX -> Pos_pred_double [] ; + Ring_polynom_PsubX -> Ring_polynom_Popp [] ; + Ring_polynom_PsubX -> Ring_polynom_mkPX [] ; + Ring_polynom_mkPinj -> Pos_add [] ; + Ring_polynom_mkPinj -> Ring_polynom_Pol [] ; + Ring_polynom_mkPinj -> Ring_polynom_Pinj [] ; + Ring_polynom_PmulC -> Ring_polynom_PmulC_aux [] ; + Ring_polynom_PmulI -> Z_pos_sub [] ; + Ring_polynom_PmulI -> Pos_pred_double [] ; + Ring_polynom_PmulI -> Ring_polynom_PmulC [] ; + Ring_polynom_PmulC_aux -> Ring_polynom_mkPX [] ; + Ring_polynom_PaddI -> Z_pos_sub [] ; + Ring_polynom_PaddI -> Pos_pred_double [] ; + Ring_polynom_PaddI -> Ring_polynom_PaddC [] ; + Ring_polynom_PaddI -> Ring_polynom_mkPinj [] ; + Ring_polynom_PaddX -> Z_pos_sub [] ; + Ring_polynom_PaddX -> Pos_pred_double [] ; + Ring_polynom_PaddX -> Ring_polynom_mkPX [] ; + Ring_polynom_PSubstL -> Ring_polynom_PSubstL1 [] ; + Ring_polynom_PSubstL -> Ring_polynom_PNSubst [] ; + Ring_polynom_PSubstL1 -> _list [] ; + Ring_polynom_PSubstL1 -> Ring_polynom_PNSubst1 [] ; + Ring_polynom_PNSubst -> Ring_polynom_PNSubst1 [] ; + Ring_polynom_POneSubst -> _option [] ; + Ring_polynom_POneSubst -> _Some [] ; + Ring_polynom_POneSubst -> _None [] ; + Ring_polynom_POneSubst -> Ring_polynom_Pmul [] ; + Ring_polynom_POneSubst -> Ring_polynom_MFactor [] ; + Ring_polynom_PNSubst1 -> _nat [] ; + Ring_polynom_PNSubst1 -> Ring_polynom_POneSubst [] ; + Ring_polynom_MFactor -> Pos_sub [] ; + Ring_polynom_MFactor -> Ring_polynom_zmon_pred [] ; + Ring_polynom_MFactor -> Ring_polynom_vmon [] ; + Ring_polynom_MFactor -> Ring_polynom_CFactor [] ; + Ring_polynom_CFactor -> _prod [] ; + Ring_polynom_CFactor -> _pair [] ; + Ring_polynom_CFactor -> Ring_polynom_mkPX [] ; + Z_lt_le_trans -> Z_Private_OrderTac_Tac_le_lt_trans [] ; + Z_lt_le_trans -> Z_Private_OrderTac_Tac_lt_irrefl [] ; + Z_lt_le_trans -> Z_Private_OrderTac_Tac_not_ge_lt [] ; + Pos_le_1_l -> _xO [] ; + Pos_le_1_l -> _xH [] ; + Pos_le_1_l -> _xI [] ; + Pos_le_1_l -> _False_ind [] ; + Pos_le_1_l -> _eq_ind [] ; + Pos_le_1_l -> _True [] ; + Pos_le_1_l -> _eq_refl [] ; + Pos_le_1_l -> _I [] ; + Pos_le_1_l -> Pos_le [] ; + Pos2Z_pos_le_pos -> Z_le [] ; + Pos2Z_pos_le_pos -> _Zpos [] ; + Pos2Z_pos_le_pos -> Pos_le [] ; + Pos2Z_inj_mul -> _eq [] ; + Pos2Z_inj_mul -> Pos_mul [] ; + Pos2Z_inj_mul -> Z_mul [] ; + Pos2Z_inj_mul -> _eq_refl [] ; + Z_mul_le_mono_nonneg -> Z_mul_lt_mono_nonneg [] ; + Z_mul_lt_mono_nonneg -> Z_le_lt_trans [] ; + Z_mul_lt_mono_nonneg -> Z_mul_le_mono_nonneg_r [] ; + Z_mul_le_mono_nonneg_l -> Z_mul_lt_mono_pos_l [] ; + Z_mul_le_mono_nonneg_l -> Z_eq_le_incl [] ; + Z_mul_le_mono_nonneg_r -> Z_mul_comm [] ; + Z_mul_le_mono_nonneg_r -> Z_mul_le_mono_nonneg_l [] ; + Pos_le -> _eq [] ; + Pos_le -> _not [] ; + Pos_le -> Pos_compare [] ; + SetoidTactics_DefaultRelation -> Relation_Definitions_relation [] ; + SetoidTactics_Build_DefaultRelation -> Relation_Definitions_relation [] ; + SuccNat2Pos_inv -> Pos2Nat_inj [] ; + SuccNat2Pos_inv -> SuccNat2Pos_id_succ [] ; + Pos2Nat_is_succ -> _ex [] ; + Pos2Nat_is_succ -> _ex_intro [] ; + Pos2Nat_is_succ -> Pos_peano_ind [] ; + Pos2Nat_is_succ -> Pos2Nat_inj_succ [] ; + Pos2Nat_inj_succ -> Nat_add_assoc [] ; + Pos2Nat_inj_succ -> Pos_to_nat [] ; + Pos2Nat_inj_succ -> Pos_iter_op_succ [] ; + Pos_iter_op -> _positive [] ; + Pos_iter_op_succ -> Pos_succ [] ; + Pos_iter_op_succ -> _eq_ind_r [] ; + Pos_iter_op_succ -> _positive_ind [] ; + Pos_iter_op_succ -> Pos_iter_op [] ; + Pos_of_succ_nat -> Pos_succ [] ; + Pos_of_succ_nat -> _nat [] ; + Pos2Nat_inj -> Pos2Nat_id [] ; + SuccNat2Pos_id_succ -> Pos_of_nat_succ [] ; + SuccNat2Pos_id_succ -> Nat2Pos_id [] ; + RelationClasses_neq_Symmetric -> RelationClasses_Symmetric [] ; + RelationClasses_neq_Symmetric -> _not_eq_sym [] ; + Pos_of_nat_succ -> Pos_of_nat [] ; + Pos_of_nat_succ -> _eq_ind_r [] ; + Pos_of_nat_succ -> _nat_ind [] ; + Pos_of_nat_succ -> _f_equal [] ; + Pos_of_nat_succ -> _eq_trans [] ; + Pos_of_nat_succ -> Pos_of_succ_nat [] ; + Nat2Pos_id -> Pos_of_nat [] ; + Nat2Pos_id -> _f_equal [] ; + Nat2Pos_id -> Pos2Nat_inj_succ [] ; + Nat2Pos_id -> RelationClasses_neq_Symmetric [] ; + Nat2Pos_id -> _O_S [] ; + _O_S -> _not [] ; + _O_S -> _O [] ; + _O_S -> _S [] ; + _O_S -> _nat [] ; + _O_S -> _False_ind [] ; + _O_S -> _eq_ind [] ; + _O_S -> _True [] ; + _O_S -> _I [] ; + Pos2Nat_id -> Pos_of_nat [] ; + Pos2Nat_id -> Morphisms_rewrite_relation_eq_dom [] ; + Pos2Nat_id -> Morphisms_reflexive_proper [] ; + Pos2Nat_id -> Morphisms_reflexive_eq_dom_reflexive [] ; + Pos2Nat_id -> Pos2Nat_is_succ [] ; + Pos2Nat_id -> Morphisms_eq_rewrite_relation [] ; + Morphisms_eq_rewrite_relation -> _eq [] ; + Morphisms_eq_rewrite_relation -> RelationClasses_RewriteRelation [] ; + Morphisms_eq_rewrite_relation -> RelationClasses_Build_RewriteRelation [] ; + BinList_nth -> List_hd [] ; + BinList_nth -> BinList_jump [] ; + List_hd -> _list [] ; + List_tl -> _list [] ; + List_tl -> _nil [] ; + BinList_jump -> _positive [] ; + BinList_jump -> List_tl [] ; + QOrderedType_Q_as_OT_eq_equiv -> QArith_base_Q_Setoid [] ; + QArith_base_Q_Setoid -> QArith_base_Qeq_trans [] ; + QArith_base_Q_Setoid -> QArith_base_Qeq_sym [] ; + QArith_base_Q_Setoid -> QArith_base_Qeq_refl [] ; + QArith_base_Qeq_trans -> QArith_base_Qeq [] ; + QArith_base_Qeq_trans -> Z_mul_shuffle0 [] ; + QArith_base_Qeq_trans -> Z_mul_reg_r [] ; + QArith_base_Qeq_sym -> _eq_sym [] ; + QArith_base_Qeq_sym -> QArith_base_Qeq [] ; + QArith_base_Qeq_refl -> _eq_refl [] ; + QArith_base_Qeq_refl -> QArith_base_Qeq [] ; + Z_mul_reg_r -> Z_mul_cancel_r [] ; + Z_mul_reg_r -> _proj1 [] ; + Z_mul_cancel_r -> Z_mul_comm [] ; + Z_mul_cancel_r -> Z_mul_cancel_l [] ; + _proj1 -> _and [] ; + N_mul -> Pos_mul [] ; + N_mul -> _N [] ; + N_mul -> _N0 [] ; + N_mul -> _Npos [] ; + _nat_N_Z -> _eq [] ; + _nat_N_Z -> _O [] ; + _nat_N_Z -> _S [] ; + _nat_N_Z -> _eq_refl [] ; + _nat_N_Z -> Z_of_N [] ; + _nat_N_Z -> Z_of_nat [] ; + _nat_N_Z -> N_of_nat [] ; + N_of_nat -> PosDef_Pos_of_succ_nat [] ; + N_of_nat -> _N [] ; + N_of_nat -> _N0 [] ; + N_of_nat -> _Npos [] ; + N2Z_inj_mul -> _eq [] ; + N2Z_inj_mul -> Z_mul [] ; + N2Z_inj_mul -> _eq_refl [] ; + N2Z_inj_mul -> Z_of_N [] ; + N2Z_inj_mul -> N_mul [] ; + Nnat_Nat2N_inj_mul -> Nnat_Nat2N_id [] ; + Nnat_Nat2N_inj_mul -> Nnat_N2Nat_inj_mul [] ; + Nnat_Nat2N_inj_mul -> Nnat_N2Nat_inj [] ; + Nnat_Nat2N_id -> SuccNat2Pos_id_succ [] ; + Nnat_Nat2N_id -> N_of_nat [] ; + Nnat_Nat2N_id -> N_to_nat [] ; + Nnat_N2Nat_inj_mul -> N_mul [] ; + Nnat_N2Nat_inj_mul -> N_to_nat [] ; + Nnat_N2Nat_inj_mul -> Pos2Nat_inj_mul [] ; + Nnat_N2Nat_inj_mul -> _mult_n_O [] ; + Nnat_N2Nat_inj -> Nnat_N2Nat_id [] ; + Nnat_N2Nat_inj -> BinNatDef_N_of_nat [] ; + N_to_nat -> PosDef_Pos_to_nat [] ; + N_to_nat -> _N [] ; + Nnat_N2Nat_id -> Pos2Nat_inj [] ; + Nnat_N2Nat_id -> SuccNat2Pos_id_succ [] ; + Nnat_N2Nat_id -> N_of_nat [] ; + Nnat_N2Nat_id -> N_to_nat [] ; + BinNatDef_N_of_nat -> PosDef_Pos_of_succ_nat [] ; + BinNatDef_N_of_nat -> _N [] ; + BinNatDef_N_of_nat -> _N0 [] ; + BinNatDef_N_of_nat -> _Npos [] ; + _N0 -> _positive [] ; + _Npos -> _positive [] ; + Pos2Nat_inj_mul -> _plus_n_O [] ; + Pos2Nat_inj_mul -> Init_Nat_mul [] ; + Pos2Nat_inj_mul -> Pos_mul_succ_l [] ; + Pos2Nat_inj_mul -> Pos2Nat_inj_add [] ; + _mult_n_O -> _eq [] ; + _mult_n_O -> _eq_refl [] ; + _mult_n_O -> _nat_ind [] ; + _mult_n_O -> Init_Nat_mul [] ; + Pos_mul_succ_l -> Pos_mul [] ; + Pos_mul_succ_l -> Pos_add_assoc [] ; + Pos_mul_succ_l -> Pos_add_xO [] ; + Pos_mul_succ_l -> Pos_add_diag [] ; + Pos2Nat_inj_add -> Pos_add_1_l [] ; + Pos2Nat_inj_add -> Pos_peano_ind [] ; + Pos2Nat_inj_add -> Pos_add_succ_l [] ; + Pos2Nat_inj_add -> Pos2Nat_inj_succ [] ; + Pos_add_xO -> _eq [] ; + Pos_add_xO -> Pos_add [] ; + Pos_add_xO -> _eq_refl [] ; + Pos_add_diag -> _eq_ind_r [] ; + Pos_add_diag -> Pos_add_carry_spec [] ; + QOrderedType_Q_as_OT_lt_compat -> QArith_base_Qlt_compat [] ; + QArith_base_Qlt_compat -> QArith_base_Qlt_alt [] ; + QArith_base_Qlt_compat -> QArith_base_Q_Setoid [] ; + QArith_base_Qlt_compat -> QArith_base_Qcompare_comp [] ; + QArith_base_Qcompare_comp -> QArith_base_Qmake [] ; + QArith_base_Qcompare_comp -> _ring_subst_niter [] ; + QArith_base_Qcompare_comp -> QArith_base_Qeq [] ; + QArith_base_Qcompare_comp -> QArith_base_Qcompare [] ; + QArith_base_Qcompare_comp -> _Zr_ring_lemma1 [] ; + QArith_base_Qcompare_comp -> _Zcompare_mult_compat [] ; + _Zr_ring_lemma1 -> _Ztriv_div_th [] ; + _Zr_ring_lemma1 -> _Eq_ext [] ; + _Zr_ring_lemma1 -> _Zpower_theory [] ; + _Zr_ring_lemma1 -> _IDmorph [] ; + _Zr_ring_lemma1 -> ZArithRing_Private_proj1_eqb_eq [] ; + _Zr_ring_lemma1 -> _Rth_ARth [] ; + _Zr_ring_lemma1 -> _Zth [] ; + _Zr_ring_lemma1 -> _Eqsth [] ; + _Zr_ring_lemma1 -> Ring_polynom_ring_correct [] ; + Z_quotrem -> Z_opp [] ; + Z_quotrem -> Z_of_N [] ; + Z_quotrem -> NatDef_N_pos_div_eucl [] ; + _Zcompare_mult_compat -> Z_compare [] ; + _Zcompare_mult_compat -> Z_mul [] ; + _Zcompare_mult_compat -> Pos_mul_compare_mono_l [] ; + Ring_polynom_PEmul -> _N [] ; + NatDef_N_pos_div_eucl -> _prod [] ; + NatDef_N_pos_div_eucl -> _pair [] ; + NatDef_N_pos_div_eucl -> NatDef_N_leb [] ; + NatDef_N_pos_div_eucl -> NatDef_N_sub [] ; + NatDef_N_pos_div_eucl -> NatDef_N_double [] ; + NatDef_N_pos_div_eucl -> NatDef_N_succ_double [] ; + NatDef_N_leb -> _bool [] ; + NatDef_N_leb -> _true [] ; + NatDef_N_leb -> _false [] ; + NatDef_N_leb -> NatDef_N_compare [] ; + NatDef_N_sub -> _N [] ; + NatDef_N_sub -> PosDef_Pos_sub_mask [] ; + NatDef_N_sub -> _N0 [] ; + NatDef_N_sub -> _Npos [] ; + NatDef_N_double -> _xO [] ; + NatDef_N_double -> _N [] ; + NatDef_N_double -> _N0 [] ; + NatDef_N_double -> _Npos [] ; + NatDef_N_succ_double -> _xH [] ; + NatDef_N_succ_double -> _xI [] ; + NatDef_N_succ_double -> _N [] ; + NatDef_N_succ_double -> _Npos [] ; + NatDef_N_compare -> PosDef_Pos_compare [] ; + NatDef_N_compare -> _N [] ; + _Ztriv_div_th -> Z_mul_comm [] ; + _Ztriv_div_th -> _div_theory [] ; + _Ztriv_div_th -> Setoid_Seq_refl [] ; + _Ztriv_div_th -> Z_quotrem_eq [] ; + _Ztriv_div_th -> _mkdiv_th [] ; + _Eq_ext -> Morphisms_reflexive_reflexive_proxy [] ; + _Eq_ext -> Morphisms_Reflexive_partial_app_morphism [] ; + _Eq_ext -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _Eq_ext -> Morphisms_eq_proper_proxy [] ; + _Eq_ext -> RelationClasses_eq_Reflexive [] ; + _Eq_ext -> RelationClasses_eq_Transitive [] ; + _Eq_ext -> Morphisms_rewrite_relation_eq_dom [] ; + _Eq_ext -> Morphisms_reflexive_proper [] ; + _Eq_ext -> Morphisms_reflexive_eq_dom_reflexive [] ; + _Eq_ext -> Morphisms_eq_rewrite_relation [] ; + _Eq_ext -> _ring_eq_ext [] ; + _Eq_ext -> _mk_reqe [] ; + Z_pow -> Z_pow_pos [] ; + _Zpower_theory -> Z_of_N [] ; + _Zpower_theory -> Z_mul_1_r [] ; + _Zpower_theory -> Z_mul_assoc [] ; + _Zpower_theory -> _N0 [] ; + _Zpower_theory -> _Npos [] ; + _Zpower_theory -> Z_pow [] ; + _Zpower_theory -> _power_theory [] ; + _Zpower_theory -> _mkpow_th [] ; + _IDmorph -> RelationClasses_reflexivity [] ; + _IDmorph -> RelationClasses_Equivalence_Reflexive [] ; + _IDmorph -> _IDphi [] ; + _IDmorph -> _ring_morph [] ; + _IDmorph -> _mkmorph [] ; + ZArithRing_Private_proj1_eqb_eq -> Z_eqb_eq [] ; + _Rth_ARth -> _almost_ring_theory [] ; + _Rth_ARth -> _Rmul_comm [] ; + _Rth_ARth -> _Ropp_mul_l [] ; + _Rth_ARth -> _Ropp_add [] ; + _Rth_ARth -> _Rsub_def [] ; + _Rth_ARth -> _Rmul_assoc [] ; + _Rth_ARth -> _mk_art [] ; + Ring_polynom_interp_PElist -> _prod [] ; + Ring_polynom_interp_PElist -> _and [] ; + Ring_polynom_interp_PElist -> _True [] ; + Ring_polynom_interp_PElist -> Ring_polynom_PEeval [] ; + _Zth -> Z_mul_comm [] ; + _Zth -> Z_mul_assoc [] ; + _Zth -> Z_mul_1_l [] ; + _Zth -> Z_sub_diag [] ; + _Zth -> _ring_theory [] ; + _Zth -> _mk_rt [] ; + _Eqsth -> RelationClasses_eq_equivalence [] ; + Ring_polynom_ring_correct -> Ring_polynom_norm_subst_ok [] ; + Ring_polynom_Pphi -> _pow_pos [] ; + Ring_polynom_Pphi -> Ring_polynom_Pol [] ; + Ring_polynom_Pphi -> List_hd [] ; + Ring_polynom_Pphi -> BinList_jump [] ; + Ring_polynom_Peq_ok -> Morphisms_reflexive_reflexive_proxy [] ; + Ring_polynom_Peq_ok -> Morphisms_Reflexive_partial_app_morphism [] ; + Ring_polynom_Peq_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Ring_polynom_Peq_ok -> Morphisms_eq_proper_proxy [] ; + Ring_polynom_Peq_ok -> Morphisms_reflexive_proper_proxy [] ; + Ring_polynom_Peq_ok -> RelationClasses_Equivalence_Reflexive [] ; + Ring_polynom_Peq_ok -> Pos_compare_spec [] ; + Ring_polynom_Peq_ok -> Ring_polynom_Peq [] ; + Ring_polynom_Peq_ok -> Ring_polynom_rmul_ext_Proper [] ; + Ring_polynom_Peq_ok -> Ring_polynom_radd_ext_Proper [] ; + Ring_polynom_Peq_ok -> Ring_polynom_Pol_ind [] ; + Ring_polynom_Peq_ok -> Ring_polynom_Pequiv [] ; + Ring_polynom_Peq_ok -> _morph_eq [] ; + Ring_polynom_norm_subst_ok -> Ring_polynom_interp_PElist_ok [] ; + _div_theory -> _prod [] ; + _ring_morph -> _bool [] ; + _ring_morph -> _eq [] ; + _ring_morph -> _true [] ; + _ring_eq_ext -> Morphisms_Proper [] ; + _ring_eq_ext -> Morphisms_respectful [] ; + _power_theory -> _pow_N [] ; + _pow_N -> _pow_pos [] ; + _pow_N -> _N [] ; + Ring_polynom_interp_PElist_ok -> Ring_polynom_mk_monpol_list [] ; + Ring_polynom_interp_PElist_ok -> Ring_polynom_interp_PElist [] ; + Ring_polynom_interp_PElist_ok -> Ring_polynom_norm_subst_spec [] ; + Ring_polynom_interp_PElist_ok -> Ring_polynom_mon_of_pol_ok [] ; + Ring_polynom_norm_subst_spec -> Ring_polynom_norm_subst [] ; + Ring_polynom_norm_subst_spec -> Ring_polynom_PNSubstL_ok [] ; + Ring_polynom_norm_subst_spec -> Ring_polynom_norm_aux_spec [] ; + Ring_polynom_PNSubstL_ok -> Ring_polynom_PNSubstL [] ; + Ring_polynom_PNSubstL_ok -> Ring_polynom_PSubstL_ok [] ; + Ring_polynom_MPcond -> _and [] ; + Ring_polynom_MPcond -> _True [] ; + Ring_polynom_MPcond -> Ring_polynom_Pphi [] ; + Ring_polynom_MPcond -> Ring_polynom_Mphi [] ; + Ring_polynom_MPcond -> _fst [] ; + Ring_polynom_MPcond -> _snd [] ; + Ring_polynom_norm_aux_spec -> Ring_polynom_PEeval [] ; + Ring_polynom_norm_aux_spec -> Ring_polynom_Ppow_N_ok [] ; + Ring_polynom_norm_aux_spec -> Ring_polynom_Psub_ok [] ; + Ring_polynom_norm_aux_spec -> Ring_polynom_rsub_ext_Proper [] ; + Ring_polynom_norm_aux_spec -> Ring_polynom_ropp_ext_Proper [] ; + Ring_polynom_norm_aux_spec -> _rpow_pow_N [] ; + Ring_polynom_norm_aux_spec -> Ring_polynom_mkX_ok [] ; + Ring_polynom_norm_aux_spec -> Ring_polynom_PExpr_ind [] ; + Ring_polynom_norm_aux_spec -> Ring_polynom_norm_aux_PEadd [] ; + Ring_polynom_norm_aux_spec -> Ring_polynom_norm_aux_PEopp [] ; + Ring_polynom_Ppow_N_ok -> Ring_polynom_Ppow_N [] ; + Ring_polynom_Ppow_N_ok -> _N0 [] ; + Ring_polynom_Ppow_N_ok -> _Npos [] ; + Ring_polynom_Ppow_N_ok -> _pow_N [] ; + Ring_polynom_Ppow_N_ok -> Ring_polynom_Pphi1 [] ; + Ring_polynom_Ppow_N_ok -> Ring_polynom_Ppow_pos_ok [] ; + Ring_polynom_Pmul_ok -> Ring_polynom_Padd_ok [] ; + Ring_polynom_Pmul_ok -> Ring_polynom_PmulI_ok [] ; + Ring_polynom_Pmul_ok -> _ARdistr_r [] ; + Ring_polynom_Popp_ok -> Morphisms_reflexive_reflexive_proxy [] ; + Ring_polynom_Popp_ok -> Morphisms_Reflexive_partial_app_morphism [] ; + Ring_polynom_Popp_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Ring_polynom_Popp_ok -> Morphisms_eq_proper_proxy [] ; + Ring_polynom_Popp_ok -> RelationClasses_Equivalence_PER [] ; + Ring_polynom_Popp_ok -> Morphisms_reflexive_proper_proxy [] ; + Ring_polynom_Popp_ok -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Ring_polynom_Popp_ok -> Ring_polynom_Popp [] ; + Ring_polynom_Popp_ok -> Ring_polynom_Pphi [] ; + Ring_polynom_Popp_ok -> Ring_polynom_rmul_ext_Proper [] ; + Ring_polynom_Popp_ok -> Setoid_Seq_refl [] ; + Ring_polynom_Popp_ok -> Ring_polynom_radd_ext_Proper [] ; + Ring_polynom_Popp_ok -> Ring_polynom_Pol_ind [] ; + Ring_polynom_Popp_ok -> _morph_opp [] ; + Ring_polynom_Popp_ok -> _ARopp_mul_l [] ; + Ring_polynom_Popp_ok -> _ARopp_add [] ; + Ring_polynom_Psub_ok -> Ring_polynom_Popp_ok [] ; + Ring_polynom_Psub_ok -> Ring_polynom_Padd_ok [] ; + Ring_polynom_Psub_ok -> Ring_polynom_Psub_opp [] ; + Ring_polynom_rsub_ext_Proper -> _ARsub_ext [] ; + Ring_polynom_ropp_ext_Proper -> _Ropp_ext [] ; + Ring_polynom_rmul_ext_Proper -> _Rmul_ext [] ; + _morph0 -> _ring_morph [] ; + _morph1 -> _ring_morph [] ; + _rpow_pow_N -> _power_theory [] ; + _ARadd_comm -> _almost_ring_theory [] ; + Ring_polynom_mkX_ok -> Morphisms_reflexive_reflexive_proxy [] ; + Ring_polynom_mkX_ok -> RelationClasses_Equivalence_PER [] ; + Ring_polynom_mkX_ok -> Morphisms_reflexive_proper_proxy [] ; + Ring_polynom_mkX_ok -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Ring_polynom_mkX_ok -> Ring_polynom_mk_X [] ; + Ring_polynom_mkX_ok -> Ring_polynom_Pphi [] ; + Ring_polynom_mkX_ok -> Ring_polynom_rmul_ext_Proper [] ; + Ring_polynom_mkX_ok -> _morph0 [] ; + Ring_polynom_mkX_ok -> _morph1 [] ; + Ring_polynom_mkX_ok -> Setoid_Seq_refl [] ; + Ring_polynom_mkX_ok -> Ring_polynom_radd_ext_Proper [] ; + Ring_polynom_mkX_ok -> _ARadd_0_r [] ; + Ring_polynom_mkX_ok -> _ARmul_1_l [] ; + Ring_polynom_mkX_ok -> BinList_nth_pred_double [] ; + Ring_polynom_mkX_ok -> BinList_nth_jump [] ; + Setoid_Seq_refl -> RelationClasses_reflexivity [] ; + Setoid_Seq_refl -> RelationClasses_Equivalence_Reflexive [] ; + Setoid_Seq_refl -> Setoid_Setoid_Theory [] ; + Ring_polynom_PExpr_ind -> Ring_polynom_PExpr [] ; + Ring_polynom_PExpr_ind -> Ring_polynom_PEX [] ; + Ring_polynom_PExpr_ind -> Ring_polynom_PEadd [] ; + Ring_polynom_PExpr_ind -> Ring_polynom_PEsub [] ; + Ring_polynom_PExpr_ind -> Ring_polynom_PEmul [] ; + Ring_polynom_PExpr_ind -> Ring_polynom_PEO [] ; + Ring_polynom_PExpr_ind -> Ring_polynom_PEI [] ; + Ring_polynom_PExpr_ind -> Ring_polynom_PEc [] ; + Ring_polynom_PExpr_ind -> Ring_polynom_PEopp [] ; + Ring_polynom_PExpr_ind -> Ring_polynom_PEpow [] ; + _ARsub_def -> _almost_ring_theory [] ; + Ring_polynom_radd_ext_Proper -> _Radd_ext [] ; + _Radd_ext -> _ring_eq_ext [] ; + Ring_polynom_get_PEopp -> Ring_polynom_PExpr [] ; + Ring_polynom_get_PEopp -> _option [] ; + Ring_polynom_get_PEopp -> _Some [] ; + Ring_polynom_get_PEopp -> _None [] ; + Ring_polynom_norm_aux_PEadd -> _eq [] ; + Ring_polynom_norm_aux_PEadd -> _eq_refl [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_PEX [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_PEadd [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_PEsub [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_norm_aux [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_PEmul [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_get_PEopp [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_PEO [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_PEI [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_PEc [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_PEopp [] ; + Ring_polynom_norm_aux_PEadd -> Ring_polynom_PEpow [] ; + Ring_polynom_norm_aux_PEopp -> _eq [] ; + Ring_polynom_norm_aux_PEopp -> _True [] ; + Ring_polynom_norm_aux_PEopp -> _eq_refl [] ; + Ring_polynom_norm_aux_PEopp -> _I [] ; + Ring_polynom_norm_aux_PEopp -> Ring_polynom_norm_aux [] ; + Ring_polynom_norm_aux_PEopp -> Ring_polynom_get_PEopp [] ; + Ring_polynom_Padd_ok -> Ring_polynom_PaddC_ok [] ; + Ring_polynom_Padd_ok -> Ring_polynom_PaddX_ok [] ; + Ring_polynom_Padd_ok -> _ARadd_assoc1 [] ; + Ring_polynom_PEO -> _N [] ; + Ring_polynom_PEI -> _N [] ; + Ring_polynom_PEc -> _N [] ; + Ring_polynom_PEopp -> _N [] ; + Ring_polynom_PEpow -> _N [] ; + Ring_polynom_Pol_ind -> Ring_polynom_Pol [] ; + Ring_polynom_Pol_ind -> Ring_polynom_Pc [] ; + Ring_polynom_Pol_ind -> Ring_polynom_Pinj [] ; + Ring_polynom_Pol_ind -> Ring_polynom_PX [] ; + Ring_polynom_mkPinj_ok -> Ring_polynom_Pc [] ; + Ring_polynom_mkPinj_ok -> Ring_polynom_PX [] ; + Ring_polynom_mkPinj_ok -> Ring_polynom_mkPinj [] ; + Ring_polynom_mkPinj_ok -> Ring_polynom_Pphi [] ; + Ring_polynom_mkPinj_ok -> Setoid_Seq_refl [] ; + Ring_polynom_mkPinj_ok -> Ring_polynom_jump_add_ [] ; + Ring_polynom_pow_pos_add -> _ARmul_assoc [] ; + Ring_polynom_pow_pos_add -> _Rmul_ext [] ; + Ring_polynom_pow_pos_add -> _pow_pos_add [] ; + _ARadd_assoc -> _almost_ring_theory [] ; + BinList_jump_pred_double -> Pos_pred_double [] ; + BinList_jump_pred_double -> BinList_jump_tl [] ; + Ring_polynom_mkPX_ok -> Ring_polynom_mkPX [] ; + Ring_polynom_mkPX_ok -> Ring_polynom_mkPinj_ok [] ; + Ring_polynom_mkPX_ok -> Ring_polynom_pow_pos_add [] ; + Ring_polynom_mkPX_ok -> _ARadd_0_r [] ; + Ring_polynom_mkPX_ok -> Ring_polynom_Pphi_ext [] ; + Ring_polynom_mkPX_ok -> Ring_polynom_Pphi0 [] ; + Ring_polynom_mkPX_ok -> _ARmul_0_l [] ; + Ring_polynom_mkPX_ok -> Ring_polynom_ceqb_spec [] ; + Ring_polynom_mkPX_ok -> Ring_polynom_Peq_spec [] ; + Z_pos_sub_discr -> Pos_sub_add [] ; + Z_pos_sub_discr -> Z_pos_sub_spec [] ; + Ring_polynom_jump_add_ -> BinList_jump_add [] ; + Ring_polynom_PaddC_ok -> Morphisms_reflexive_reflexive_proxy [] ; + Ring_polynom_PaddC_ok -> Morphisms_Reflexive_partial_app_morphism [] ; + Ring_polynom_PaddC_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Ring_polynom_PaddC_ok -> Morphisms_eq_proper_proxy [] ; + Ring_polynom_PaddC_ok -> Morphisms_reflexive_proper_proxy [] ; + Ring_polynom_PaddC_ok -> RelationClasses_Equivalence_Transitive [] ; + Ring_polynom_PaddC_ok -> Ring_polynom_PaddC [] ; + Ring_polynom_PaddC_ok -> Ring_polynom_Pphi [] ; + Ring_polynom_PaddC_ok -> Setoid_Seq_refl [] ; + Ring_polynom_PaddC_ok -> Ring_polynom_radd_ext_Proper [] ; + Ring_polynom_PaddC_ok -> Ring_polynom_Pol_ind [] ; + Ring_polynom_PaddC_ok -> _ARadd_assoc [] ; + Ring_polynom_PaddC_ok -> _morph_add [] ; + Ring_polynom_PaddX_ok -> Ring_polynom_Padd [] ; + Ring_polynom_PaddX_ok -> BinList_jump_pred_double [] ; + Ring_polynom_PaddX_ok -> Ring_polynom_mkPX_ok [] ; + Ring_polynom_PaddX_ok -> Z_pos_sub_discr [] ; + Ring_polynom_PaddX_ok -> _ARadd_assoc2 [] ; + Ring_polynom_PaddX_ok -> _ARdistr_l [] ; + _ARmul_assoc -> _almost_ring_theory [] ; + _ARadd_0_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _ARadd_0_r -> RelationClasses_reflexivity [] ; + _ARadd_0_r -> Morphisms_eq_proper_proxy [] ; + _ARadd_0_r -> RelationClasses_Equivalence_Reflexive [] ; + _ARadd_0_r -> RelationClasses_Equivalence_Transitive [] ; + _ARadd_0_r -> RelationClasses_Equivalence_Symmetric [] ; + _ARadd_0_r -> RelationClasses_symmetry [] ; + _ARadd_0_r -> _ARadd_comm [] ; + _ARadd_0_r -> _ARadd_0_l [] ; + _ARadd_assoc1 -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _ARadd_assoc1 -> RelationClasses_reflexivity [] ; + _ARadd_assoc1 -> Morphisms_eq_proper_proxy [] ; + _ARadd_assoc1 -> RelationClasses_Equivalence_Reflexive [] ; + _ARadd_assoc1 -> RelationClasses_Equivalence_Transitive [] ; + _ARadd_assoc1 -> RelationClasses_Equivalence_Symmetric [] ; + _ARadd_assoc1 -> RelationClasses_symmetry [] ; + _ARadd_assoc1 -> _ARadd_comm [] ; + _ARadd_assoc1 -> _ARadd_assoc [] ; + _ARadd_assoc2 -> Morphisms_reflexive_reflexive_proxy [] ; + _ARadd_assoc2 -> Morphisms_Reflexive_partial_app_morphism [] ; + _ARadd_assoc2 -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _ARadd_assoc2 -> RelationClasses_reflexivity [] ; + _ARadd_assoc2 -> Morphisms_eq_proper_proxy [] ; + _ARadd_assoc2 -> RelationClasses_Equivalence_PER [] ; + _ARadd_assoc2 -> Morphisms_reflexive_proper_proxy [] ; + _ARadd_assoc2 -> RelationClasses_Equivalence_Reflexive [] ; + _ARadd_assoc2 -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _ARadd_assoc2 -> _ARadd_comm [] ; + _ARadd_assoc2 -> _ARadd_assoc [] ; + _ARadd_assoc2 -> _radd_ext2_Proper [] ; + _ARdistr_l -> _almost_ring_theory [] ; + _radd_ext2_Proper -> _Radd_ext [] ; + _ARadd_0_l -> _almost_ring_theory [] ; + _morph_add -> _ring_morph [] ; + BinList_jump_add -> Pos_add_1_l [] ; + BinList_jump_add -> Pos_peano_ind [] ; + BinList_jump_add -> Pos_add_succ_l [] ; + BinList_jump_add -> BinList_jump_succ [] ; + BinList_jump_succ -> Pos_succ [] ; + BinList_jump_succ -> BinList_jump_tl [] ; + BinList_jump_tl -> _eq_ind_r [] ; + BinList_jump_tl -> _positive_ind [] ; + BinList_jump_tl -> BinList_jump [] ; + Ring_polynom_Pphi_ext -> _eq_ind [] ; + Ring_polynom_Pphi_ext -> Morphisms_Proper [] ; + Ring_polynom_Pphi_ext -> Morphisms_respectful [] ; + Ring_polynom_Pphi_ext -> Ring_polynom_Pequiv [] ; + Ring_polynom_Pphi0 -> Ring_polynom_P0 [] ; + Ring_polynom_Pphi0 -> Ring_polynom_Pphi [] ; + Ring_polynom_Pphi0 -> _morph0 [] ; + _ARmul_0_l -> _almost_ring_theory [] ; + Ring_polynom_ceqb_spec -> _True [] ; + Ring_polynom_ceqb_spec -> _eq_refl [] ; + Ring_polynom_ceqb_spec -> _I [] ; + Ring_polynom_ceqb_spec -> _BoolSpec [] ; + Ring_polynom_ceqb_spec -> _BoolSpecT [] ; + Ring_polynom_ceqb_spec -> _BoolSpecF [] ; + Ring_polynom_ceqb_spec -> _morph_eq [] ; + Ring_polynom_Pequiv -> Ring_polynom_Pphi [] ; + Ring_polynom_Peq_spec -> Ring_polynom_Peq_ok [] ; + Ring_polynom_Peq_spec -> _BoolSpec [] ; + Ring_polynom_Peq_spec -> _BoolSpecT [] ; + Ring_polynom_Peq_spec -> _BoolSpecF [] ; + _BoolSpec -> _true [] ; + _BoolSpec -> _false [] ; + _BoolSpecT -> _true [] ; + _BoolSpecT -> _false [] ; + _BoolSpecF -> _true [] ; + _BoolSpecF -> _false [] ; + _morph_eq -> _ring_morph [] ; + _Rmul_ext -> _ring_eq_ext [] ; + _pow_pos_add -> Pos_add_1_l [] ; + _pow_pos_add -> Pos_peano_ind [] ; + _pow_pos_add -> Pos_add_succ_l [] ; + _pow_pos_add -> _pow_pos_succ [] ; + _pow_pos_succ -> Pos_succ [] ; + _pow_pos_succ -> _pow_pos_swap [] ; + _pow_pos_swap -> _pow_pos [] ; + _pow_pos_swap -> Morphisms_reflexive_reflexive_proxy [] ; + _pow_pos_swap -> Morphisms_Reflexive_partial_app_morphism [] ; + _pow_pos_swap -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _pow_pos_swap -> RelationClasses_reflexivity [] ; + _pow_pos_swap -> Morphisms_eq_proper_proxy [] ; + _pow_pos_swap -> RelationClasses_Equivalence_PER [] ; + _pow_pos_swap -> Morphisms_reflexive_proper_proxy [] ; + _pow_pos_swap -> RelationClasses_Equivalence_Reflexive [] ; + _pow_pos_swap -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _pow_pos_swap -> _positive_ind [] ; + Setoid_Setoid_Theory -> RelationClasses_Equivalence [] ; + _ARmul_1_l -> _almost_ring_theory [] ; + BinList_nth_pred_double -> BinList_nth [] ; + BinList_nth_pred_double -> BinList_jump_pred_double [] ; + BinList_nth_jump -> BinList_nth [] ; + BinList_nth_jump -> BinList_jump_tl [] ; + _Ropp_ext -> _ring_eq_ext [] ; + _ARsub_ext -> Morphisms_reflexive_reflexive_proxy [] ; + _ARsub_ext -> Morphisms_Reflexive_partial_app_morphism [] ; + _ARsub_ext -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _ARsub_ext -> RelationClasses_reflexivity [] ; + _ARsub_ext -> Morphisms_eq_proper_proxy [] ; + _ARsub_ext -> RelationClasses_Equivalence_PER [] ; + _ARsub_ext -> Morphisms_reflexive_proper_proxy [] ; + _ARsub_ext -> RelationClasses_Equivalence_Reflexive [] ; + _ARsub_ext -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _ARsub_ext -> _ARsub_def [] ; + _ARsub_ext -> _radd_ext2_Proper [] ; + _ARsub_ext -> _ropp_ext2_Proper [] ; + _ropp_ext2_Proper -> _Ropp_ext [] ; + Ring_polynom_Psub_opp -> Morphisms_PER_morphism [] ; + Ring_polynom_Psub_opp -> Ring_polynom_Padd [] ; + Ring_polynom_Psub_opp -> Ring_polynom_Psub [] ; + Ring_polynom_Psub_opp -> Z_pos_sub_discr [] ; + Ring_polynom_Psub_opp -> Ring_polynom_PaddC_ok [] ; + Ring_polynom_Psub_opp -> Ring_polynom_PsubC_ok [] ; + Ring_polynom_Psub_opp -> Ring_polynom_PX_ext [] ; + Ring_polynom_Psub_opp -> Ring_polynom_mkPinj_ext [] ; + Ring_polynom_Psub_opp -> _morph_opp [] ; + Ring_polynom_Psub_opp -> Ring_polynom_mkPX_ext [] ; + Ring_polynom_Psub_opp -> Ring_polynom_Pequiv_eq [] ; + Ring_polynom_PsubC_ok -> Morphisms_reflexive_reflexive_proxy [] ; + Ring_polynom_PsubC_ok -> Morphisms_Reflexive_partial_app_morphism [] ; + Ring_polynom_PsubC_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Ring_polynom_PsubC_ok -> Morphisms_eq_proper_proxy [] ; + Ring_polynom_PsubC_ok -> RelationClasses_Equivalence_PER [] ; + Ring_polynom_PsubC_ok -> Morphisms_reflexive_proper_proxy [] ; + Ring_polynom_PsubC_ok -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Ring_polynom_PsubC_ok -> Ring_polynom_PsubC [] ; + Ring_polynom_PsubC_ok -> Ring_polynom_Pphi [] ; + Ring_polynom_PsubC_ok -> Setoid_Seq_refl [] ; + Ring_polynom_PsubC_ok -> _ARsub_def [] ; + Ring_polynom_PsubC_ok -> Ring_polynom_radd_ext_Proper [] ; + Ring_polynom_PsubC_ok -> Ring_polynom_Pol_ind [] ; + Ring_polynom_PsubC_ok -> _ARadd_assoc [] ; + Ring_polynom_PsubC_ok -> _morph_sub [] ; + Ring_polynom_PX_ext -> Morphisms_reflexive_reflexive_proxy [] ; + Ring_polynom_PX_ext -> Morphisms_Reflexive_partial_app_morphism [] ; + Ring_polynom_PX_ext -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Ring_polynom_PX_ext -> RelationClasses_reflexivity [] ; + Ring_polynom_PX_ext -> Morphisms_eq_proper_proxy [] ; + Ring_polynom_PX_ext -> Morphisms_reflexive_proper_proxy [] ; + Ring_polynom_PX_ext -> RelationClasses_Equivalence_Reflexive [] ; + Ring_polynom_PX_ext -> RelationClasses_Equivalence_Transitive [] ; + Ring_polynom_PX_ext -> Ring_polynom_PX [] ; + Ring_polynom_PX_ext -> Ring_polynom_rmul_ext_Proper [] ; + Ring_polynom_PX_ext -> Ring_polynom_radd_ext_Proper [] ; + Ring_polynom_PX_ext -> Ring_polynom_Pphi_ext [] ; + Ring_polynom_mkPinj_ext -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Ring_polynom_mkPinj_ext -> Morphisms_eq_proper_proxy [] ; + Ring_polynom_mkPinj_ext -> RelationClasses_Equivalence_PER [] ; + Ring_polynom_mkPinj_ext -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Ring_polynom_mkPinj_ext -> Ring_polynom_mkPinj_ok [] ; + Ring_polynom_mkPinj_ext -> Ring_polynom_Pequiv [] ; + _morph_opp -> _ring_morph [] ; + Ring_polynom_mkPX_ext -> Ring_polynom_mkPX_ok [] ; + Ring_polynom_Pequiv_eq -> RelationClasses_reflexivity [] ; + Ring_polynom_Pequiv_eq -> RelationClasses_Equivalence_Reflexive [] ; + Ring_polynom_Pequiv_eq -> RelationClasses_Equivalence_Transitive [] ; + Ring_polynom_Pequiv_eq -> RelationClasses_Equivalence_Symmetric [] ; + Ring_polynom_Pequiv_eq -> RelationClasses_symmetry [] ; + Ring_polynom_Pequiv_eq -> RelationClasses_transitivity [] ; + Ring_polynom_Pequiv_eq -> RelationClasses_Build_Equivalence [] ; + Ring_polynom_Pequiv_eq -> Ring_polynom_Pequiv [] ; + _morph_sub -> _ring_morph [] ; + _ARopp_mul_l -> _almost_ring_theory [] ; + _ARopp_add -> _almost_ring_theory [] ; + _ARmul_comm -> _almost_ring_theory [] ; + _ARmul_assoc2 -> Morphisms_reflexive_reflexive_proxy [] ; + _ARmul_assoc2 -> Morphisms_Reflexive_partial_app_morphism [] ; + _ARmul_assoc2 -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _ARmul_assoc2 -> RelationClasses_reflexivity [] ; + _ARmul_assoc2 -> Morphisms_eq_proper_proxy [] ; + _ARmul_assoc2 -> RelationClasses_Equivalence_PER [] ; + _ARmul_assoc2 -> Morphisms_reflexive_proper_proxy [] ; + _ARmul_assoc2 -> RelationClasses_Equivalence_Reflexive [] ; + _ARmul_assoc2 -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _ARmul_assoc2 -> _ARmul_assoc [] ; + _ARmul_assoc2 -> _ARmul_comm [] ; + _ARmul_assoc2 -> _rmul_ext2_Proper [] ; + Ring_polynom_PmulC_ok -> Morphisms_subrelation_proper [] ; + Ring_polynom_PmulC_ok -> Morphisms_subrelation_refl [] ; + Ring_polynom_PmulC_ok -> Morphisms_PER_morphism [] ; + Ring_polynom_PmulC_ok -> Morphisms_iff_flip_impl_subrelation [] ; + Ring_polynom_PmulC_ok -> Morphisms_subrelation_respectful [] ; + Ring_polynom_PmulC_ok -> _tt [] ; + Ring_polynom_PmulC_ok -> Ring_polynom_PmulC [] ; + Ring_polynom_PmulC_ok -> _morph1 [] ; + Ring_polynom_PmulC_ok -> _ARmul_0_r [] ; + Ring_polynom_PmulC_ok -> _ARmul_1_r [] ; + Ring_polynom_PmulC_ok -> Ring_polynom_PmulC_aux_ok [] ; + Ring_polynom_PmulI_ok -> Ring_polynom_Pmul [] ; + Ring_polynom_PmulI_ok -> BinList_jump_pred_double [] ; + Ring_polynom_PmulI_ok -> Z_pos_sub_discr [] ; + Ring_polynom_PmulI_ok -> Ring_polynom_PmulC_ok [] ; + _ARdistr_r -> Morphisms_reflexive_reflexive_proxy [] ; + _ARdistr_r -> Morphisms_Reflexive_partial_app_morphism [] ; + _ARdistr_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _ARdistr_r -> RelationClasses_reflexivity [] ; + _ARdistr_r -> Morphisms_eq_proper_proxy [] ; + _ARdistr_r -> RelationClasses_Equivalence_PER [] ; + _ARdistr_r -> Morphisms_reflexive_proper_proxy [] ; + _ARdistr_r -> RelationClasses_Equivalence_Reflexive [] ; + _ARdistr_r -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _ARdistr_r -> _ARdistr_l [] ; + _ARdistr_r -> _radd_ext2_Proper [] ; + _ARdistr_r -> _ARmul_comm [] ; + _ARmul_0_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _ARmul_0_r -> RelationClasses_reflexivity [] ; + _ARmul_0_r -> Morphisms_eq_proper_proxy [] ; + _ARmul_0_r -> RelationClasses_Equivalence_Reflexive [] ; + _ARmul_0_r -> RelationClasses_Equivalence_Transitive [] ; + _ARmul_0_r -> RelationClasses_Equivalence_Symmetric [] ; + _ARmul_0_r -> RelationClasses_symmetry [] ; + _ARmul_0_r -> _ARmul_0_l [] ; + _ARmul_0_r -> _ARmul_comm [] ; + _ARmul_1_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _ARmul_1_r -> RelationClasses_reflexivity [] ; + _ARmul_1_r -> Morphisms_eq_proper_proxy [] ; + _ARmul_1_r -> RelationClasses_Equivalence_Reflexive [] ; + _ARmul_1_r -> RelationClasses_Equivalence_Transitive [] ; + _ARmul_1_r -> RelationClasses_Equivalence_Symmetric [] ; + _ARmul_1_r -> RelationClasses_symmetry [] ; + _ARmul_1_r -> _ARmul_1_l [] ; + _ARmul_1_r -> _ARmul_comm [] ; + Ring_polynom_PmulC_aux_ok -> Ring_polynom_PmulC_aux [] ; + Ring_polynom_PmulC_aux_ok -> Ring_polynom_mkPX_ok [] ; + Ring_polynom_PmulC_aux_ok -> _ARdistr_l [] ; + Ring_polynom_PmulC_aux_ok -> _ARmul_assoc2 [] ; + Ring_polynom_PmulC_aux_ok -> _morph_mul [] ; + _morph_mul -> _ring_morph [] ; + _rmul_ext2_Proper -> _Rmul_ext [] ; + Ring_polynom_Pphi1 -> Ring_polynom_P1 [] ; + Ring_polynom_Pphi1 -> Ring_polynom_Pphi [] ; + Ring_polynom_Pphi1 -> _morph1 [] ; + Ring_polynom_Ppow_pos_ok -> Ring_polynom_Ppow_pos [] ; + Ring_polynom_Ppow_pos_ok -> Ring_polynom_Pmul_ok [] ; + Ring_polynom_Ppow_pos_ok -> _ARmul_assoc1 [] ; + _ARmul_assoc1 -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _ARmul_assoc1 -> RelationClasses_reflexivity [] ; + _ARmul_assoc1 -> Morphisms_eq_proper_proxy [] ; + _ARmul_assoc1 -> RelationClasses_Equivalence_Reflexive [] ; + _ARmul_assoc1 -> RelationClasses_Equivalence_Transitive [] ; + _ARmul_assoc1 -> RelationClasses_Equivalence_Symmetric [] ; + _ARmul_assoc1 -> RelationClasses_symmetry [] ; + _ARmul_assoc1 -> _ARmul_assoc [] ; + _ARmul_assoc1 -> _ARmul_comm [] ; + Ring_polynom_Mphi -> _pow_pos [] ; + Ring_polynom_Mphi -> Ring_polynom_Mon [] ; + Ring_polynom_Mphi -> List_hd [] ; + Ring_polynom_Mphi -> BinList_jump [] ; + _fst -> _prod [] ; + _snd -> _prod [] ; + Ring_polynom_PSubstL_ok -> Ring_polynom_PSubstL [] ; + Ring_polynom_PSubstL_ok -> Ring_polynom_PSubstL1_ok [] ; + Ring_polynom_PSubstL_ok -> Ring_polynom_PNSubst_ok [] ; + _list_ind -> _list [] ; + _list_ind -> _nil [] ; + _list_ind -> _cons [] ; + Ring_polynom_PSubstL1_ok -> Ring_polynom_PSubstL1 [] ; + Ring_polynom_PSubstL1_ok -> Ring_polynom_MPcond [] ; + Ring_polynom_PSubstL1_ok -> _list_ind [] ; + Ring_polynom_PSubstL1_ok -> Ring_polynom_PNSubst1_ok [] ; + Ring_polynom_PNSubst_ok -> Ring_polynom_PNSubst [] ; + Ring_polynom_PNSubst_ok -> Ring_polynom_PNSubst1_ok [] ; + Ring_polynom_PNSubst1_ok -> _nat_ind [] ; + Ring_polynom_PNSubst1_ok -> Ring_polynom_PNSubst1 [] ; + Ring_polynom_PNSubst1_ok -> Ring_polynom_POneSubst_ok [] ; + Ring_polynom_POneSubst_ok -> Morphisms_impl_pars [] ; + Ring_polynom_POneSubst_ok -> Ring_polynom_POneSubst [] ; + Ring_polynom_POneSubst_ok -> Ring_polynom_Pmul_ok [] ; + Ring_polynom_POneSubst_ok -> _fst [] ; + Ring_polynom_POneSubst_ok -> _snd [] ; + Ring_polynom_POneSubst_ok -> Ring_polynom_Mphi_ok [] ; + Ring_polynom_Mphi_ok -> Pos_sub_add [] ; + Ring_polynom_Mphi_ok -> Ring_polynom_MFactor [] ; + Ring_polynom_Mphi_ok -> _morph1 [] ; + Ring_polynom_Mphi_ok -> _ARmul_assoc2 [] ; + Ring_polynom_Mphi_ok -> _ARmul_0_r [] ; + Ring_polynom_Mphi_ok -> _ARmul_1_r [] ; + Ring_polynom_Mphi_ok -> _ARmul_assoc1 [] ; + Ring_polynom_Mphi_ok -> Ring_polynom_zmon_pred_ok [] ; + Ring_polynom_Mphi_ok -> Ring_polynom_Mcphi_ok [] ; + _div_eucl_th -> _div_theory [] ; + Ring_polynom_mkZmon_ok -> Ring_polynom_mkZmon [] ; + Ring_polynom_mkZmon_ok -> Ring_polynom_vmon [] ; + Ring_polynom_mkZmon_ok -> Setoid_Seq_refl [] ; + Ring_polynom_mkZmon_ok -> Ring_polynom_Mphi [] ; + Ring_polynom_zmon_pred_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Ring_polynom_zmon_pred_ok -> Morphisms_eq_proper_proxy [] ; + Ring_polynom_zmon_pred_ok -> RelationClasses_Equivalence_Transitive [] ; + Ring_polynom_zmon_pred_ok -> Ring_polynom_zmon_pred [] ; + Ring_polynom_zmon_pred_ok -> BinList_jump_pred_double [] ; + Ring_polynom_zmon_pred_ok -> Ring_polynom_mkZmon_ok [] ; + Ring_polynom_Mcphi_ok -> Ring_polynom_CFactor [] ; + Ring_polynom_Mcphi_ok -> Ring_polynom_mkPX_ok [] ; + Ring_polynom_Mcphi_ok -> _ARadd_assoc2 [] ; + Ring_polynom_Mcphi_ok -> _morph_add [] ; + Ring_polynom_Mcphi_ok -> _ARdistr_r [] ; + Ring_polynom_Mcphi_ok -> _morph_mul [] ; + Ring_polynom_Mcphi_ok -> _div_eucl_th [] ; + Ring_polynom_mon_of_pol_ok -> Morphisms_subrelation_proper [] ; + Ring_polynom_mon_of_pol_ok -> Morphisms_subrelation_refl [] ; + Ring_polynom_mon_of_pol_ok -> Morphisms_PER_morphism [] ; + Ring_polynom_mon_of_pol_ok -> Morphisms_iff_flip_impl_subrelation [] ; + Ring_polynom_mon_of_pol_ok -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + Ring_polynom_mon_of_pol_ok -> Morphisms_subrelation_respectful [] ; + Ring_polynom_mon_of_pol_ok -> _tt [] ; + Ring_polynom_mon_of_pol_ok -> Morphisms_impl_pars [] ; + Ring_polynom_mon_of_pol_ok -> Ring_polynom_mon_of_pol [] ; + Ring_polynom_mon_of_pol_ok -> Ring_polynom_Peq_ok [] ; + Ring_polynom_mon_of_pol_ok -> _ARadd_0_r [] ; + Ring_polynom_mon_of_pol_ok -> Ring_polynom_Pphi_ext [] ; + Ring_polynom_mon_of_pol_ok -> Ring_polynom_Pphi0 [] ; + Ring_polynom_mon_of_pol_ok -> _ARmul_1_r [] ; + Ring_polynom_mon_of_pol_ok -> _fst [] ; + Ring_polynom_mon_of_pol_ok -> _snd [] ; + Ring_polynom_mon_of_pol_ok -> Ring_polynom_mkVmon_ok [] ; + Ring_polynom_mkVmon_ok -> Ring_polynom_mkVmon [] ; + Ring_polynom_mkVmon_ok -> Ring_polynom_rmul_ext_Proper [] ; + Ring_polynom_mkVmon_ok -> Ring_polynom_pow_pos_add [] ; + Ring_polynom_mkVmon_ok -> Ring_polynom_zmon_pred_ok [] ; + Z_mul_1_l -> Z_eq_equiv [] ; + Z_mul_1_l -> Z_mul_wd [] ; + Z_mul_1_l -> Z_mul_succ_l [] ; + Z_mul_1_l -> Z_mul_0_l [] ; + Z_mul_1_l -> Z_add_wd [] ; + Z_mul_1_l -> Z_add_0_l [] ; + Z_mul_1_l -> Z_one_succ [] ; + Z_sub_diag -> Z_sub_succ_l [] ; + Z_sub_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Z_sub_wd -> RelationClasses_eq_Reflexive [] ; + Z_sub_wd -> Morphisms_reflexive_proper [] ; + Z_sub_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_sub_wd -> Z_eq [] ; + Z_sub_wd -> Z_sub [] ; + Z_sub_0_r -> Z_Private_BootStrap_add_0_r [] ; + Z_sub_0_r -> Z_sub [] ; + Z_sub_succ_l -> Z_add_opp_r [] ; + Z_add_opp_r -> Z_sub_succ_r [] ; + Z_add_opp_r -> Z_sub_wd [] ; + Z_add_opp_r -> Z_sub_0_r [] ; + Z_add_opp_r -> Z_pred_inj_wd [] ; + Z_add_opp_r -> Z_opp_wd [] ; + Z_add_opp_r -> Z_add_pred_r [] ; + Z_add_opp_r -> Z_opp_succ [] ; + Z_add_opp_r -> Z_opp_0 [] ; + Z_pred_inj_wd -> Z_pred_wd [] ; + Z_pred_inj_wd -> Z_pred_inj [] ; + Z_opp_wd -> Z_opp [] ; + Z_opp_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Z_opp_wd -> RelationClasses_eq_Reflexive [] ; + Z_opp_wd -> Morphisms_reflexive_proper [] ; + Z_opp_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + Z_opp_wd -> Z_eq [] ; + Z_add_pred_r -> Z_add_comm [] ; + Z_add_pred_r -> Z_add_pred_l [] ; + Z_opp_succ -> Z_succ [] ; + Z_opp_succ -> Z_Private_BootStrap_opp_add_distr [] ; + Z_opp_succ -> Z_pred [] ; + Z_opp_0 -> _eq [] ; + Z_opp_0 -> Z_opp [] ; + Z_opp_0 -> _eq_refl [] ; + Z_add_pred_l -> Z_eq_equiv [] ; + Z_add_pred_l -> Z_add_wd [] ; + Z_add_pred_l -> Z_add_succ_l [] ; + Z_add_pred_l -> Z_pred_succ [] ; + Z_add_pred_l -> Z_pred_wd [] ; + Z_add_pred_l -> Z_succ_pred [] ; + Z_pred_inj -> Morphisms_PER_morphism [] ; + Z_pred_inj -> Morphisms_trans_co_impl_morphism [] ; + Z_pred_inj -> Z_eq_equiv [] ; + Z_pred_inj -> Z_succ_wd [] ; + Z_pred_inj -> Z_succ_pred [] ; + _Rmul_comm -> _ring_theory [] ; + _Ropp_mul_l -> _Rmul_0_l [] ; + _Radd_assoc -> _ring_theory [] ; + _Rmul_0_l -> Morphisms_reflexive_reflexive_proxy [] ; + _Rmul_0_l -> Morphisms_Reflexive_partial_app_morphism [] ; + _Rmul_0_l -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _Rmul_0_l -> RelationClasses_reflexivity [] ; + _Rmul_0_l -> Morphisms_eq_proper_proxy [] ; + _Rmul_0_l -> RelationClasses_Equivalence_PER [] ; + _Rmul_0_l -> Morphisms_reflexive_proper_proxy [] ; + _Rmul_0_l -> RelationClasses_Equivalence_Reflexive [] ; + _Rmul_0_l -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _Rmul_0_l -> SetoidTactics_default_relation [] ; + _Rmul_0_l -> SetoidTactics_equivalence_default [] ; + _Rmul_0_l -> _radd_ext2_Proper [] ; + _Rmul_0_l -> _rmul_ext2_Proper [] ; + _Rmul_0_l -> _Radd_assoc [] ; + _Rmul_0_l -> _Rmul_1_l [] ; + _Rmul_0_l -> _Radd_comm [] ; + _Rmul_0_l -> _Radd_0_l [] ; + _Rmul_0_l -> _Rdistr_l [] ; + _Rmul_0_l -> _Ropp_def [] ; + _Rmul_1_l -> _ring_theory [] ; + _Radd_comm -> _ring_theory [] ; + _Ropp_add -> Morphisms_reflexive_reflexive_proxy [] ; + _Ropp_add -> Morphisms_Reflexive_partial_app_morphism [] ; + _Ropp_add -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _Ropp_add -> Morphisms_eq_proper_proxy [] ; + _Ropp_add -> Morphisms_reflexive_proper_proxy [] ; + _Ropp_add -> RelationClasses_Equivalence_Reflexive [] ; + _Ropp_add -> RelationClasses_Equivalence_Transitive [] ; + _Ropp_add -> RelationClasses_Equivalence_Symmetric [] ; + _Ropp_add -> RelationClasses_symmetry [] ; + _Ropp_add -> _radd_ext2_Proper [] ; + _Ropp_add -> _Radd_assoc [] ; + _Ropp_add -> _Radd_comm [] ; + _Ropp_add -> _Radd_0_l [] ; + _Ropp_add -> _Ropp_def [] ; + _Rsub_def -> _ring_theory [] ; + _Rmul_assoc -> _ring_theory [] ; + _Radd_0_l -> _ring_theory [] ; + _Rdistr_l -> _ring_theory [] ; + _Ropp_def -> _ring_theory [] ; + Z_eqb_eq -> _Z0 [] ; + Z_eqb_eq -> _Zpos [] ; + Z_eqb_eq -> _Zneg [] ; + Z_eqb_eq -> Z_eqb [] ; + Z_eqb_eq -> Pos_eqb_eq [] ; + Pos_eqb_eq -> _False_ind [] ; + Pos_eqb_eq -> _eq_ind [] ; + Pos_eqb_eq -> _True [] ; + Pos_eqb_eq -> _I [] ; + Pos_eqb_eq -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Pos_eqb_eq -> Morphisms_eq_proper_proxy [] ; + Pos_eqb_eq -> RelationClasses_iff_Transitive [] ; + Pos_eqb_eq -> _eq_sym [] ; + Pos_eqb_eq -> _f_equal [] ; + Pos_eqb_eq -> _eq_trans [] ; + Pos_eqb_eq -> _positive_ind [] ; + Pos_eqb_eq -> Pos_eqb [] ; + Pos_eqb -> _positive [] ; + Pos_eqb -> _bool [] ; + Pos_eqb -> _true [] ; + Pos_eqb -> _false [] ; + _mkmorph -> _bool [] ; + _mkmorph -> _eq [] ; + _mkmorph -> _true [] ; + PosDef_Pos_iter -> _positive [] ; + Z_pow_pos -> Z_mul [] ; + Z_pow_pos -> PosDef_Pos_iter [] ; + _mkpow_th -> _pow_N [] ; + _mk_reqe -> Morphisms_Proper [] ; + _mk_reqe -> Morphisms_respectful [] ; + Z_quotrem_eq -> Z_mul [] ; + Z_quotrem_eq -> Z_add [] ; + Z_quotrem_eq -> Z_quotrem [] ; + Z_quotrem_eq -> N_pos_div_eucl_spec [] ; + _mkdiv_th -> _prod [] ; + N_add -> Pos_add [] ; + N_add -> _N [] ; + N_add -> _Npos [] ; + N_pos_div_eucl -> _prod [] ; + N_pos_div_eucl -> _pair [] ; + N_pos_div_eucl -> N_leb [] ; + N_pos_div_eucl -> N_sub [] ; + N_pos_div_eucl -> N_double [] ; + N_pos_div_eucl -> N_succ_double [] ; + N_pos_div_eucl_spec -> N_pos_div_eucl [] ; + N_pos_div_eucl_spec -> N_add_assoc [] ; + N_pos_div_eucl_spec -> N_double_add [] ; + N_pos_div_eucl_spec -> N_double_mul [] ; + N_pos_div_eucl_spec -> N_sub_add [] ; + N_pos_div_eucl_spec -> N_leb_spec [] ; + N_pos_div_eucl_spec -> N_succ_double_add [] ; + N_pos_div_eucl_spec -> N_succ_double_mul [] ; + N_le -> _eq [] ; + N_le -> _not [] ; + N_le -> N_compare [] ; + N_lt -> _eq [] ; + N_lt -> N_compare [] ; + N_add_assoc -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + N_add_assoc -> RelationClasses_reflexivity [] ; + N_add_assoc -> Morphisms_eq_proper_proxy [] ; + N_add_assoc -> RelationClasses_iff_equivalence [] ; + N_add_assoc -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + N_add_assoc -> Morphisms_per_partial_app_morphism [] ; + N_add_assoc -> N_bi_induction [] ; + N_add_assoc -> N_add_wd [] ; + N_add_assoc -> N_succ_inj_wd [] ; + N_add_assoc -> N_add_succ_l [] ; + N_add_assoc -> N_add_0_l [] ; + N_leb -> _bool [] ; + N_leb -> _true [] ; + N_leb -> _false [] ; + N_leb -> N_compare [] ; + N_sub -> _N [] ; + N_sub -> PosDef_Pos_sub_mask [] ; + N_sub -> _N0 [] ; + N_sub -> _Npos [] ; + N_double_add -> _eq [] ; + N_double_add -> _eq_refl [] ; + N_double_add -> N_add [] ; + N_double_add -> N_double [] ; + N_double_mul -> _eq [] ; + N_double_mul -> _eq_refl [] ; + N_double_mul -> N_mul [] ; + N_double_mul -> N_double [] ; + N_sub_add -> N_add_sub [] ; + N_add_comm -> Morphisms_Reflexive_partial_app_morphism [] ; + N_add_comm -> N_add_succ_r [] ; + N_add_comm -> N_add_0_r [] ; + N_double -> _xO [] ; + N_double -> _N [] ; + N_double -> _N0 [] ; + N_double -> _Npos [] ; + N_succ_double -> _xH [] ; + N_succ_double -> _xI [] ; + N_succ_double -> _N [] ; + N_succ_double -> _Npos [] ; + N_leb_spec -> Morphisms_iff_flip_impl_subrelation [] ; + N_leb_spec -> _BoolSpec [] ; + N_leb_spec -> _BoolSpecT [] ; + N_leb_spec -> _BoolSpecF [] ; + N_leb_spec -> N_leb_spec0 [] ; + N_leb_spec -> N_compare_nge_iff [] ; + N_leb_spec -> N_compare_lt_iff [] ; + N_succ_double_add -> _eq [] ; + N_succ_double_add -> _eq_refl [] ; + N_succ_double_add -> N_add [] ; + N_succ_double_add -> N_double [] ; + N_succ_double_add -> N_succ_double [] ; + N_succ_double_mul -> Pos_add_comm [] ; + N_succ_double_mul -> N_mul [] ; + N_succ_double_mul -> N_add [] ; + N_succ_double_mul -> N_double [] ; + N_succ_double_mul -> N_succ_double [] ; + N_leb_spec0 -> RelationClasses_iff_Symmetric [] ; + N_leb_spec0 -> RelationClasses_symmetry [] ; + N_leb_spec0 -> Bool_iff_reflect [] ; + N_leb_spec0 -> N_leb_le [] ; + N_compare_nge_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + N_compare_nge_iff -> Morphisms_eq_proper_proxy [] ; + N_compare_nge_iff -> _CompOpp_iff [] ; + N_compare_nge_iff -> N_compare_nle_iff [] ; + N_compare_nge_iff -> N_compare_antisym [] ; + N_compare_lt_iff -> RelationClasses_reflexivity [] ; + N_compare_lt_iff -> RelationClasses_iff_Reflexive [] ; + N_compare_lt_iff -> N_lt [] ; + N_compare -> PosDef_Pos_compare [] ; + N_compare -> _N [] ; + _reflect -> _true [] ; + _reflect -> _false [] ; + _reflect -> _not [] ; + N_compare_nle_iff -> _eq_ind [] ; + N_compare_nle_iff -> _True [] ; + N_compare_nle_iff -> _eq_refl [] ; + N_compare_nle_iff -> _I [] ; + N_compare_nle_iff -> RelationClasses_Equivalence_PER [] ; + N_compare_nle_iff -> RelationClasses_iff_equivalence [] ; + N_compare_nle_iff -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + N_compare_nle_iff -> Morphisms_Prop_not_iff_morphism [] ; + N_compare_nle_iff -> N_compare_le_iff [] ; + N_compare_antisym -> Pos_compare_antisym [] ; + N_compare_antisym -> _N0 [] ; + N_compare_antisym -> _Npos [] ; + N_compare_antisym -> N_compare [] ; + N_compare_le_iff -> RelationClasses_reflexivity [] ; + N_compare_le_iff -> RelationClasses_iff_Reflexive [] ; + N_compare_le_iff -> N_le [] ; + Bool_iff_reflect -> _eq_refl [] ; + Bool_iff_reflect -> _iff [] ; + Bool_iff_reflect -> _reflect [] ; + Bool_iff_reflect -> _and_rec [] ; + Bool_iff_reflect -> Bool_diff_false_true [] ; + Bool_iff_reflect -> _ReflectT [] ; + Bool_iff_reflect -> _ReflectF [] ; + N_leb_le -> _False_ind [] ; + N_leb_le -> _eq_ind [] ; + N_leb_le -> _True [] ; + N_leb_le -> _eq_refl [] ; + N_leb_le -> _I [] ; + N_leb_le -> _iff [] ; + N_leb_le -> _conj [] ; + N_leb_le -> N_le [] ; + N_leb_le -> N_leb [] ; + _and_rec -> _and [] ; + Bool_diff_false_true -> _bool [] ; + Bool_diff_false_true -> _true [] ; + Bool_diff_false_true -> _false [] ; + Bool_diff_false_true -> _not [] ; + Bool_diff_false_true -> _False_ind [] ; + Bool_diff_false_true -> _eq_ind [] ; + Bool_diff_false_true -> _True [] ; + Bool_diff_false_true -> _I [] ; + _ReflectT -> _true [] ; + _ReflectT -> _false [] ; + _ReflectT -> _not [] ; + _ReflectF -> _true [] ; + _ReflectF -> _false [] ; + _ReflectF -> _not [] ; + N_bi_induction -> _eq [] ; + N_bi_induction -> _iff [] ; + N_bi_induction -> Morphisms_Proper [] ; + N_bi_induction -> Morphisms_respectful [] ; + N_bi_induction -> N_peano_rect [] ; + N_succ -> PosDef_Pos_succ [] ; + N_succ -> _N [] ; + N_succ -> _Npos [] ; + N_add_wd -> Morphisms_reflexive_reflexive_proxy [] ; + N_add_wd -> RelationClasses_eq_Reflexive [] ; + N_add_wd -> Morphisms_reflexive_proper [] ; + N_add_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + N_add_wd -> N_add [] ; + N_add_wd -> N_eq [] ; + N_eq_equiv -> RelationClasses_eq_equivalence [] ; + N_eq_equiv -> _N [] ; + N_succ_inj_wd -> N_succ_wd [] ; + N_succ_inj_wd -> N_succ_inj [] ; + N_add_succ_l -> Pos_add_1_l [] ; + N_add_succ_l -> Pos_add_succ_l [] ; + N_add_succ_l -> _N0 [] ; + N_add_succ_l -> N_add [] ; + N_add_succ_l -> N_succ [] ; + N_add_succ_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + N_add_succ_r -> RelationClasses_reflexivity [] ; + N_add_succ_r -> Morphisms_eq_proper_proxy [] ; + N_add_succ_r -> RelationClasses_iff_equivalence [] ; + N_add_succ_r -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + N_add_succ_r -> Morphisms_per_partial_app_morphism [] ; + N_add_succ_r -> N_bi_induction [] ; + N_add_succ_r -> N_add_wd [] ; + N_add_succ_r -> N_succ_inj_wd [] ; + N_add_succ_r -> N_add_succ_l [] ; + N_add_succ_r -> N_add_0_l [] ; + N_add_0_l -> _eq [] ; + N_add_0_l -> _eq_refl [] ; + N_add_0_l -> _N0 [] ; + N_add_0_l -> N_add [] ; + N_add_0_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + N_add_0_r -> RelationClasses_reflexivity [] ; + N_add_0_r -> Morphisms_eq_proper_proxy [] ; + N_add_0_r -> RelationClasses_iff_equivalence [] ; + N_add_0_r -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + N_add_0_r -> N_bi_induction [] ; + N_add_0_r -> N_add_wd [] ; + N_add_0_r -> N_succ_inj_wd [] ; + N_add_0_r -> N_add_succ_l [] ; + N_add_0_r -> N_add_0_l [] ; + N_succ_wd -> Morphisms_reflexive_reflexive_proxy [] ; + N_succ_wd -> RelationClasses_eq_Reflexive [] ; + N_succ_wd -> Morphisms_reflexive_proper [] ; + N_succ_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + N_succ_wd -> N_succ [] ; + N_succ_wd -> N_eq [] ; + N_eq -> _eq [] ; + N_eq -> _N [] ; + N_succ_inj -> Morphisms_subrelation_proper [] ; + N_succ_inj -> Morphisms_subrelation_refl [] ; + N_succ_inj -> Morphisms_PER_morphism [] ; + N_succ_inj -> RelationClasses_Equivalence_PER [] ; + N_succ_inj -> Morphisms_reflexive_proper_proxy [] ; + N_succ_inj -> RelationClasses_Equivalence_Reflexive [] ; + N_succ_inj -> Morphisms_subrelation_respectful [] ; + N_succ_inj -> _tt [] ; + N_succ_inj -> Morphisms_iff_impl_subrelation [] ; + N_succ_inj -> Morphisms_trans_co_impl_morphism [] ; + N_succ_inj -> N_eq_equiv [] ; + N_succ_inj -> N_pred_succ [] ; + N_succ_inj -> N_pred_wd [] ; + N_pred_succ -> N_succ [] ; + N_pred_succ -> N_pred [] ; + N_pred_succ -> Pos_pred_N_succ [] ; + N_pred_wd -> Morphisms_reflexive_reflexive_proxy [] ; + N_pred_wd -> RelationClasses_eq_Reflexive [] ; + N_pred_wd -> Morphisms_reflexive_proper [] ; + N_pred_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + N_pred_wd -> N_eq [] ; + N_pred_wd -> N_pred [] ; + N_pred -> PosDef_Pos_pred_N [] ; + PosDef_Pos_pred_N -> PosDef_Pos_pred_double [] ; + PosDef_Pos_pred_N -> _N [] ; + PosDef_Pos_pred_N -> _N0 [] ; + PosDef_Pos_pred_N -> _Npos [] ; + Pos_pred_N_succ -> PosDef_Pos_pred_double [] ; + Pos_pred_N_succ -> Pos_pred_double_succ [] ; + Pos_pred_N_succ -> Pos_pred_N [] ; + Pos_pred_double_succ -> Pos_succ [] ; + Pos_pred_double_succ -> _f_equal [] ; + Pos_pred_double_succ -> _eq_trans [] ; + Pos_pred_double_succ -> _positive_ind [] ; + Pos_pred_double_succ -> Pos_pred_double [] ; + Pos_pred_N -> _N [] ; + Pos_pred_N -> Pos_pred_double [] ; + Pos_pred_N -> _N0 [] ; + Pos_pred_N -> _Npos [] ; + N_peano_rect -> Pos_peano_rect [] ; + N_peano_rect -> _N0 [] ; + N_peano_rect -> N_succ [] ; + N_add_sub_assoc -> N_sub_gt [] ; + N_add_sub_assoc -> N_add_pred_r [] ; + N_sub_wd -> Morphisms_reflexive_reflexive_proxy [] ; + N_sub_wd -> RelationClasses_eq_Reflexive [] ; + N_sub_wd -> Morphisms_reflexive_proper [] ; + N_sub_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + N_sub_wd -> N_sub [] ; + N_sub_wd -> N_eq [] ; + N_add_sub -> N_add_sub_assoc [] ; + N_add_sub -> N_sub_diag [] ; + N_le_refl -> RelationClasses_Equivalence_Reflexive [] ; + N_le_refl -> N_eq_equiv [] ; + N_le_refl -> N_lt_eq_cases [] ; + N_sub_diag -> N_sub_succ [] ; + N_induction -> N_le_0_l [] ; + N_induction -> N_right_induction [] ; + N_sub_succ -> N_sub_wd [] ; + N_sub_succ -> N_induction [] ; + N_sub_succ -> N_sub_0_r [] ; + N_sub_succ -> N_sub_succ_r [] ; + N_sub_0_r -> _eq [] ; + N_sub_0_r -> _eq_refl [] ; + N_sub_0_r -> N_sub [] ; + N_sub_succ_r -> Pos_sub_mask_carry_spec [] ; + N_sub_succ_r -> N_sub [] ; + N_sub_succ_r -> N_succ [] ; + N_sub_succ_r -> N_pred [] ; + N_sub_succ_r -> Pos_sub_mask_succ_r [] ; + Pos_sub_mask_succ_r -> Pos_succ [] ; + Pos_sub_mask_succ_r -> _f_equal [] ; + Pos_sub_mask_succ_r -> _eq_trans [] ; + Pos_sub_mask_succ_r -> _positive_ind [] ; + Pos_sub_mask_succ_r -> Pos_sub_mask [] ; + Pos_sub_mask_succ_r -> Pos_sub_mask_carry [] ; + Pos_sub_mask_succ_r -> PosDef_Pos_succ_double_mask [] ; + N_le_0_l -> N_le_le_succ_r [] ; + N_le_0_l -> N_le_succ_r [] ; + N_le_0_l -> N_neq_succ_0 [] ; + N_le_0_l -> N_eq_le_incl [] ; + N_right_induction -> N_strong_right_induction [] ; + N_right_induction -> N_lt_exists_pred [] ; + N_lt_succ_diag_r -> Morphisms_iff_flip_impl_subrelation [] ; + N_lt_succ_diag_r -> N_le_refl [] ; + N_lt_succ_diag_r -> N_lt_succ_r [] ; + N_lt_eq_cases -> Morphisms_reflexive_reflexive_proxy [] ; + N_lt_eq_cases -> Morphisms_Reflexive_partial_app_morphism [] ; + N_lt_eq_cases -> Morphisms_reflexive_proper_proxy [] ; + N_lt_eq_cases -> Morphisms_Prop_or_iff_morphism [] ; + N_lt_eq_cases -> N_compare_lt_iff [] ; + N_lt_eq_cases -> N_compare_le_iff [] ; + N_lt_eq_cases -> N_compare_eq_iff [] ; + N_lt_wd -> Morphisms_reflexive_reflexive_proxy [] ; + N_lt_wd -> RelationClasses_iff_Reflexive [] ; + N_lt_wd -> Morphisms_reflexive_proper [] ; + N_lt_wd -> Morphisms_reflexive_eq_dom_reflexive [] ; + N_lt_wd -> N_lt [] ; + N_lt_wd -> N_eq [] ; + N_strong_right_induction -> _well_founded_induction [] ; + N_strong_right_induction -> N_lt_wf [] ; + N_strong_right_induction -> N_Private_OrderTac_Tac_not_ge_lt [] ; + N_lt_exists_pred -> Morphisms_Prop_all_iff_morphism [] ; + N_lt_exists_pred -> _ex [] ; + N_lt_exists_pred -> RelationClasses_PreOrder_Reflexive [] ; + N_lt_exists_pred -> _ex_intro [] ; + N_lt_exists_pred -> N_le_preorder [] ; + N_lt_exists_pred -> N_Private_OrderTac_Tac_le_lt_trans [] ; + N_lt_exists_pred -> N_le_le_succ_r [] ; + N_lt_exists_pred -> N_le_succ_r [] ; + N_central_induction -> Morphisms_reflexive_reflexive_proxy [] ; + N_central_induction -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + N_central_induction -> RelationClasses_reflexivity [] ; + N_central_induction -> Morphisms_eq_proper_proxy [] ; + N_central_induction -> RelationClasses_iff_Transitive [] ; + N_central_induction -> RelationClasses_iff_Reflexive [] ; + N_central_induction -> Morphisms_reflexive_proper_proxy [] ; + N_central_induction -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + N_central_induction -> N_bi_induction [] ; + N_le_wd -> Morphisms_Reflexive_partial_app_morphism [] ; + N_le_wd -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + N_le_wd -> RelationClasses_reflexivity [] ; + N_le_wd -> Morphisms_eq_proper_proxy [] ; + N_le_wd -> RelationClasses_Equivalence_PER [] ; + N_le_wd -> Morphisms_reflexive_proper_proxy [] ; + N_le_wd -> RelationClasses_Equivalence_Reflexive [] ; + N_le_wd -> RelationClasses_iff_equivalence [] ; + N_le_wd -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + N_le_wd -> N_eq_equiv [] ; + N_le_wd -> N_succ_wd [] ; + N_le_wd -> N_lt_wd [] ; + N_le_wd -> N_lt_succ_r [] ; + N_lt_succ_r -> _N0 [] ; + N_lt_succ_r -> N_le [] ; + N_lt_succ_r -> N_lt [] ; + N_lt_succ_r -> N_succ [] ; + N_lt_succ_r -> Pos_lt_succ_r [] ; + N_le_preorder -> RelationClasses_PreOrder [] ; + N_le_preorder -> RelationClasses_Build_PreOrder [] ; + N_le_preorder -> N_le_trans [] ; + N_Private_OrderTac_Tac_le_lt_trans -> N_Private_OrderTac_Tac_trans [] ; + N_le_le_succ_r -> N_Private_OrderTac_Tac_lt_irrefl [] ; + N_le_le_succ_r -> N_Private_OrderTac_Tac_not_gt_le [] ; + N_le_le_succ_r -> N_Private_OrderTac_Tac_lt_trans [] ; + N_le_succ_r -> N_lt_eq_cases [] ; + N_le_succ_r -> N_lt_succ_r [] ; + N_Private_OrderTac_Tac_lt_irrefl -> RelationClasses_StrictOrder_Irreflexive [] ; + N_Private_OrderTac_Tac_lt_irrefl -> N_Private_OrderTac_IsTotal_lt_strorder [] ; + N_Private_OrderTac_IsTotal_lt_strorder -> N_lt_strorder [] ; + N_lt_strorder -> RelationClasses_StrictOrder [] ; + N_lt_strorder -> RelationClasses_Build_StrictOrder [] ; + N_lt_strorder -> N_lt_trans [] ; + N_lt_trans -> Morphisms_impl_pars [] ; + N_lt_trans -> N_lt_asymm [] ; + N_lt_irrefl -> Morphisms_subrelation_proper [] ; + N_lt_irrefl -> Morphisms_subrelation_refl [] ; + N_lt_irrefl -> Morphisms_iff_flip_impl_subrelation [] ; + N_lt_irrefl -> Morphisms_subrelation_respectful [] ; + N_lt_irrefl -> _tt [] ; + N_lt_irrefl -> Morphisms_Prop_not_iff_morphism [] ; + N_lt_irrefl -> N_compare_lt_iff [] ; + N_lt_irrefl -> N_compare_refl [] ; + N_compare_refl -> RelationClasses_reflexivity [] ; + N_compare_refl -> RelationClasses_Equivalence_Reflexive [] ; + N_compare_refl -> N_eq_equiv [] ; + N_compare_refl -> N_compare_eq_iff [] ; + N_compare_eq_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + N_compare_eq_iff -> Morphisms_eq_proper_proxy [] ; + N_compare_eq_iff -> Pos_compare_eq_iff [] ; + N_compare_eq_iff -> _N0 [] ; + N_compare_eq_iff -> _Npos [] ; + N_compare_eq_iff -> N_compare [] ; + N_lt_asymm -> N_le_succ_l [] ; + N_lt_le_incl -> N_lt_eq_cases [] ; + N_nlt_succ_diag_l -> N_lt_succ_r [] ; + N_nlt_succ_diag_l -> N_lt_irrefl [] ; + N_nlt_succ_diag_l -> N_lt_le_incl [] ; + N_le_succ_l -> Morphisms_per_partial_app_morphism [] ; + N_le_succ_l -> _or_cancel_r [] ; + N_le_succ_l -> N_succ_inj_wd [] ; + N_le_succ_l -> N_central_induction [] ; + N_le_succ_l -> N_le_wd [] ; + N_le_succ_l -> N_nle_succ_diag_l [] ; + N_nle_succ_diag_l -> Morphisms_iff_impl_subrelation [] ; + N_nle_succ_diag_l -> N_nlt_succ_diag_l [] ; + N_nle_succ_diag_l -> N_neq_succ_diag_l [] ; + N_neq_succ_diag_l -> N_lt_succ_diag_r [] ; + N_neq_succ_diag_l -> N_lt_wd [] ; + N_neq_succ_diag_l -> N_lt_irrefl [] ; + N_Private_OrderTac_Tac_not_gt_le -> N_Private_OrderTac_IsTotal_le_lteq [] ; + N_Private_OrderTac_Tac_not_gt_le -> N_Private_OrderTac_IsTotal_lt_total [] ; + N_Private_OrderTac_Tac_lt_trans -> N_Private_OrderTac_Tac_trans [] ; + N_Private_OrderTac_Tac_trans -> OrdersTac_OEQ [] ; + N_Private_OrderTac_Tac_trans -> RelationClasses_StrictOrder_Transitive [] ; + N_Private_OrderTac_Tac_trans -> OrdersTac_trans_ord [] ; + N_Private_OrderTac_Tac_trans -> N_Private_OrderTac_IsTotal_lt_strorder [] ; + N_Private_OrderTac_Tac_trans -> N_Private_OrderTac_IsTotal_lt_compat [] ; + N_Private_OrderTac_Tac_trans -> N_Private_OrderTac_IsTotal_eq_equiv [] ; + N_Private_OrderTac_Tac_trans -> N_Private_OrderTac_Tac_interp_ord [] ; + N_Private_OrderTac_Tac_trans -> N_Private_OrderTac_IsTotal_le_lteq [] ; + N_Private_OrderTac_IsTotal_lt_compat -> N_lt_compat [] ; + N_Private_OrderTac_IsTotal_eq_equiv -> N_eq_equiv [] ; + N_Private_OrderTac_Tac_interp_ord -> OrdersTac_ord [] ; + N_Private_OrderTac_Tac_interp_ord -> N_le [] ; + N_Private_OrderTac_Tac_interp_ord -> N_lt [] ; + N_Private_OrderTac_IsTotal_le_lteq -> N_le_lteq [] ; + N_le_lteq -> N_lt_eq_cases [] ; + N_lt_compat -> N_lt_wd [] ; + N_Private_OrderTac_IsTotal_lt_total -> N_lt_total [] ; + N_lt_total -> N_lt_trichotomy [] ; + N_lt_trichotomy -> N_le_gt_cases [] ; + N_le_gt_cases -> N_le_succ_l [] ; + N_le_trans -> N_lt_trans [] ; + Pos_lt_succ_r -> _False_ind [] ; + Pos_lt_succ_r -> _True [] ; + Pos_lt_succ_r -> _I [] ; + Pos_lt_succ_r -> _iff [] ; + Pos_lt_succ_r -> _conj [] ; + Pos_lt_succ_r -> Pos_lt [] ; + Pos_lt_succ_r -> Pos_compare_succ_r [] ; + Pos_lt_succ_r -> Pos_le [] ; + N_lt_wf -> Morphisms_Prop_all_iff_morphism [] ; + N_lt_wf -> Morphisms_Prop_Acc_pt_morphism [] ; + N_lt_wf -> _well_founded [] ; + N_lt_wf -> N_Private_OrderTac_Tac_le_lt_trans [] ; + N_lt_wf -> N_lt_lt_succ_r [] ; + N_lt_wf -> N_Rlt_wd [] ; + N_Private_OrderTac_Tac_not_ge_lt -> N_Private_OrderTac_IsTotal_eq_equiv [] ; + N_Private_OrderTac_Tac_not_ge_lt -> N_Private_OrderTac_IsTotal_le_lteq [] ; + N_Private_OrderTac_Tac_not_ge_lt -> N_Private_OrderTac_IsTotal_lt_total [] ; + N_lt_lt_succ_r -> N_Private_OrderTac_Tac_lt_irrefl [] ; + N_lt_lt_succ_r -> N_Private_OrderTac_Tac_not_gt_le [] ; + N_lt_lt_succ_r -> N_Private_OrderTac_Tac_lt_trans [] ; + N_Rlt_wd -> Morphisms_Prop_and_iff_morphism [] ; + N_Rlt_wd -> N_le_wd [] ; + N_neq_succ_0 -> Morphisms_PER_morphism [] ; + N_neq_succ_0 -> Morphisms_iff_impl_subrelation [] ; + N_neq_succ_0 -> N_succ_wd [] ; + N_neq_succ_0 -> N_pred_succ [] ; + N_neq_succ_0 -> N_pred_wd [] ; + N_neq_succ_0 -> N_neq_succ_diag_l [] ; + N_neq_succ_0 -> N_pred_0 [] ; + N_eq_le_incl -> N_Private_OrderTac_Tac_lt_irrefl [] ; + N_eq_le_incl -> N_Private_OrderTac_Tac_not_gt_le [] ; + N_eq_le_incl -> N_Private_OrderTac_Tac_lt_eq [] ; + N_Private_OrderTac_Tac_lt_eq -> N_Private_OrderTac_Tac_trans [] ; + N_pred_0 -> _eq [] ; + N_pred_0 -> _eq_refl [] ; + N_pred_0 -> N_pred [] ; + N_sub_gt -> N_sub_succ [] ; + N_sub_gt -> N_lt_ind_rel [] ; + N_add_pred_r -> N_add_comm [] ; + N_add_pred_r -> N_add_pred_l [] ; + N_add_pred_l -> N_add_wd [] ; + N_add_pred_l -> N_add_succ_l [] ; + N_add_pred_l -> N_case_analysis [] ; + N_case_analysis -> N_induction [] ; + N_lt_ind_rel -> N_induction [] ; + N_lt_ind_rel -> N_lt_ind [] ; + N_lt_ind_rel -> N_lt_succ_l [] ; + N_lt_ind -> N_right_induction [] ; + N_lt_succ_l -> N_Private_OrderTac_Tac_lt_irrefl [] ; + N_lt_succ_l -> N_Private_OrderTac_Tac_not_gt_le [] ; + N_lt_succ_l -> N_Private_OrderTac_Tac_lt_trans [] ; + QArith_base_Qle_refl -> QArith_base_Qle [] ; + QArith_base_Qle_refl -> RelationClasses_PreOrder_Reflexive [] ; + QArith_base_Qle_refl -> Z_le_preorder [] ; + QArith_base_Qplus_le_l -> QArith_base_Qplus_comp [] ; + QArith_base_Qplus_le_l -> QArith_base_Qle_refl [] ; + QArith_base_Qplus_le_l -> QArith_base_Qplus_assoc [] ; + QArith_base_Qplus_le_l -> QArith_base_Qle_comp [] ; + QArith_base_Qplus_le_l -> QArith_base_Qplus_le_compat [] ; + QArith_base_Qplus_le_l -> QArith_base_Qplus_0_r [] ; + QArith_base_Qplus_le_l -> QArith_base_Qplus_opp_r [] ; + QArith_base_Qplus_le_r -> QArith_base_Qplus_le_l [] ; + QArith_base_Qplus_le_r -> QArith_base_Qplus_comm [] ; + _False_rec -> _False [] ; + Nat2Z_inj_add -> _nat_N_Z [] ; + Nat2Z_inj_add -> N2Z_inj_add [] ; + Nat2Z_inj_add -> Nnat_Nat2N_inj_add [] ; + QArith_base_Qplus_assoc -> QArith_base_Qplus [] ; + QArith_base_Qplus_assoc -> _ring_subst_niter [] ; + QArith_base_Qplus_assoc -> QArith_base_Qeq [] ; + QArith_base_Qplus_assoc -> Pos2Z_inj_mul [] ; + QArith_base_Qplus_assoc -> _Zr_ring_lemma1 [] ; + QArith_base_Qinv_plus_distr -> QArith_base_Qplus [] ; + QArith_base_Qinv_plus_distr -> _ring_subst_niter [] ; + QArith_base_Qinv_plus_distr -> QArith_base_Qeq [] ; + QArith_base_Qinv_plus_distr -> Pos2Z_inj_mul [] ; + QArith_base_Qinv_plus_distr -> _Zr_ring_lemma1 [] ; + N2Z_inj_add -> _eq [] ; + N2Z_inj_add -> Z_add [] ; + N2Z_inj_add -> _eq_refl [] ; + N2Z_inj_add -> Z_of_N [] ; + N2Z_inj_add -> _N0 [] ; + N2Z_inj_add -> N_add [] ; + Nnat_Nat2N_inj_add -> Nnat_Nat2N_id [] ; + Nnat_Nat2N_inj_add -> Nnat_N2Nat_inj [] ; + Nnat_Nat2N_inj_add -> Nnat_N2Nat_inj_add [] ; + Nnat_N2Nat_inj_add -> _plus_n_O [] ; + Nnat_N2Nat_inj_add -> N_to_nat [] ; + Nnat_N2Nat_inj_add -> _N0 [] ; + Nnat_N2Nat_inj_add -> Pos2Nat_inj_add [] ; + Nnat_N2Nat_inj_add -> N_add [] ; + QArith_base_Qle_comp -> QArith_base_Qle_alt [] ; + QArith_base_Qle_comp -> QArith_base_Q_Setoid [] ; + QArith_base_Qle_comp -> QArith_base_Qcompare_comp [] ; + QArith_base_Qplus_comm -> QArith_base_Qplus [] ; + QArith_base_Qplus_comm -> _ring_subst_niter [] ; + QArith_base_Qplus_comm -> QArith_base_Qeq [] ; + QArith_base_Qplus_comm -> _Zr_ring_lemma1 [] ; + QArith_base_Qplus_le_compat -> QArith_base_Qplus [] ; + QArith_base_Qplus_le_compat -> QArith_base_Qle [] ; + QArith_base_Qplus_le_compat -> _ring_subst_niter [] ; + QArith_base_Qplus_le_compat -> Z_add_le_mono [] ; + QArith_base_Qplus_le_compat -> Pos2Z_inj_mul [] ; + QArith_base_Qplus_le_compat -> Z_mul_le_mono_nonneg_r [] ; + QArith_base_Qplus_le_compat -> _Zr_ring_lemma2 [] ; + QArith_base_Qplus_le_compat -> Pos2Z_is_nonneg [] ; + QArith_base_Qplus_0_r -> QArith_base_Qplus [] ; + QArith_base_Qplus_0_r -> _ring_subst_niter [] ; + QArith_base_Qplus_0_r -> QArith_base_Qeq [] ; + QArith_base_Qplus_0_r -> _Zr_ring_lemma1 [] ; + QArith_base_Qplus_opp_r -> QArith_base_Qopp [] ; + QArith_base_Qplus_opp_r -> QArith_base_Qplus [] ; + QArith_base_Qplus_opp_r -> _ring_subst_niter [] ; + QArith_base_Qplus_opp_r -> QArith_base_Qeq [] ; + QArith_base_Qplus_opp_r -> _Zr_ring_lemma1 [] ; + _Zr_ring_lemma2 -> _Ztriv_div_th [] ; + _Zr_ring_lemma2 -> _Eq_ext [] ; + _Zr_ring_lemma2 -> _Zpower_theory [] ; + _Zr_ring_lemma2 -> _IDmorph [] ; + _Zr_ring_lemma2 -> ZArithRing_Private_proj1_eqb_eq [] ; + _Zr_ring_lemma2 -> _Rth_ARth [] ; + _Zr_ring_lemma2 -> _Zth [] ; + _Zr_ring_lemma2 -> _Eqsth [] ; + _Zr_ring_lemma2 -> _get_signZ_th [] ; + _Zr_ring_lemma2 -> Ring_polynom_ring_rw_pow_correct [] ; + _get_signZ -> _Z [] ; + _get_signZ -> _Zpos [] ; + _get_signZ -> _option [] ; + _get_signZ -> _Some [] ; + _get_signZ -> _None [] ; + Pos2Z_is_nonneg -> Z_le [] ; + Pos2Z_is_nonneg -> _Z0 [] ; + Pos2Z_is_nonneg -> _Zpos [] ; + Pos2Z_is_nonneg -> _False_ind [] ; + Pos2Z_is_nonneg -> _eq_ind [] ; + Pos2Z_is_nonneg -> _True [] ; + Pos2Z_is_nonneg -> _eq_refl [] ; + Pos2Z_is_nonneg -> _I [] ; + _get_signZ_th -> Z_opp [] ; + _get_signZ_th -> Z_eqb [] ; + _get_signZ_th -> _get_signZ [] ; + _get_signZ_th -> _sign_theory [] ; + _get_signZ_th -> Pos_eqb_refl [] ; + _get_signZ_th -> _mksign_th [] ; + Ring_polynom_ring_rw_pow_correct -> Ring_polynom_norm_subst_ok [] ; + Ring_polynom_ring_rw_pow_correct -> Ring_polynom_Pphi_pow_ok [] ; + Ring_polynom_Pphi_pow_ok -> Ring_polynom_Pphi_pow [] ; + Ring_polynom_Pphi_pow_ok -> Ring_polynom_Pphi_avoid_ok [] ; + Ring_polynom_Pphi_pow_ok -> Ring_polynom_local_mkpow_ok [] ; + _sign_theory -> _bool [] ; + _sign_theory -> _eq [] ; + _sign_theory -> _true [] ; + _sign_theory -> _option [] ; + _sign_theory -> _Some [] ; + Ring_polynom_Pphi_avoid_ok -> Ring_polynom_mult_dev_ok [] ; + Ring_polynom_Pphi_avoid_ok -> Ring_polynom_Pphi_avoid [] ; + Ring_polynom_local_mkpow_ok -> _xO [] ; + Ring_polynom_local_mkpow_ok -> _xH [] ; + Ring_polynom_local_mkpow_ok -> _xI [] ; + Ring_polynom_local_mkpow_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Ring_polynom_local_mkpow_ok -> RelationClasses_reflexivity [] ; + Ring_polynom_local_mkpow_ok -> Morphisms_eq_proper_proxy [] ; + Ring_polynom_local_mkpow_ok -> RelationClasses_Equivalence_Reflexive [] ; + Ring_polynom_local_mkpow_ok -> RelationClasses_Equivalence_Transitive [] ; + Ring_polynom_local_mkpow_ok -> _Npos [] ; + Ring_polynom_local_mkpow_ok -> _rpow_pow_N [] ; + Ring_polynom_mult_dev_ok -> Morphisms_subrelation_proper [] ; + Ring_polynom_mult_dev_ok -> Morphisms_subrelation_refl [] ; + Ring_polynom_mult_dev_ok -> Morphisms_PER_morphism [] ; + Ring_polynom_mult_dev_ok -> Morphisms_iff_flip_impl_subrelation [] ; + Ring_polynom_mult_dev_ok -> Morphisms_subrelation_respectful [] ; + Ring_polynom_mult_dev_ok -> _tt [] ; + Ring_polynom_mult_dev_ok -> _ARmul_0_l [] ; + Ring_polynom_mult_dev_ok -> Ring_polynom_mult_dev [] ; + Ring_polynom_mult_dev_ok -> Ring_polynom_mkmult_c_ok [] ; + Ring_polynom_mult_dev_ok -> Ring_polynom_add_mult_dev_ok [] ; + Ring_polynom_Pphi_avoid -> Ring_polynom_mult_dev [] ; + Ring_polynom_mult_dev -> Ring_polynom_add_mult_dev [] ; + Ring_polynom_mult_dev -> Ring_polynom_mkmult_c [] ; + Ring_polynom_r_list_pow -> _prod [] ; + Ring_polynom_r_list_pow -> _pow_pos [] ; + Ring_polynom_r_list_pow -> _list [] ; + Ring_polynom_add_mult_dev -> Ring_polynom_P0 [] ; + Ring_polynom_add_mult_dev -> Ring_polynom_Peq [] ; + Ring_polynom_add_mult_dev -> List_hd [] ; + Ring_polynom_add_mult_dev -> BinList_jump [] ; + Ring_polynom_add_mult_dev -> _N0 [] ; + Ring_polynom_add_mult_dev -> N_add [] ; + Ring_polynom_add_mult_dev -> Ring_polynom_add_pow_list [] ; + Ring_polynom_add_mult_dev -> Ring_polynom_mkadd_mult [] ; + Ring_polynom_add_pow_list -> _prod [] ; + Ring_polynom_add_pow_list -> _list [] ; + Ring_polynom_add_pow_list -> _cons [] ; + Ring_polynom_add_pow_list -> _N [] ; + Ring_polynom_add_pow_list -> _pair [] ; + Ring_polynom_mkmult_c -> _option [] ; + Ring_polynom_mkmult_c -> Ring_polynom_mkmult_c_pos [] ; + Ring_polynom_mkmult_c -> Ring_polynom_mkmultm1 [] ; + Ring_polynom_mkmult_rec -> _prod [] ; + Ring_polynom_mkmult_rec -> _positive [] ; + Ring_polynom_mkmult_rec -> _list [] ; + Ring_polynom_mkmult_c_pos -> _bool [] ; + Ring_polynom_mkmult_c_pos -> List_rev_ [] ; + Ring_polynom_mkmult_c_pos -> Ring_polynom_mkmult1 [] ; + List_rev_ -> _nil [] ; + List_rev_ -> List_rev_append [] ; + Ring_polynom_mkmultm1 -> Ring_polynom_mkmult_rec [] ; + List_rev_append -> _list [] ; + List_rev_append -> _cons [] ; + Ring_polynom_mkmult1 -> Ring_polynom_mkmult_rec [] ; + Ring_polynom_mkadd_mult -> _option [] ; + Ring_polynom_mkadd_mult -> Ring_polynom_mkmult_c_pos [] ; + Ring_polynom_mkmult_c_ok -> _None [] ; + Ring_polynom_mkmult_c_ok -> Ring_polynom_ropp_ext_Proper [] ; + Ring_polynom_mkmult_c_ok -> _morph_opp [] ; + Ring_polynom_mkmult_c_ok -> Ring_polynom_mkmult_c [] ; + Ring_polynom_mkmult_c_ok -> Ring_polynom_mkmult_c_pos_ok [] ; + Ring_polynom_mkmult_c_ok -> _sign_spec [] ; + Ring_polynom_mkmult_c_ok -> Ring_polynom_mkmultm1_ok [] ; + Ring_polynom_add_pow_list_ok -> RelationClasses_Equivalence_PER [] ; + Ring_polynom_add_pow_list_ok -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Ring_polynom_add_pow_list_ok -> _N0 [] ; + Ring_polynom_add_pow_list_ok -> _Npos [] ; + Ring_polynom_add_pow_list_ok -> _pow_N [] ; + Ring_polynom_add_pow_list_ok -> Setoid_Seq_refl [] ; + Ring_polynom_add_pow_list_ok -> _ARmul_1_l [] ; + Ring_polynom_add_pow_list_ok -> Ring_polynom_r_list_pow [] ; + Ring_polynom_add_pow_list_ok -> Ring_polynom_add_pow_list [] ; + Ring_polynom_add_mult_dev_ok -> Ring_polynom_Peq_ok [] ; + Ring_polynom_add_mult_dev_ok -> _morph0 [] ; + Ring_polynom_add_mult_dev_ok -> Ring_polynom_pow_pos_add [] ; + Ring_polynom_add_mult_dev_ok -> _ARadd_assoc [] ; + Ring_polynom_add_mult_dev_ok -> _ARadd_0_r [] ; + Ring_polynom_add_mult_dev_ok -> _ARdistr_l [] ; + Ring_polynom_add_mult_dev_ok -> Ring_polynom_Pphi_ext [] ; + Ring_polynom_add_mult_dev_ok -> _ARmul_assoc2 [] ; + Ring_polynom_add_mult_dev_ok -> Ring_polynom_add_mult_dev [] ; + Ring_polynom_add_mult_dev_ok -> Ring_polynom_add_pow_list_ok [] ; + Ring_polynom_add_mult_dev_ok -> Ring_polynom_mkadd_mult_ok [] ; + Ring_polynom_mkadd_mult_ok -> _None [] ; + Ring_polynom_mkadd_mult_ok -> Ring_polynom_ropp_ext_Proper [] ; + Ring_polynom_mkadd_mult_ok -> _ARsub_def [] ; + Ring_polynom_mkadd_mult_ok -> Ring_polynom_radd_ext_Proper [] ; + Ring_polynom_mkadd_mult_ok -> _morph_opp [] ; + Ring_polynom_mkadd_mult_ok -> _ARopp_mul_l [] ; + Ring_polynom_mkadd_mult_ok -> Ring_polynom_mkadd_mult [] ; + Ring_polynom_mkadd_mult_ok -> Ring_polynom_mkmult_c_pos_ok [] ; + Ring_polynom_mkadd_mult_ok -> _sign_spec [] ; + Ring_polynom_mkmult_c_pos_ok -> _false [] ; + Ring_polynom_mkmult_c_pos_ok -> Morphisms_Reflexive_partial_app_morphism [] ; + Ring_polynom_mkmult_c_pos_ok -> _morph1 [] ; + Ring_polynom_mkmult_c_pos_ok -> _morph_eq [] ; + Ring_polynom_mkmult_c_pos_ok -> Ring_polynom_mkmult_c_pos [] ; + Ring_polynom_mkmult_c_pos_ok -> Ring_polynom_mkmult1_ok [] ; + Ring_polynom_mkmult_c_pos_ok -> Ring_polynom_r_list_pow_rev [] ; + _sign_spec -> _sign_theory [] ; + Ring_polynom_mkmult1_ok -> Ring_polynom_mkmult1 [] ; + Ring_polynom_mkmult1_ok -> Ring_polynom_mkmult_rec_ok [] ; + Ring_polynom_mkmult_rec_ok -> Morphisms_reflexive_reflexive_proxy [] ; + Ring_polynom_mkmult_rec_ok -> RelationClasses_Equivalence_PER [] ; + Ring_polynom_mkmult_rec_ok -> Morphisms_reflexive_proper_proxy [] ; + Ring_polynom_mkmult_rec_ok -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Ring_polynom_mkmult_rec_ok -> Ring_polynom_rmul_ext_Proper [] ; + Ring_polynom_mkmult_rec_ok -> Setoid_Seq_refl [] ; + Ring_polynom_mkmult_rec_ok -> _ARmul_assoc [] ; + Ring_polynom_mkmult_rec_ok -> _ARmul_1_r [] ; + Ring_polynom_mkmult_rec_ok -> _list_ind [] ; + Ring_polynom_mkmult_rec_ok -> Ring_polynom_r_list_pow [] ; + Ring_polynom_mkmult_rec_ok -> Ring_polynom_mkmult_rec [] ; + Ring_polynom_r_list_pow_rev -> Morphisms_reflexive_reflexive_proxy [] ; + Ring_polynom_r_list_pow_rev -> RelationClasses_Equivalence_PER [] ; + Ring_polynom_r_list_pow_rev -> Morphisms_reflexive_proper_proxy [] ; + Ring_polynom_r_list_pow_rev -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Ring_polynom_r_list_pow_rev -> _pair [] ; + Ring_polynom_r_list_pow_rev -> Ring_polynom_rmul_ext_Proper [] ; + Ring_polynom_r_list_pow_rev -> Setoid_Seq_refl [] ; + Ring_polynom_r_list_pow_rev -> _ARmul_assoc [] ; + Ring_polynom_r_list_pow_rev -> _ARmul_1_r [] ; + Ring_polynom_r_list_pow_rev -> _list_ind [] ; + Ring_polynom_r_list_pow_rev -> Ring_polynom_r_list_pow [] ; + Ring_polynom_r_list_pow_rev -> List_rev_ [] ; + Ring_polynom_mkmultm1_ok -> _ARopp_mul_l [] ; + Ring_polynom_mkmultm1_ok -> Ring_polynom_mkmultm1 [] ; + Ring_polynom_mkmultm1_ok -> Ring_polynom_mkmult_rec_ok [] ; + Pos_eqb_refl -> RelationClasses_reflexivity [] ; + Pos_eqb_refl -> RelationClasses_Equivalence_Reflexive [] ; + Pos_eqb_refl -> Pos_eq_equiv [] ; + Pos_eqb_refl -> Pos_eqb_eq [] ; + _mksign_th -> _bool [] ; + _mksign_th -> _eq [] ; + _mksign_th -> _true [] ; + _mksign_th -> _option [] ; + _mksign_th -> _Some [] ; + ClassicalDedekindReals_sig_forall_dec -> _sig [] ; + ClassicalDedekindReals_sig_forall_dec -> _not [] ; + ClassicalDedekindReals_sig_forall_dec -> _nat [] ; + ClassicalDedekindReals_sig_forall_dec -> _sumor [] ; + ClassicalDedekindReals_sig_forall_dec -> _sumbool [] ; + QArith_base_Qplus_lt_le_compat -> QArith_base_Qlt [] ; + QArith_base_Qplus_lt_le_compat -> QArith_base_Qplus [] ; + QArith_base_Qplus_lt_le_compat -> QArith_base_Qle [] ; + QArith_base_Qplus_lt_le_compat -> _ring_subst_niter [] ; + QArith_base_Qplus_lt_le_compat -> Z_mul_lt_mono_pos_r [] ; + QArith_base_Qplus_lt_le_compat -> Pos2Z_inj_mul [] ; + QArith_base_Qplus_lt_le_compat -> Z_mul_le_mono_nonneg_r [] ; + QArith_base_Qplus_lt_le_compat -> _Zr_ring_lemma2 [] ; + QArith_base_Qplus_lt_le_compat -> Pos2Z_is_nonneg [] ; + QArith_base_Qplus_lt_le_compat -> Z_add_le_lt_mono [] ; + Z_add_le_lt_mono -> Z_le_lt_trans [] ; + Z_add_le_lt_mono -> Z_add_lt_mono_l [] ; + Z_add_le_lt_mono -> Z_add_le_mono_r [] ; + Setoid_Build_Setoid_Theory -> RelationClasses_Equivalence [] ; + Setoid_Build_Setoid_Theory -> RelationClasses_Build_Equivalence [] ; + Qfield_Qpower_theory -> QArith_base_Qpower [] ; + Qfield_Qpower_theory -> Z_of_N [] ; + Qfield_Qpower_theory -> QArith_base_Q_Setoid [] ; + Qfield_Qpower_theory -> _N0 [] ; + Qfield_Qpower_theory -> _Npos [] ; + Qfield_Qpower_theory -> _power_theory [] ; + Qfield_Qpower_theory -> _mkpow_th [] ; + _get_sign_None_th -> _False_ind [] ; + _get_sign_None_th -> _eq_ind [] ; + _get_sign_None_th -> _True [] ; + _get_sign_None_th -> _I [] ; + _get_sign_None_th -> _get_sign_None [] ; + _get_sign_None_th -> _sign_theory [] ; + _get_sign_None_th -> _mksign_th [] ; + _triv_div_th -> _false [] ; + _triv_div_th -> Morphisms_reflexive_reflexive_proxy [] ; + _triv_div_th -> Morphisms_Reflexive_partial_app_morphism [] ; + _triv_div_th -> RelationClasses_Equivalence_PER [] ; + _triv_div_th -> Morphisms_reflexive_proper_proxy [] ; + _triv_div_th -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _triv_div_th -> _triv_div [] ; + _triv_div_th -> _div_theory [] ; + _triv_div_th -> _morph0 [] ; + _triv_div_th -> _morph1 [] ; + _triv_div_th -> Setoid_Seq_refl [] ; + _triv_div_th -> _ARadd_0_r [] ; + _triv_div_th -> _morph_add [] ; + _triv_div_th -> _morph_eq [] ; + _triv_div_th -> _ARmul_0_r [] ; + _triv_div_th -> _ARmul_1_r [] ; + _triv_div_th -> _morph_mul [] ; + _triv_div_th -> _mkdiv_th [] ; + _triv_div_th -> _R_set1_Transitive [] ; + _triv_div_th -> _R_set1 [] ; + _triv_div_th -> _radd_ext_Proper [] ; + _triv_div_th -> _R_set1_Reflexive [] ; + _triv_div_th -> _rmul_ext_Proper [] ; + QArith_base_Qopp_comp -> QArith_base_Qopp [] ; + QArith_base_Qopp_comp -> _ring_subst_niter [] ; + QArith_base_Qopp_comp -> QArith_base_Qeq [] ; + QArith_base_Qopp_comp -> _Zr_ring_lemma1 [] ; + QArith_base_Qdiv -> QArith_base_Qinv [] ; + QArith_base_Qdiv -> QArith_base_Qmult [] ; + Qfield_Qsft -> QArith_base_Qdiv [] ; + Qfield_Qsft -> _field_theory [] ; + Qfield_Qsft -> Qfield_Qsrt [] ; + Qfield_Qsft -> QArith_base_Qmult_inv_r [] ; + Qfield_Qsft -> _mk_field [] ; + QArith_base_Qmult_comp -> QArith_base_Qmult [] ; + QArith_base_Qmult_comp -> _ring_subst_niter [] ; + QArith_base_Qmult_comp -> QArith_base_Qeq [] ; + QArith_base_Qmult_comp -> Pos2Z_inj_mul [] ; + QArith_base_Qmult_comp -> _Zr_ring_lemma1 [] ; + QArith_base_Qmult_comp -> _Zr_ring_lemma2 [] ; + Morphisms_proper_prf -> Morphisms_Proper [] ; + QArith_base_Qeq_bool_eq -> QArith_base_Qeq_bool_iff [] ; + _F_R -> _field_theory [] ; + _field_theory -> _not [] ; + _field_theory -> _ring_theory [] ; + QArith_base_Qeq_bool_iff -> QArith_base_Qeq [] ; + QArith_base_Qeq_bool_iff -> QArith_base_Qeq_bool [] ; + QArith_base_Qeq_bool_iff -> Z_eqb_eq [] ; + Qfield_Qsrt -> QArith_base_Qminus [] ; + Qfield_Qsrt -> QArith_base_Q_Setoid [] ; + Qfield_Qsrt -> QArith_base_Qplus_assoc [] ; + Qfield_Qsrt -> QArith_base_Qplus_comm [] ; + Qfield_Qsrt -> QArith_base_Qplus_opp_r [] ; + Qfield_Qsrt -> QArith_base_Qmult_comm [] ; + Qfield_Qsrt -> QArith_base_Qmult_1_l [] ; + Qfield_Qsrt -> QArith_base_Qplus_0_l [] ; + Qfield_Qsrt -> QArith_base_Qmult_plus_distr_l [] ; + Qfield_Qsrt -> QArith_base_Qmult_assoc [] ; + QArith_base_Qmult_comm -> QArith_base_Qmult [] ; + QArith_base_Qmult_comm -> _ring_subst_niter [] ; + QArith_base_Qmult_comm -> QArith_base_Qeq [] ; + QArith_base_Qmult_comm -> _Zr_ring_lemma1 [] ; + QArith_base_Qmult_inv_r -> QArith_base_Qinv [] ; + QArith_base_Qmult_inv_r -> QArith_base_Qmult [] ; + QArith_base_Qmult_inv_r -> _ring_subst_niter [] ; + QArith_base_Qmult_inv_r -> QArith_base_Qeq [] ; + QArith_base_Qmult_inv_r -> Pos2Z_inj_mul [] ; + QArith_base_Qmult_inv_r -> _Zr_ring_lemma1 [] ; + _mk_field -> _not [] ; + _mk_field -> _ring_theory [] ; + QArith_base_Qmult_1_l -> QArith_base_Qmult [] ; + QArith_base_Qmult_1_l -> _eq_refl [] ; + QArith_base_Qmult_1_l -> QArith_base_Qeq [] ; + QArith_base_Qplus_0_l -> QArith_base_Qplus [] ; + QArith_base_Qplus_0_l -> _ring_subst_niter [] ; + QArith_base_Qplus_0_l -> QArith_base_Qeq [] ; + QArith_base_Qplus_0_l -> _Zr_ring_lemma1 [] ; + QArith_base_Qmult_plus_distr_l -> QArith_base_Qmult [] ; + QArith_base_Qmult_plus_distr_l -> QArith_base_Qplus [] ; + QArith_base_Qmult_plus_distr_l -> _ring_subst_niter [] ; + QArith_base_Qmult_plus_distr_l -> QArith_base_Qeq [] ; + QArith_base_Qmult_plus_distr_l -> Pos2Z_inj_mul [] ; + QArith_base_Qmult_plus_distr_l -> _Zr_ring_lemma1 [] ; + QArith_base_Qmult_assoc -> QArith_base_Qmult [] ; + QArith_base_Qmult_assoc -> _ring_subst_niter [] ; + QArith_base_Qmult_assoc -> QArith_base_Qeq [] ; + QArith_base_Qmult_assoc -> _Zr_ring_lemma1 [] ; + QArith_base_Qmult_assoc -> Pos_mul_assoc [] ; + Pos_mul_assoc -> Pos_mul_add_distr_r [] ; + _R_set1_Transitive -> RelationClasses_Equivalence_Transitive [] ; + _R_set1_Transitive -> Setoid_Setoid_Theory [] ; + _R_set1 -> RelationClasses_Equivalence_Reflexive [] ; + _R_set1 -> RelationClasses_Equivalence_Transitive [] ; + _R_set1 -> RelationClasses_Equivalence_Symmetric [] ; + _R_set1 -> RelationClasses_Build_Equivalence [] ; + _R_set1 -> Setoid_Setoid_Theory [] ; + _radd_ext_Proper -> _Radd_ext [] ; + _R_set1_Reflexive -> RelationClasses_Equivalence_Reflexive [] ; + _R_set1_Reflexive -> Setoid_Setoid_Theory [] ; + _rmul_ext_Proper -> _Rmul_ext [] ; + Nat_succ_pred -> Nat_case_analysis [] ; + QExtra_Qbound_lt_ZExp2 -> QArith_base_Qden [] ; + QExtra_Qbound_lt_ZExp2 -> QArith_base_Qnum [] ; + QExtra_Qbound_lt_ZExp2 -> Z_pos_sub [] ; + QExtra_Qbound_lt_ZExp2 -> QExtra_Pos_log2floor_plus1 [] ; + QExtra_Pos_log2floor_plus1 -> Pos_succ [] ; + QMicromega_QTautoChecker -> Tauto_BFormula [] ; + QMicromega_QTautoChecker -> QMicromega_QWitness [] ; + QMicromega_QTautoChecker -> QMicromega_Qnegate [] ; + QMicromega_QTautoChecker -> ListDef_map [] ; + QMicromega_QTautoChecker -> QMicromega_Qnormalise [] ; + QMicromega_QTautoChecker -> QMicromega_qdeduce [] ; + QMicromega_QTautoChecker -> QMicromega_qunsat [] ; + QMicromega_QTautoChecker -> QMicromega_QWeakChecker [] ; + QMicromega_QTautoChecker -> Tauto_tauto_checker [] ; + Qabs_Qabs_triangle_reverse -> QArith_base_Qle_comp [] ; + Qabs_Qabs_triangle_reverse -> Qfield_Qfield_ring_lemma1 [] ; + Qabs_Qabs_triangle_reverse -> QArith_base_Qle_minus_iff [] ; + Qabs_Qabs_triangle_reverse -> Qabs_Qabs_wd [] ; + Qabs_Qabs_triangle_reverse -> Qabs_Qabs_triangle [] ; + Tauto_BFormula -> _unit [] ; + Tauto_BFormula -> Tauto_eKind [] ; + Tauto_BFormula -> Tauto_GFormula [] ; + ConstructiveRcomplete_Qlt_trans_swap_hyp -> QArith_base_Qlt_trans [] ; + ClassicalDedekindReals_CReal_of_DReal_seq_bound -> ClassicalDedekindReals_CReal_of_DReal_cauchy [] ; + ClassicalDedekindReals_CReal_of_DReal_seq_bound -> _Z_gt_le_dec [] ; + ClassicalDedekindReals_CReal_of_DReal_seq_bound -> ClassicalDedekindReals_CReal_of_DReal_seq_max_prec_1 [] ; + QExtra_Qbound_lt_ZExp2_spec -> QExtra_Qbound_lt_ZExp2 [] ; + QExtra_Qbound_lt_ZExp2_spec -> QMicromega_QTautoChecker_sound [] ; + QExtra_Qbound_lt_ZExp2_spec -> _Zmult_lt_compat2 [] ; + QExtra_Qbound_lt_ZExp2_spec -> Qpower_Qpower_minus [] ; + QExtra_Qbound_lt_ZExp2_spec -> ZifyClasses_and_morph [] ; + QExtra_Qbound_lt_ZExp2_spec -> QExtra_Pos_log2floor_plus1_spec [] ; + QExtra_Qbound_lt_ZExp2_spec -> Pos2Z_inj_succ [] ; + QExtra_Qbound_lt_ZExp2_spec -> Qpower_Qpower_decomp_pos [] ; + QExtra_Qbound_lt_ZExp2_spec -> Z_to_N [] ; + QExtra_Qbound_lt_ZExp2_spec -> _Zmult_lt_reg_r [] ; + QExtra_Qbound_lt_ZExp2_spec -> PosExtra_Pos_pow_1_r [] ; + QExtra_Qbound_lt_ZExp2_spec -> QArith_base_Qlt_shift_div_l [] ; + QExtra_Qbound_lt_ZExp2_spec -> Qpower_Qpower_0_lt [] ; + VarMap_find -> _positive [] ; + VarMap_find -> VarMap_t [] ; + QMicromega_QWitness -> QArith_base_Q [] ; + QMicromega_QWitness -> RingMicromega_Psatz [] ; + QMicromega_QTautoChecker_sound -> QMicromega_QTautoChecker [] ; + QMicromega_QTautoChecker_sound -> QMicromega_Qeval_nformula_dec [] ; + QMicromega_QTautoChecker_sound -> Tauto_tauto_checker_sound [] ; + QMicromega_QTautoChecker_sound -> QMicromega_QWeakChecker_sound [] ; + QMicromega_QTautoChecker_sound -> Tauto_eval_bf [] ; + QMicromega_QTautoChecker_sound -> QMicromega_Qeval_formula_compat [] ; + QMicromega_QTautoChecker_sound -> RingMicromega_cnf_negate_correct [] ; + QMicromega_QTautoChecker_sound -> RingMicromega_cnf_normalise_correct [] ; + QMicromega_QTautoChecker_sound -> Refl_make_impl_map [] ; + Tauto_eKind -> _bool [] ; + Tauto_eKind -> Tauto_kind [] ; + RingMicromega_Formula -> EnvRing_PExpr [] ; + RingMicromega_Formula -> RingMicromega_Op2 [] ; + EnvRing_PEc -> _N [] ; + EnvRing_PEX -> _N [] ; + EnvRing_PEadd -> _N [] ; + EnvRing_PEsub -> _N [] ; + EnvRing_PEmul -> _N [] ; + Tauto_A -> _option [] ; + Tauto_A -> Tauto_isProp [] ; + Tauto_A -> Tauto_kind [] ; + Tauto_A -> Tauto_isBool [] ; + RingMicromega_Build_Formula -> EnvRing_PExpr [] ; + RingMicromega_Build_Formula -> RingMicromega_Op2 [] ; + EnvRing_PExpr -> _N [] ; + RingMicromega_nformula_plus_nformula -> _pair [] ; + RingMicromega_nformula_plus_nformula -> RingMicromega_NFormula [] ; + RingMicromega_nformula_plus_nformula -> EnvRing_Padd [] ; + RingMicromega_nformula_plus_nformula -> RingMicromega_map_option [] ; + RingMicromega_nformula_plus_nformula -> RingMicromega_OpAdd [] ; + QMicromega_Qnegate -> QArith_base_Qmult [] ; + QMicromega_Qnegate -> QArith_base_Qminus [] ; + QMicromega_Qnegate -> QArith_base_Qeq_bool [] ; + QMicromega_Qnegate -> QArith_base_Qle_bool [] ; + QMicromega_Qnegate -> RingMicromega_cnf_negate [] ; + QArith_base_Qle_bool -> Z_leb [] ; + QArith_base_Qle_bool -> Z_mul [] ; + QArith_base_Qle_bool -> QArith_base_Qden [] ; + QArith_base_Qle_bool -> QArith_base_Qnum [] ; + RingMicromega_eval_nformula -> RingMicromega_NFormula [] ; + RingMicromega_eval_nformula -> RingMicromega_eval_op1 [] ; + RingMicromega_eval_nformula -> RingMicromega_eval_pol [] ; + QMicromega_Qeval_nformula -> QArith_base_Qlt [] ; + QMicromega_Qeval_nformula -> QArith_base_Qmult [] ; + QMicromega_Qeval_nformula -> QArith_base_Qplus [] ; + QMicromega_Qeval_nformula -> QArith_base_Qle [] ; + QMicromega_Qeval_nformula -> QArith_base_Qeq [] ; + QMicromega_Qeval_nformula -> RingMicromega_eval_nformula [] ; + RingMicromega_nformula_plus_nformula_correct -> RingMicromega_nformula_plus_nformula [] ; + RingMicromega_nformula_plus_nformula_correct -> RingMicromega_eval_nformula [] ; + RingMicromega_nformula_plus_nformula_correct -> RingMicromega_Rops_wd [] ; + RingMicromega_nformula_plus_nformula_correct -> RingMicromega_SORrm [] ; + RingMicromega_nformula_plus_nformula_correct -> EnvRing_Padd_ok [] ; + RingMicromega_nformula_plus_nformula_correct -> RingMicromega_OpAdd_sound [] ; + QMicromega_QSORaddon -> QArith_base_Qmult [] ; + QMicromega_QSORaddon -> QArith_base_Qminus [] ; + QMicromega_QSORaddon -> QArith_base_Q_Setoid [] ; + QMicromega_QSORaddon -> _mkmorph [] ; + QMicromega_QSORaddon -> _mkpow_th [] ; + QMicromega_QSORaddon -> QArith_base_Qeq_bool_eq [] ; + QMicromega_QSORaddon -> RingMicromega_SORaddon [] ; + QMicromega_QSORaddon -> QArith_base_Qeq_bool_neq [] ; + QMicromega_QSORaddon -> QArith_base_Qle_bool_imp_le [] ; + QMicromega_QSORaddon -> RingMicromega_mk_SOR_addon [] ; + ListDef_map -> _list [] ; + ListDef_map -> _nil [] ; + ListDef_map -> _cons [] ; + RingMicromega_check_inconsistent_sound -> _pair [] ; + RingMicromega_check_inconsistent_sound -> _morph0 [] ; + RingMicromega_check_inconsistent_sound -> _morph_eq [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_check_inconsistent [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_eval_op1 [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_eval_pol [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_Equal [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_NonEqual [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_Strict [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_NonStrict [] ; + RingMicromega_check_inconsistent_sound -> EnvRing_Pinj [] ; + RingMicromega_check_inconsistent_sound -> EnvRing_PX [] ; + RingMicromega_check_inconsistent_sound -> EnvRing_Pc [] ; + RingMicromega_check_inconsistent_sound -> OrderedRing_Rle_ngt [] ; + RingMicromega_check_inconsistent_sound -> OrderedRing_Rlt_nge [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_micomega_sor_setoid [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_rle_morph_Proper [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_rlt_morph_Proper [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_micomega_sor_setoid_Reflexive [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_SORrm [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_micomega_sor_setoid_Symmetric [] ; + RingMicromega_check_inconsistent_sound -> RingMicromega_cltb_sound [] ; + RingMicromega_check_inconsistent_sound -> _eq_rect [] ; + QMicromega_Qsor -> QArith_base_Qplus_comp [] ; + QMicromega_Qsor -> QArith_base_Qlt_le_weak [] ; + QMicromega_Qsor -> QArith_base_Qlt_compat [] ; + QMicromega_Qsor -> QArith_base_Qle_refl [] ; + QMicromega_Qsor -> QArith_base_Qle_comp [] ; + QMicromega_Qsor -> QArith_base_Qplus_le_compat [] ; + QMicromega_Qsor -> QArith_base_Qopp_comp [] ; + QMicromega_Qsor -> QArith_base_Qmult_comp [] ; + QMicromega_Qsor -> Qfield_Qsrt [] ; + QMicromega_Qsor -> OrderedRing_SOR [] ; + QMicromega_Qsor -> QArith_base_Qmult_0_l [] ; + QMicromega_Qsor -> QArith_base_Qmult_lt_compat_r [] ; + QMicromega_Qsor -> QArith_base_Qle_trans [] ; + QMicromega_Qsor -> QArith_base_Qlt_not_eq [] ; + QMicromega_Qsor -> QArith_base_Q_dec [] ; + QMicromega_Qsor -> QArith_base_Qle_antisym [] ; + QMicromega_Qsor -> QArith_base_Qnot_le_lt [] ; + QMicromega_Qsor -> OrderedRing_mk_SOR_theory [] ; + Refl_make_impl -> _list [] ; + QMicromega_Qeval_nformula_dec -> QMicromega_Qeval_nformula [] ; + QMicromega_Qeval_nformula_dec -> QMicromega_Qsor [] ; + QMicromega_Qeval_nformula_dec -> RingMicromega_eval_nformula_dec [] ; + QMicromega_Qeval_formula -> RingMicromega_Formula [] ; + QMicromega_Qeval_formula -> QMicromega_Qeval_expr [] ; + QMicromega_Qeval_formula -> QMicromega_Qeval_op2 [] ; + RingMicromega_eval_formula -> RingMicromega_Formula [] ; + RingMicromega_eval_formula -> RingMicromega_eval_pexpr [] ; + RingMicromega_eval_formula -> RingMicromega_eval_op2 [] ; + Tauto_hold_eNOT -> _False_ind [] ; + Tauto_hold_eNOT -> _eq_ind [] ; + Tauto_hold_eNOT -> _True [] ; + Tauto_hold_eNOT -> _I [] ; + Tauto_hold_eNOT -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Tauto_hold_eNOT -> Morphisms_eq_proper_proxy [] ; + Tauto_hold_eNOT -> RelationClasses_iff_Transitive [] ; + Tauto_hold_eNOT -> _iff_refl [] ; + Tauto_hold_eNOT -> Tauto_isBool [] ; + Tauto_hold_eNOT -> Tauto_eNOT [] ; + Tauto_hold_eNOT -> Tauto_hold [] ; + Tauto_hold_eNOT -> Bool_negb_true_iff [] ; + RingMicromega_PolC -> EnvRing_Pol [] ; + QMicromega_Qnormalise -> QArith_base_Qmult [] ; + QMicromega_Qnormalise -> QArith_base_Qminus [] ; + QMicromega_Qnormalise -> QArith_base_Qeq_bool [] ; + QMicromega_Qnormalise -> QArith_base_Qle_bool [] ; + QMicromega_Qnormalise -> RingMicromega_cnf_normalise [] ; + Tauto_eval_cnf -> Tauto_cnf [] ; + Tauto_eval_cnf -> Tauto_eval_clause [] ; + QMicromega_qdeduce -> QArith_base_Qplus [] ; + QMicromega_qdeduce -> QArith_base_Qeq_bool [] ; + QMicromega_qdeduce -> RingMicromega_nformula_plus_nformula [] ; + Tauto_tauto_checker_sound -> Tauto_cnf_checker_sound [] ; + Tauto_tauto_checker_sound -> Tauto_tauto_checker [] ; + Tauto_tauto_checker_sound -> Tauto_xcnf_correct [] ; + RingMicromega_cnf_normalise -> RingMicromega_xnormalise [] ; + RingMicromega_cnf_normalise -> Tauto_cnf_ff [] ; + RingMicromega_cnf_normalise -> RingMicromega_cnf_of_list [] ; + RingMicromega_cnf_normalise -> RingMicromega_normalise [] ; + RingMicromega_PolEnv -> Env_Env [] ; + QMicromega_qunsat -> QArith_base_Qmake [] ; + QMicromega_qunsat -> QArith_base_Qeq_bool [] ; + QMicromega_qunsat -> QArith_base_Qle_bool [] ; + QMicromega_qunsat -> RingMicromega_check_inconsistent [] ; + QMicromega_QWeakChecker_sound -> QMicromega_QWitness [] ; + QMicromega_QWeakChecker_sound -> QMicromega_Qeval_nformula [] ; + QMicromega_QWeakChecker_sound -> QMicromega_QSORaddon [] ; + QMicromega_QWeakChecker_sound -> QMicromega_Qsor [] ; + QMicromega_QWeakChecker_sound -> QMicromega_QWeakChecker [] ; + QMicromega_QWeakChecker_sound -> RingMicromega_checker_nf_sound [] ; + RingMicromega_NFormula -> _prod [] ; + RingMicromega_NFormula -> RingMicromega_PolC [] ; + RingMicromega_NFormula -> RingMicromega_Op1 [] ; + QMicromega_QWeakChecker -> QArith_base_Qmult [] ; + QMicromega_QWeakChecker -> QArith_base_Qplus [] ; + QMicromega_QWeakChecker -> QArith_base_Qeq_bool [] ; + QMicromega_QWeakChecker -> QArith_base_Qle_bool [] ; + QMicromega_QWeakChecker -> RingMicromega_check_normalised_formulas [] ; + RingMicromega_cnf_negate -> RingMicromega_cnf_of_list [] ; + RingMicromega_cnf_negate -> RingMicromega_normalise [] ; + RingMicromega_cnf_negate -> RingMicromega_xnegate [] ; + Tauto_eval_bf -> Tauto_BFormula [] ; + Tauto_eval_bf -> Tauto_e_rtyp [] ; + Tauto_eval_bf -> Tauto_eval_f [] ; + Tauto_eval_tt -> _fst [] ; + QMicromega_Qeval_formula_compat -> RingMicromega_Build_Formula [] ; + QMicromega_Qeval_formula_compat -> QMicromega_Qeval_formula [] ; + QMicromega_Qeval_formula_compat -> QMicromega_Qeval_formula_ [] ; + QMicromega_Qeval_formula_compat -> QMicromega_Qeval_op2_hold [] ; + QMicromega_Qeval_formula_compat -> QMicromega_Qeval_expr_compat [] ; + _prod_ind -> _prod [] ; + _prod_ind -> _pair [] ; + RingMicromega_cnf_negate_correct -> RingMicromega_cnf_negate [] ; + RingMicromega_cnf_negate_correct -> RingMicromega_normalise_sound [] ; + RingMicromega_cnf_negate_correct -> RingMicromega_cnf_of_list_correct [] ; + RingMicromega_cnf_negate_correct -> RingMicromega_xnegate_correct [] ; + RingMicromega_cnf_negate_correct -> Tauto_eval_cnf_tt [] ; + RingMicromega_cnf_normalise_correct -> RingMicromega_cnf_normalise [] ; + RingMicromega_cnf_normalise_correct -> RingMicromega_normalise_sound [] ; + RingMicromega_cnf_normalise_correct -> RingMicromega_xnormalise_correct [] ; + RingMicromega_cnf_normalise_correct -> Tauto_eval_cnf_ff [] ; + RingMicromega_cnf_normalise_correct -> RingMicromega_cnf_of_list_correct [] ; + Refl_make_impl_map -> Morphisms_reflexive_reflexive_proxy [] ; + Refl_make_impl_map -> Morphisms_Reflexive_partial_app_morphism [] ; + Refl_make_impl_map -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Refl_make_impl_map -> Morphisms_eq_proper_proxy [] ; + Refl_make_impl_map -> RelationClasses_iff_Transitive [] ; + Refl_make_impl_map -> RelationClasses_iff_Reflexive [] ; + Refl_make_impl_map -> Morphisms_reflexive_proper_proxy [] ; + Refl_make_impl_map -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + Refl_make_impl_map -> Morphisms_impl_pars [] ; + Refl_make_impl_map -> _fst [] ; + Refl_make_impl_map -> _list_ind [] ; + Refl_make_impl_map -> ListDef_map [] ; + Refl_make_impl_map -> Refl_make_impl [] ; + Refl_make_impl_map -> _prod_ind [] ; + QMicromega_Qeval_formula_ -> QArith_base_Qlt [] ; + QMicromega_Qeval_formula_ -> QArith_base_Qmult [] ; + QMicromega_Qeval_formula_ -> QArith_base_Qminus [] ; + QMicromega_Qeval_formula_ -> QArith_base_Qle [] ; + QMicromega_Qeval_formula_ -> QArith_base_Qeq [] ; + QMicromega_Qeval_formula_ -> _pow_N [] ; + QMicromega_Qeval_formula_ -> RingMicromega_eval_formula [] ; + Tauto_eNOT -> _not [] ; + Tauto_eNOT -> Tauto_rtyp [] ; + Tauto_eNOT -> _negb [] ; + Tauto_hold -> Tauto_isProp [] ; + Tauto_hold -> _is_true [] ; + Tauto_hold -> Tauto_rtyp [] ; + _is_true -> _bool [] ; + _is_true -> _eq [] ; + _is_true -> _true [] ; + Tauto_rtyp -> _bool [] ; + Tauto_rtyp -> Tauto_kind [] ; + _negb -> _bool [] ; + _negb -> _true [] ; + _negb -> _false [] ; + RingMicromega_xnormalise -> _list [] ; + RingMicromega_xnormalise -> _nil [] ; + RingMicromega_xnormalise -> _cons [] ; + RingMicromega_xnormalise -> _pair [] ; + RingMicromega_xnormalise -> RingMicromega_NFormula [] ; + RingMicromega_xnormalise -> RingMicromega_Equal [] ; + RingMicromega_xnormalise -> RingMicromega_Strict [] ; + RingMicromega_xnormalise -> RingMicromega_NonStrict [] ; + RingMicromega_xnormalise -> RingMicromega_popp [] ; + Tauto_cnf_ff -> _nil [] ; + Tauto_cnf_ff -> _cons [] ; + Tauto_cnf_ff -> Tauto_cnf [] ; + Refl_make_conj -> _and [] ; + Refl_make_conj -> _True [] ; + Refl_make_conj -> _list [] ; + RingMicromega_normalise_sound -> RingMicromega_OpEq [] ; + RingMicromega_normalise_sound -> RingMicromega_OpLt [] ; + RingMicromega_normalise_sound -> RingMicromega_Build_Formula [] ; + RingMicromega_normalise_sound -> RingMicromega_eval_nformula [] ; + RingMicromega_normalise_sound -> RingMicromega_eval_formula [] ; + RingMicromega_normalise_sound -> RingMicromega_normalise [] ; + RingMicromega_normalise_sound -> OrderedRing_Rle_le_minus [] ; + RingMicromega_normalise_sound -> RingMicromega_micomega_sor_setoid [] ; + RingMicromega_normalise_sound -> RingMicromega_rle_morph_Proper [] ; + RingMicromega_normalise_sound -> OrderedRing_Rlt_lt_minus [] ; + RingMicromega_normalise_sound -> RingMicromega_rlt_morph_Proper [] ; + RingMicromega_normalise_sound -> RingMicromega_micomega_sor_setoid_Reflexive [] ; + RingMicromega_normalise_sound -> RingMicromega_micomega_sor_setoid_Symmetric [] ; + RingMicromega_normalise_sound -> RingMicromega_rminus_morph_Proper [] ; + RingMicromega_normalise_sound -> RingMicromega_eval_pol_norm [] ; + RingMicromega_normalise_sound -> OrderedRing_Rminus_eq_0 [] ; + RingMicromega_normalise_sound -> RingMicromega_eval_pol_sub [] ; + RingMicromega_normalise_sound -> RingMicromega_OpNEq [] ; + RingMicromega_normalise_sound -> RingMicromega_OpLe [] ; + RingMicromega_normalise_sound -> RingMicromega_OpGe [] ; + RingMicromega_normalise_sound -> RingMicromega_OpGt [] ; + RingMicromega_check_inconsistent -> RingMicromega_NFormula [] ; + RingMicromega_check_inconsistent -> RingMicromega_cltb [] ; + RingMicromega_xnormalise_correct -> RingMicromega_eval_nformula [] ; + RingMicromega_xnormalise_correct -> RingMicromega_xnormalise [] ; + RingMicromega_xnormalise_correct -> Refl_make_conj [] ; + RingMicromega_xnormalise_correct -> RingMicromega_NonEqual [] ; + RingMicromega_xnormalise_correct -> OrderedRing_Rlt_nge [] ; + RingMicromega_xnormalise_correct -> RingMicromega_eq0_cnf [] ; + RingMicromega_xnormalise_correct -> OrderedRing_Rle_le_minus [] ; + RingMicromega_xnormalise_correct -> RingMicromega_rle_morph_Proper [] ; + RingMicromega_xnormalise_correct -> RingMicromega_eval_pol_opp [] ; + Tauto_eval_cnf_ff -> _False_ind [] ; + Tauto_eval_cnf_ff -> _I [] ; + Tauto_eval_cnf_ff -> _iff [] ; + Tauto_eval_cnf_ff -> _conj [] ; + Tauto_eval_cnf_ff -> Tauto_eval_cnf [] ; + Tauto_eval_cnf_ff -> Tauto_cnf_ff [] ; + RingMicromega_cnf_of_list_correct -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + RingMicromega_cnf_of_list_correct -> Morphisms_eq_proper_proxy [] ; + RingMicromega_cnf_of_list_correct -> Morphisms_Prop_and_iff_morphism [] ; + RingMicromega_cnf_of_list_correct -> _list_ind [] ; + RingMicromega_cnf_of_list_correct -> RingMicromega_eval_nformula [] ; + RingMicromega_cnf_of_list_correct -> RingMicromega_check_inconsistent_sound [] ; + RingMicromega_cnf_of_list_correct -> RingMicromega_cnf_of_list [] ; + RingMicromega_cnf_of_list_correct -> Tauto_eval_cnf_cons_iff [] ; + RingMicromega_cnf_of_list -> _cons [] ; + RingMicromega_cnf_of_list -> _pair [] ; + RingMicromega_cnf_of_list -> RingMicromega_check_inconsistent [] ; + RingMicromega_cnf_of_list -> Tauto_cnf_tt [] ; + RingMicromega_cnf_of_list -> List_fold_right [] ; + RingMicromega_eval_op1 -> _not [] ; + RingMicromega_eval_op1 -> RingMicromega_Op1 [] ; + RingMicromega_eval_pol -> RingMicromega_PolC [] ; + RingMicromega_eval_pol -> RingMicromega_PolEnv [] ; + RingMicromega_eval_pol -> EnvRing_Pphi [] ; + RingMicromega_normalise -> _pair [] ; + RingMicromega_normalise -> RingMicromega_Formula [] ; + RingMicromega_normalise -> RingMicromega_NFormula [] ; + RingMicromega_normalise -> RingMicromega_norm [] ; + RingMicromega_normalise -> RingMicromega_psub [] ; + RingMicromega_normalise -> RingMicromega_Equal [] ; + RingMicromega_normalise -> RingMicromega_NonEqual [] ; + RingMicromega_normalise -> RingMicromega_Strict [] ; + RingMicromega_normalise -> RingMicromega_NonStrict [] ; + Tauto_cnf -> Tauto_clause [] ; + RingMicromega_SORaddon -> _false [] ; + RingMicromega_SORaddon -> _not [] ; + RingMicromega_SORaddon -> _ring_morph [] ; + RingMicromega_SORaddon -> _power_theory [] ; + OrderedRing_SOR -> _not [] ; + OrderedRing_SOR -> _or [] ; + OrderedRing_SOR -> _iff [] ; + OrderedRing_SOR -> Setoid_Setoid_Theory [] ; + OrderedRing_SOR -> _ring_theory [] ; + Tauto_clause -> _prod [] ; + Tauto_clause -> _list [] ; + RingMicromega_norm -> EnvRing_norm_aux [] ; + RingMicromega_psub -> EnvRing_Psub [] ; + EnvRing_Pol -> _positive [] ; + EnvRing_Psub -> EnvRing_PsubC [] ; + EnvRing_Psub -> EnvRing_PsubI [] ; + EnvRing_Psub -> EnvRing_PsubX [] ; + EnvRing_P0 -> EnvRing_Pol [] ; + EnvRing_P0 -> EnvRing_Pc [] ; + EnvRing_Popp -> EnvRing_Pol [] ; + EnvRing_Popp -> EnvRing_Pinj [] ; + EnvRing_Popp -> EnvRing_PX [] ; + EnvRing_Popp -> EnvRing_Pc [] ; + EnvRing_mkPX -> EnvRing_P0 [] ; + EnvRing_mkPX -> EnvRing_PX [] ; + EnvRing_mkPX -> EnvRing_mkPinj [] ; + EnvRing_mkPX -> EnvRing_Peq [] ; + EnvRing_PaddC -> EnvRing_Pol [] ; + EnvRing_PaddC -> EnvRing_Pinj [] ; + EnvRing_PaddC -> EnvRing_PX [] ; + EnvRing_PaddC -> EnvRing_Pc [] ; + EnvRing_PsubC -> EnvRing_Pol [] ; + EnvRing_PsubC -> EnvRing_Pinj [] ; + EnvRing_PsubC -> EnvRing_PX [] ; + EnvRing_PsubC -> EnvRing_Pc [] ; + EnvRing_PsubI -> Z_pos_sub [] ; + EnvRing_PsubI -> Pos_pred_double [] ; + EnvRing_PsubI -> EnvRing_Popp [] ; + EnvRing_PsubI -> EnvRing_PaddC [] ; + EnvRing_PsubI -> EnvRing_mkPinj [] ; + EnvRing_PsubX -> Z_pos_sub [] ; + EnvRing_PsubX -> Pos_pred_double [] ; + EnvRing_PsubX -> EnvRing_Popp [] ; + EnvRing_PsubX -> EnvRing_mkPX [] ; + EnvRing_Pinj -> _positive [] ; + EnvRing_PX -> _positive [] ; + EnvRing_mkPinj -> Pos_add [] ; + EnvRing_mkPinj -> EnvRing_Pol [] ; + EnvRing_mkPinj -> EnvRing_Pinj [] ; + EnvRing_Pc -> _positive [] ; + EnvRing_Peq -> _bool [] ; + EnvRing_Peq -> _false [] ; + EnvRing_Peq -> Pos_compare [] ; + EnvRing_Peq -> EnvRing_Pol [] ; + EnvRing_norm_aux -> EnvRing_PExpr [] ; + EnvRing_norm_aux -> EnvRing_Psub [] ; + EnvRing_norm_aux -> EnvRing_mk_X [] ; + EnvRing_norm_aux -> EnvRing_Ppow_N [] ; + EnvRing_Padd -> EnvRing_PaddI [] ; + EnvRing_Padd -> EnvRing_PaddX [] ; + EnvRing_Pmul -> EnvRing_Padd [] ; + EnvRing_Pmul -> EnvRing_PmulI [] ; + EnvRing_mk_X -> EnvRing_mkX [] ; + EnvRing_mk_X -> EnvRing_mkPinj_pred [] ; + EnvRing_Ppow_N -> _N [] ; + EnvRing_Ppow_N -> EnvRing_P1 [] ; + EnvRing_Ppow_N -> EnvRing_Ppow_pos [] ; + EnvRing_P1 -> EnvRing_Pol [] ; + EnvRing_P1 -> EnvRing_Pc [] ; + EnvRing_Ppow_pos -> EnvRing_Pmul [] ; + EnvRing_mkX -> _xH [] ; + EnvRing_mkX -> EnvRing_mkXi [] ; + EnvRing_mkPinj_pred -> Pos_pred_double [] ; + EnvRing_mkPinj_pred -> EnvRing_Pol [] ; + EnvRing_mkPinj_pred -> EnvRing_Pinj [] ; + EnvRing_mkXi -> EnvRing_P0 [] ; + EnvRing_mkXi -> EnvRing_PX [] ; + EnvRing_mkXi -> EnvRing_P1 [] ; + EnvRing_PmulC -> EnvRing_PmulC_aux [] ; + EnvRing_PmulI -> Z_pos_sub [] ; + EnvRing_PmulI -> Pos_pred_double [] ; + EnvRing_PmulI -> EnvRing_PmulC [] ; + EnvRing_PmulC_aux -> EnvRing_mkPX [] ; + EnvRing_PaddI -> Z_pos_sub [] ; + EnvRing_PaddI -> Pos_pred_double [] ; + EnvRing_PaddI -> EnvRing_PaddC [] ; + EnvRing_PaddI -> EnvRing_mkPinj [] ; + EnvRing_PaddX -> Z_pos_sub [] ; + EnvRing_PaddX -> Pos_pred_double [] ; + EnvRing_PaddX -> EnvRing_mkPX [] ; + EnvRing_Pphi -> _pow_pos [] ; + EnvRing_Pphi -> EnvRing_Pol [] ; + EnvRing_Pphi -> Env_hd [] ; + EnvRing_Pphi -> Env_tail [] ; + Env_hd -> _xH [] ; + Env_hd -> Env_nth [] ; + Env_Env -> _positive [] ; + Env_jump -> Pos_add [] ; + Env_jump -> Env_Env [] ; + Env_tail -> Env_jump [] ; + Env_nth -> Env_Env [] ; + Tauto_cnf_tt -> _nil [] ; + Tauto_cnf_tt -> Tauto_cnf [] ; + List_fold_right -> _list [] ; + Tauto_eval_cnf_cons_iff -> _False_ind [] ; + Tauto_eval_cnf_cons_iff -> RelationClasses_Equivalence_PER [] ; + Tauto_eval_cnf_cons_iff -> RelationClasses_iff_equivalence [] ; + Tauto_eval_cnf_cons_iff -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Tauto_eval_cnf_cons_iff -> Tauto_eval_cnf [] ; + Tauto_eval_cnf_cons_iff -> Refl_make_conj_cons [] ; + Refl_make_conj_cons -> _I [] ; + Refl_make_conj_cons -> _iff [] ; + Refl_make_conj_cons -> _and_ind [] ; + Refl_make_conj_cons -> _conj [] ; + Refl_make_conj_cons -> _nil [] ; + Refl_make_conj_cons -> _cons [] ; + Refl_make_conj_cons -> Refl_make_conj [] ; + Tauto_eval_clause -> _not [] ; + Tauto_eval_clause -> Tauto_eval_tt [] ; + Tauto_eval_clause -> Refl_make_conj [] ; + Tauto_eval_clause -> Tauto_clause [] ; + OrderedRing_Rle_ngt -> OrderedRing_Rlt_neq [] ; + OrderedRing_Rle_ngt -> OrderedRing_Rle_gt_cases [] ; + OrderedRing_Rle_ngt -> OrderedRing_Rle_lt_trans [] ; + OrderedRing_Rlt_nge -> OrderedRing_Rlt_neq [] ; + OrderedRing_Rlt_nge -> OrderedRing_Rlt_le_trans [] ; + OrderedRing_Rlt_nge -> OrderedRing_Rle_gt_cases [] ; + RingMicromega_eq0_cnf -> OrderedRing_Rle_ngt [] ; + RingMicromega_eq0_cnf -> RingMicromega_SORRing_ring_lemma1 [] ; + RingMicromega_eq0_cnf -> RingMicromega_micomega_sor_setoid [] ; + RingMicromega_eq0_cnf -> OrderedRing_Rlt_lt_minus [] ; + RingMicromega_eq0_cnf -> RingMicromega_rlt_morph_Proper [] ; + RingMicromega_eq0_cnf -> _proj2 [] ; + RingMicromega_SORRing_ring_lemma1 -> _Ztriv_div_th [] ; + RingMicromega_SORRing_ring_lemma1 -> Ring_polynom_ring_correct [] ; + RingMicromega_SORRing_ring_lemma1 -> _mk_reqe [] ; + RingMicromega_SORRing_ring_lemma1 -> Setoid_Build_Setoid_Theory [] ; + RingMicromega_SORRing_ring_lemma1 -> Morphisms_proper_prf [] ; + RingMicromega_SORRing_ring_lemma1 -> RingMicromega_micomega_sor_setoid_Reflexive [] ; + RingMicromega_SORRing_ring_lemma1 -> OrderedRing_SORrt [] ; + RingMicromega_SORRing_ring_lemma1 -> _pow_N_th [] ; + RingMicromega_SORRing_ring_lemma1 -> _gen_phiZ_morph [] ; + RingMicromega_SORRing_ring_lemma1 -> RingMicromega_rtimes_morph_Proper [] ; + RingMicromega_SORRing_ring_lemma1 -> RingMicromega_ropp_morph_Proper [] ; + RingMicromega_SORRing_ring_lemma1 -> RingMicromega_rplus_morph_Proper [] ; + RingMicromega_SORRing_ring_lemma1 -> RingMicromega_micomega_sor_setoid_Transitive [] ; + RingMicromega_SORRing_ring_lemma1 -> RingMicromega_micomega_sor_setoid_Symmetric [] ; + OrderedRing_Rle_le_minus -> OrderedRing_Rplus_le_mono_r [] ; + RingMicromega_micomega_sor_setoid -> RelationClasses_Equivalence_Reflexive [] ; + RingMicromega_micomega_sor_setoid -> RelationClasses_Equivalence_Transitive [] ; + RingMicromega_micomega_sor_setoid -> RelationClasses_Equivalence_Symmetric [] ; + RingMicromega_micomega_sor_setoid -> RelationClasses_Build_Equivalence [] ; + RingMicromega_micomega_sor_setoid -> OrderedRing_SORsetoid [] ; + RingMicromega_popp -> EnvRing_Popp [] ; + RingMicromega_rle_morph_Proper -> Morphisms_Proper [] ; + RingMicromega_rle_morph_Proper -> Morphisms_respectful [] ; + RingMicromega_rle_morph_Proper -> OrderedRing_SORle_wd [] ; + OrderedRing_Rlt_lt_minus -> OrderedRing_Rplus_lt_mono_r [] ; + RingMicromega_eval_pol_opp -> _Rth_ARth [] ; + RingMicromega_eval_pol_opp -> RingMicromega_eval_pol [] ; + RingMicromega_eval_pol_opp -> RingMicromega_popp [] ; + RingMicromega_eval_pol_opp -> OrderedRing_SORsetoid [] ; + RingMicromega_eval_pol_opp -> OrderedRing_SORrt [] ; + RingMicromega_eval_pol_opp -> RingMicromega_Rops_wd [] ; + RingMicromega_eval_pol_opp -> RingMicromega_SORrm [] ; + RingMicromega_eval_pol_opp -> EnvRing_Popp_ok [] ; + RingMicromega_rlt_morph_Proper -> Morphisms_Proper [] ; + RingMicromega_rlt_morph_Proper -> Morphisms_respectful [] ; + RingMicromega_rlt_morph_Proper -> OrderedRing_SORlt_wd [] ; + RingMicromega_micomega_sor_setoid_Reflexive -> RelationClasses_Equivalence_Reflexive [] ; + RingMicromega_micomega_sor_setoid_Reflexive -> OrderedRing_SORsetoid [] ; + OrderedRing_SORsetoid -> OrderedRing_SOR [] ; + OrderedRing_SORlt_wd -> OrderedRing_SOR [] ; + OrderedRing_SORrt -> OrderedRing_SOR [] ; + RingMicromega_Rops_wd -> _ring_eq_ext [] ; + RingMicromega_Rops_wd -> _mk_reqe [] ; + RingMicromega_Rops_wd -> OrderedRing_SORtimes_wd [] ; + RingMicromega_Rops_wd -> OrderedRing_SORopp_wd [] ; + RingMicromega_Rops_wd -> OrderedRing_SORplus_wd [] ; + RingMicromega_SORrm -> RingMicromega_SORaddon [] ; + EnvRing_Popp_ok -> Morphisms_reflexive_reflexive_proxy [] ; + EnvRing_Popp_ok -> Morphisms_Reflexive_partial_app_morphism [] ; + EnvRing_Popp_ok -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + EnvRing_Popp_ok -> Morphisms_eq_proper_proxy [] ; + EnvRing_Popp_ok -> RelationClasses_Equivalence_PER [] ; + EnvRing_Popp_ok -> Morphisms_reflexive_proper_proxy [] ; + EnvRing_Popp_ok -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + EnvRing_Popp_ok -> Setoid_Seq_refl [] ; + EnvRing_Popp_ok -> _morph_opp [] ; + EnvRing_Popp_ok -> _ARopp_mul_l [] ; + EnvRing_Popp_ok -> _ARopp_add [] ; + EnvRing_Popp_ok -> EnvRing_Popp [] ; + EnvRing_Popp_ok -> EnvRing_Pphi [] ; + EnvRing_Popp_ok -> EnvRing_radd_ext_Proper [] ; + EnvRing_Popp_ok -> EnvRing_Pol_ind [] ; + EnvRing_Popp_ok -> EnvRing_rmul_ext_Proper [] ; + EnvRing_radd_ext_Proper -> _Radd_ext [] ; + EnvRing_Pol_ind -> EnvRing_Pol [] ; + EnvRing_Pol_ind -> EnvRing_Pinj [] ; + EnvRing_Pol_ind -> EnvRing_PX [] ; + EnvRing_Pol_ind -> EnvRing_Pc [] ; + EnvRing_rmul_ext_Proper -> _Rmul_ext [] ; + OrderedRing_SORtimes_wd -> OrderedRing_SOR [] ; + OrderedRing_SORopp_wd -> OrderedRing_SOR [] ; + OrderedRing_SORplus_wd -> OrderedRing_SOR [] ; + OrderedRing_sor_setoid_Reflexive -> RelationClasses_Equivalence_Reflexive [] ; + OrderedRing_sor_setoid_Reflexive -> OrderedRing_SORsetoid [] ; + OrderedRing_SOR_ring_lemma1 -> _Ztriv_div_th [] ; + OrderedRing_SOR_ring_lemma1 -> Ring_polynom_ring_correct [] ; + OrderedRing_SOR_ring_lemma1 -> _mk_reqe [] ; + OrderedRing_SOR_ring_lemma1 -> Setoid_Build_Setoid_Theory [] ; + OrderedRing_SOR_ring_lemma1 -> Morphisms_proper_prf [] ; + OrderedRing_SOR_ring_lemma1 -> OrderedRing_SORrt [] ; + OrderedRing_SOR_ring_lemma1 -> OrderedRing_sor_setoid_Reflexive [] ; + OrderedRing_SOR_ring_lemma1 -> OrderedRing_rplus_morph_Proper [] ; + OrderedRing_SOR_ring_lemma1 -> OrderedRing_sor_setoid_Transitive [] ; + OrderedRing_SOR_ring_lemma1 -> OrderedRing_ropp_morph_Proper [] ; + OrderedRing_SOR_ring_lemma1 -> _pow_N_th [] ; + OrderedRing_SOR_ring_lemma1 -> _gen_phiZ_morph [] ; + OrderedRing_SOR_ring_lemma1 -> OrderedRing_sor_setoid_Symmetric [] ; + OrderedRing_SOR_ring_lemma1 -> OrderedRing_rtimes_morph_Proper [] ; + OrderedRing_rlt_morph_Proper -> Morphisms_Proper [] ; + OrderedRing_rlt_morph_Proper -> Morphisms_respectful [] ; + OrderedRing_rlt_morph_Proper -> OrderedRing_SORlt_wd [] ; + OrderedRing_sor_setoid -> RelationClasses_Equivalence_Reflexive [] ; + OrderedRing_sor_setoid -> RelationClasses_Equivalence_Transitive [] ; + OrderedRing_sor_setoid -> RelationClasses_Equivalence_Symmetric [] ; + OrderedRing_sor_setoid -> RelationClasses_Build_Equivalence [] ; + OrderedRing_sor_setoid -> OrderedRing_SORsetoid [] ; + OrderedRing_Rplus_lt_mono_r -> OrderedRing_rlt_morph_Proper [] ; + OrderedRing_Rplus_lt_mono_r -> OrderedRing_Rplus_comm [] ; + OrderedRing_Rplus_lt_mono_r -> OrderedRing_Rplus_lt_mono_l [] ; + OrderedRing_Rplus_comm -> _ring_subst_niter [] ; + OrderedRing_Rplus_comm -> OrderedRing_SOR_ring_lemma1 [] ; + OrderedRing_Rplus_lt_mono_l -> OrderedRing_Rplus_le_mono_l [] ; + OrderedRing_Rplus_lt_mono_l -> OrderedRing_Rlt_le_neq [] ; + OrderedRing_Rplus_lt_mono_l -> OrderedRing_Rplus_cancel_l [] ; + OrderedRing_Rplus_le_mono_l -> _ring_subst_niter [] ; + OrderedRing_Rplus_le_mono_l -> OrderedRing_SOR_ring_lemma1 [] ; + OrderedRing_Rplus_le_mono_l -> OrderedRing_sor_setoid [] ; + OrderedRing_Rplus_le_mono_l -> OrderedRing_SORplus_le_mono_l [] ; + OrderedRing_Rplus_le_mono_l -> OrderedRing_rle_morph_Proper [] ; + OrderedRing_Rlt_le_neq -> OrderedRing_SORlt_le_neq [] ; + OrderedRing_Rplus_cancel_l -> _ring_subst_niter [] ; + OrderedRing_Rplus_cancel_l -> OrderedRing_SOR_ring_lemma1 [] ; + OrderedRing_Rplus_cancel_l -> OrderedRing_sor_setoid [] ; + OrderedRing_rplus_morph_Proper -> Morphisms_Proper [] ; + OrderedRing_rplus_morph_Proper -> Morphisms_respectful [] ; + OrderedRing_rplus_morph_Proper -> OrderedRing_SORplus_wd [] ; + OrderedRing_sor_setoid_Transitive -> RelationClasses_Equivalence_Transitive [] ; + OrderedRing_sor_setoid_Transitive -> OrderedRing_SORsetoid [] ; + OrderedRing_SORlt_le_neq -> OrderedRing_SOR [] ; + OrderedRing_SORplus_le_mono_l -> OrderedRing_SOR [] ; + OrderedRing_rle_morph_Proper -> Morphisms_Proper [] ; + OrderedRing_rle_morph_Proper -> Morphisms_respectful [] ; + OrderedRing_rle_morph_Proper -> OrderedRing_SORle_wd [] ; + OrderedRing_SORle_wd -> OrderedRing_SOR [] ; + OrderedRing_ropp_morph_Proper -> Morphisms_Proper [] ; + OrderedRing_ropp_morph_Proper -> Morphisms_respectful [] ; + OrderedRing_ropp_morph_Proper -> OrderedRing_SORopp_wd [] ; + _pow_N_th -> _power_theory [] ; + _pow_N_th -> _mkpow_th [] ; + _pow_N_th -> _pow_N_pow_N [] ; + _gen_phiZ -> _Z [] ; + _gen_phiZ -> _gen_phiPOS [] ; + _gen_phiZ_morph -> _Zth [] ; + _gen_phiZ_morph -> _Smorph_morph [] ; + _gen_phiZ_morph -> _gen_Zeqb_ok [] ; + _gen_phiZ_morph -> _gen_phiZ_add [] ; + _gen_phiZ_morph -> _gen_phiZ_ext [] ; + _gen_phiZ_morph -> _gen_phiZ_mul [] ; + _gen_phiZ_morph -> _mkRmorph [] ; + OrderedRing_sor_setoid_Symmetric -> RelationClasses_Equivalence_Symmetric [] ; + OrderedRing_sor_setoid_Symmetric -> OrderedRing_SORsetoid [] ; + OrderedRing_rtimes_morph_Proper -> Morphisms_Proper [] ; + OrderedRing_rtimes_morph_Proper -> Morphisms_respectful [] ; + OrderedRing_rtimes_morph_Proper -> OrderedRing_SORtimes_wd [] ; + _id_phi_N -> _N [] ; + _Smorph_morph -> _ring_morph [] ; + _Smorph_morph -> _mkmorph [] ; + _Smorph_morph -> _Smorph_mul [] ; + _Smorph_morph -> _Smorph_sub [] ; + _Smorph_morph -> _Smorph_eq [] ; + _Smorph_morph -> _Smorph1 [] ; + _gen_Zeqb_ok -> RelationClasses_reflexivity [] ; + _gen_Zeqb_ok -> _eq_ind_r [] ; + _gen_Zeqb_ok -> Z_eqb_eq [] ; + _gen_Zeqb_ok -> _gen_phiZ [] ; + _gen_Zeqb_ok -> _R_setoid3_Reflexive [] ; + _gen_phiZ_add -> Z_add [] ; + _gen_phiZ_add -> _ARadd_0_r [] ; + _gen_phiZ_add -> _same_genZ [] ; + _gen_phiZ_add -> _gen_phiZ1_pos_sub [] ; + _gen_phiZ_ext -> _eq_ind_r [] ; + _gen_phiZ_ext -> Setoid_Seq_refl [] ; + _gen_phiZ_ext -> _gen_phiZ [] ; + _gen_phiZ_mul -> Z_mul [] ; + _gen_phiZ_mul -> _ARmul_0_r [] ; + _gen_phiZ_mul -> _R_setoid3_Symmetric [] ; + _gen_phiZ_mul -> _ARopp_mul_r [] ; + _gen_phiZ_mul -> _Ropp_opp [] ; + _gen_phiZ_mul -> _same_genZ [] ; + _gen_phiZ_mul -> _ARgen_phiPOS_mult [] ; + _semi_morph -> _bool [] ; + _semi_morph -> _eq [] ; + _semi_morph -> _true [] ; + _mkRmorph -> _bool [] ; + _mkRmorph -> _eq [] ; + _mkRmorph -> _true [] ; + _rmul_ext3_Proper -> _Rmul_ext [] ; + _R_setoid3_Symmetric -> RelationClasses_Equivalence_Symmetric [] ; + _R_setoid3_Symmetric -> Setoid_Setoid_Theory [] ; + _ARopp_mul_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _ARopp_mul_r -> Morphisms_eq_proper_proxy [] ; + _ARopp_mul_r -> RelationClasses_Equivalence_Transitive [] ; + _ARopp_mul_r -> _ropp_ext2_Proper [] ; + _ARopp_mul_r -> _ARopp_mul_l [] ; + _ARopp_mul_r -> _ARmul_comm [] ; + _gen_phiZ1 -> _Z [] ; + _gen_phiZ1 -> _gen_phiPOS1 [] ; + _gen_phiPOS1 -> _positive [] ; + _R_setoid3 -> RelationClasses_Equivalence_Reflexive [] ; + _R_setoid3 -> RelationClasses_Equivalence_Transitive [] ; + _R_setoid3 -> RelationClasses_Equivalence_Symmetric [] ; + _R_setoid3 -> RelationClasses_Build_Equivalence [] ; + _R_setoid3 -> Setoid_Setoid_Theory [] ; + _Ropp_opp -> Morphisms_reflexive_reflexive_proxy [] ; + _Ropp_opp -> Morphisms_Reflexive_partial_app_morphism [] ; + _Ropp_opp -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _Ropp_opp -> Morphisms_eq_proper_proxy [] ; + _Ropp_opp -> Morphisms_reflexive_proper_proxy [] ; + _Ropp_opp -> RelationClasses_Equivalence_Reflexive [] ; + _Ropp_opp -> RelationClasses_Equivalence_Transitive [] ; + _Ropp_opp -> RelationClasses_Equivalence_Symmetric [] ; + _Ropp_opp -> RelationClasses_symmetry [] ; + _Ropp_opp -> _radd_ext2_Proper [] ; + _Ropp_opp -> _Radd_assoc [] ; + _Ropp_opp -> _Radd_comm [] ; + _Ropp_opp -> _Radd_0_l [] ; + _Ropp_opp -> _Ropp_def [] ; + _R_setoid3_Reflexive -> RelationClasses_Equivalence_Reflexive [] ; + _R_setoid3_Reflexive -> Setoid_Setoid_Theory [] ; + _same_genZ -> _Z0 [] ; + _same_genZ -> _Zpos [] ; + _same_genZ -> _Zneg [] ; + _same_genZ -> _Rth_ARth [] ; + _same_genZ -> _gen_phiZ [] ; + _same_genZ -> _gen_phiZ1 [] ; + _same_genZ -> _R_setoid3 [] ; + _same_genZ -> _ropp_ext3_Proper [] ; + _same_genZ -> _same_gen [] ; + _R_setoid3_Transitive -> RelationClasses_Equivalence_Transitive [] ; + _R_setoid3_Transitive -> Setoid_Setoid_Theory [] ; + _ARgen_phiPOS_mult -> Pos_mul [] ; + _ARgen_phiPOS_mult -> _rmul_ext3_Proper [] ; + _ARgen_phiPOS_mult -> _ARgen_phiPOS_add [] ; + _ropp_ext3_Proper -> _Ropp_ext [] ; + _ARgen_phiPOS_add -> _eq_ind_r [] ; + _ARgen_phiPOS_add -> Pos_add_carry_spec [] ; + _ARgen_phiPOS_add -> _ARgen_phiPOS_Psucc [] ; + _radd_ext3_Proper -> _Radd_ext [] ; + _ARgen_phiPOS_Psucc -> Pos_succ [] ; + _ARgen_phiPOS_Psucc -> Morphisms_subrelation_proper [] ; + _ARgen_phiPOS_Psucc -> Morphisms_subrelation_refl [] ; + _ARgen_phiPOS_Psucc -> Morphisms_PER_morphism [] ; + _ARgen_phiPOS_Psucc -> Morphisms_iff_flip_impl_subrelation [] ; + _ARgen_phiPOS_Psucc -> Morphisms_subrelation_respectful [] ; + _ARgen_phiPOS_Psucc -> _tt [] ; + _ARgen_phiPOS_Psucc -> _positive_ind [] ; + _ARgen_phiPOS_Psucc -> Setoid_Seq_refl [] ; + _ARgen_phiPOS_Psucc -> _ARadd_assoc1 [] ; + _ARgen_phiPOS_Psucc -> _ARadd_assoc2 [] ; + _ARgen_phiPOS_Psucc -> _ARdistr_l [] ; + _ARgen_phiPOS_Psucc -> _ARmul_1_r [] ; + _ARgen_phiPOS_Psucc -> _gen_phiPOS1 [] ; + _ARgen_phiPOS_Psucc -> _R_setoid3 [] ; + _ARgen_phiPOS_Psucc -> _R_setoid3_Reflexive [] ; + _ARgen_phiPOS_Psucc -> _R_setoid3_Transitive [] ; + _ARgen_phiPOS_Psucc -> _radd_ext3_Proper [] ; + _same_gen -> Morphisms_reflexive_reflexive_proxy [] ; + _same_gen -> Morphisms_Reflexive_partial_app_morphism [] ; + _same_gen -> Morphisms_reflexive_proper_proxy [] ; + _same_gen -> _positive_ind [] ; + _same_gen -> Setoid_Seq_refl [] ; + _same_gen -> _ARmul_1_r [] ; + _same_gen -> _rmul_ext3_Proper [] ; + _same_gen -> _gen_phiPOS1 [] ; + _same_gen -> _R_setoid3_Reflexive [] ; + _same_gen -> _R_setoid3_Transitive [] ; + _same_gen -> _radd_ext3_Proper [] ; + _same_gen -> _gen_phiPOS [] ; + _gen_phiPOS -> _positive [] ; + _gen_phiZ1_pos_sub -> RelationClasses_eq_Symmetric [] ; + _gen_phiZ1_pos_sub -> Pos_sub_add [] ; + _gen_phiZ1_pos_sub -> Morphisms_rewrite_relation_eq_dom [] ; + _gen_phiZ1_pos_sub -> Morphisms_reflexive_proper [] ; + _gen_phiZ1_pos_sub -> Morphisms_reflexive_eq_dom_reflexive [] ; + _gen_phiZ1_pos_sub -> Z_pos_sub_spec [] ; + _gen_phiZ1_pos_sub -> _Rth_ARth [] ; + _gen_phiZ1_pos_sub -> _ARadd_0_l [] ; + _gen_phiZ1_pos_sub -> _ARopp_add [] ; + _gen_phiZ1_pos_sub -> _gen_phiZ1 [] ; + _gen_phiZ1_pos_sub -> _ropp_ext3_Proper [] ; + _gen_phiZ1_pos_sub -> _ARgen_phiPOS_add [] ; + _gen_phiZ1_pos_sub -> _R_setoid3_relation [] ; + _R_setoid3_relation -> RelationClasses_RewriteRelation [] ; + _R_setoid3_relation -> RelationClasses_Build_RewriteRelation [] ; + _Smorph_add -> _semi_morph [] ; + _Smorph_mul -> _semi_morph [] ; + _Smorph_opp -> Morphisms_reflexive_reflexive_proxy [] ; + _Smorph_opp -> Morphisms_Reflexive_partial_app_morphism [] ; + _Smorph_opp -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + _Smorph_opp -> Morphisms_eq_proper_proxy [] ; + _Smorph_opp -> Morphisms_reflexive_proper_proxy [] ; + _Smorph_opp -> RelationClasses_Equivalence_Reflexive [] ; + _Smorph_opp -> RelationClasses_Equivalence_Transitive [] ; + _Smorph_opp -> RelationClasses_Equivalence_Symmetric [] ; + _Smorph_opp -> RelationClasses_symmetry [] ; + _Smorph_opp -> _radd_ext2_Proper [] ; + _Smorph_opp -> _Radd_assoc [] ; + _Smorph_opp -> _Radd_comm [] ; + _Smorph_opp -> _Radd_0_l [] ; + _Smorph_opp -> _Ropp_def [] ; + _Smorph_opp -> _Smorph_add [] ; + _Smorph_opp -> _Smorph0 [] ; + _Smorph_opp -> _phi_ext1_Proper [] ; + _Smorph_sub -> RelationClasses_reflexivity [] ; + _Smorph_sub -> RelationClasses_Equivalence_PER [] ; + _Smorph_sub -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + _Smorph_sub -> _Rsub_def [] ; + _Smorph_sub -> _Smorph_opp [] ; + _Smorph_eq -> _semi_morph [] ; + _Smorph0 -> _semi_morph [] ; + _Smorph1 -> _semi_morph [] ; + _phi_ext1_Proper -> Morphisms_Proper [] ; + _phi_ext1_Proper -> Morphisms_respectful [] ; + _pow_N_pow_N -> RelationClasses_reflexivity [] ; + _pow_N_pow_N -> RelationClasses_Equivalence_Reflexive [] ; + _pow_N_pow_N -> _pow_N [] ; + _pow_N_pow_N -> _id_phi_N [] ; + OrderedRing_Rplus_le_mono_r -> OrderedRing_Rplus_comm [] ; + OrderedRing_Rplus_le_mono_r -> OrderedRing_Rplus_le_mono_l [] ; + RingMicromega_rtimes_morph_Proper -> Morphisms_Proper [] ; + RingMicromega_rtimes_morph_Proper -> Morphisms_respectful [] ; + RingMicromega_rtimes_morph_Proper -> OrderedRing_SORtimes_wd [] ; + RingMicromega_ropp_morph_Proper -> Morphisms_Proper [] ; + RingMicromega_ropp_morph_Proper -> Morphisms_respectful [] ; + RingMicromega_ropp_morph_Proper -> OrderedRing_SORopp_wd [] ; + RingMicromega_rplus_morph_Proper -> Morphisms_Proper [] ; + RingMicromega_rplus_morph_Proper -> Morphisms_respectful [] ; + RingMicromega_rplus_morph_Proper -> OrderedRing_SORplus_wd [] ; + RingMicromega_micomega_sor_setoid_Transitive -> RelationClasses_Equivalence_Transitive [] ; + RingMicromega_micomega_sor_setoid_Transitive -> OrderedRing_SORsetoid [] ; + RingMicromega_micomega_sor_setoid_Symmetric -> RelationClasses_Equivalence_Symmetric [] ; + RingMicromega_micomega_sor_setoid_Symmetric -> OrderedRing_SORsetoid [] ; + _proj2 -> _and [] ; + OrderedRing_SORle_antisymm -> OrderedRing_SOR [] ; + OrderedRing_Rlt_neq -> Morphisms_subrelation_proper [] ; + OrderedRing_Rlt_neq -> Morphisms_reflexive_reflexive_proxy [] ; + OrderedRing_Rlt_neq -> Morphisms_subrelation_refl [] ; + OrderedRing_Rlt_neq -> RelationClasses_iff_Reflexive [] ; + OrderedRing_Rlt_neq -> Morphisms_iff_flip_impl_subrelation [] ; + OrderedRing_Rlt_neq -> Morphisms_reflexive_proper_proxy [] ; + OrderedRing_Rlt_neq -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + OrderedRing_Rlt_neq -> Morphisms_subrelation_respectful [] ; + OrderedRing_Rlt_neq -> _tt [] ; + OrderedRing_Rlt_neq -> OrderedRing_Rlt_le_neq [] ; + OrderedRing_Rlt_le_trans -> OrderedRing_rlt_morph_Proper [] ; + OrderedRing_Rlt_le_trans -> OrderedRing_sor_setoid_Symmetric [] ; + OrderedRing_Rlt_le_trans -> OrderedRing_Rle_lt_eq [] ; + OrderedRing_Rlt_le_trans -> OrderedRing_Rlt_trans [] ; +subgraph cluster_RelationClasses { label="RelationClasses"; fillcolor="#FFFFC3"; labeljust=l; style=filled +RelationClasses_neq_Symmetric; RelationClasses_Build_RewriteRelation; RelationClasses_PreOrder_Transitive; RelationClasses_RewriteRelation; RelationClasses_equivalence_rewrite_relation; RelationClasses_impl_Reflexive_obligation_1; RelationClasses_flip_Reflexive; RelationClasses_inverse_impl_rewrite_relation; RelationClasses_impl_Reflexive; RelationClasses_eq_Symmetric; RelationClasses_eq_Transitive; RelationClasses_eq_Reflexive; RelationClasses_eq_equivalence; RelationClasses_Build_PreOrder; RelationClasses_PreOrder; RelationClasses_PreOrder_Reflexive; RelationClasses_StrictOrder_Transitive; RelationClasses_Build_StrictOrder; RelationClasses_complement; RelationClasses_Irreflexive; RelationClasses_StrictOrder; RelationClasses_StrictOrder_Irreflexive; RelationClasses_Build_Equivalence; RelationClasses_transitivity; RelationClasses_PER_Transitive; RelationClasses_PER_Symmetric; RelationClasses_symmetry; RelationClasses_iff_Symmetric; RelationClasses_iff_equivalence; RelationClasses_Build_PER; RelationClasses_PER; RelationClasses_Equivalence_Symmetric; RelationClasses_Equivalence_Transitive; RelationClasses_Transitive; RelationClasses_Symmetric; RelationClasses_Equivalence; RelationClasses_Reflexive; RelationClasses_subrelation; RelationClasses_Equivalence_Reflexive; RelationClasses_iff_Reflexive; RelationClasses_Equivalence_PER; RelationClasses_iff_Transitive; RelationClasses_reflexivity; }; +subgraph cluster_BinNatDef { label="BinNatDef"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_BinNatDef_N { label="N"; fillcolor="#FFFFA3"; labeljust=l; style=filled +BinNatDef_N_of_nat; }; +}; +subgraph cluster_ConstructiveExtra { label="ConstructiveExtra"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ConstructiveExtra_constructive_indefinite_ground_description_Z; ConstructiveExtra_Pos_pred_double_inj; ConstructiveExtra_Z_inj_nat_rev; ConstructiveExtra_Z_inj_nat_id; ConstructiveExtra_Z_inj_nat; }; +subgraph cluster_Morphisms { label="Morphisms"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Morphisms_proper_prf; Morphisms_eq_rewrite_relation; Morphisms_reflexive_eq_dom_reflexive; Morphisms_reflexive_proper; Morphisms_rewrite_relation_eq_dom; Morphisms_proper_sym_impl_iff; Morphisms_pointwise_relation; Morphisms_Build_Params; Morphisms_Params; Morphisms_impl_pars; Morphisms_PER_morphism_obligation_1; Morphisms_trans_co_eq_inv_impl_morphism_obligation_1; Morphisms_trans_co_impl_morphism_obligation_1; Morphisms_trans_co_impl_morphism; Morphisms_per_partial_app_morphism_obligation_1; Morphisms_per_partial_app_morphism; Morphisms_trans_sym_co_inv_impl_morphism_obligation_1; Morphisms_trans_sym_co_inv_impl_morphism; Morphisms_iff_impl_subrelation; Morphisms_ProperProxy; Morphisms_ReflexiveProxy; Morphisms_subrelation_respectful; Morphisms_reflexive_proper_proxy; Morphisms_iff_flip_impl_subrelation; Morphisms_eq_proper_proxy; Morphisms_trans_co_eq_inv_impl_morphism; Morphisms_respectful; Morphisms_PER_morphism; Morphisms_Proper; Morphisms_Reflexive_partial_app_morphism; Morphisms_subrelation_refl; Morphisms_reflexive_reflexive_proxy; Morphisms_subrelation_proper; }; +subgraph cluster_Nat2Pos { label="Nat2Pos"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Nat2Pos_id; Nat2Pos_inj_mul; }; +subgraph cluster_QExtra { label="QExtra"; fillcolor="#FFFFC3"; labeljust=l; style=filled +QExtra_Qbound_lt_ZExp2_spec; QExtra_Pos_log2floor_plus1; QExtra_Qbound_lt_ZExp2; QExtra_Qlowbound_ltabs_ZExp2_inv; QExtra_Qlowbound_ltabs_ZExp2; QExtra_Qlowbound_lt_ZExp2_spec; QExtra_QarchimedeanLowExp2_Z; QExtra_QarchimedeanExp2_Z; QExtra_Qbound_ltabs_ZExp2_spec; QExtra_Qbound_ltabs_ZExp2; QExtra_Pos_log2floor_plus1_spec; }; +subgraph cluster_N2Z { label="N2Z"; fillcolor="#FFFFC3"; labeljust=l; style=filled +N2Z_inj_add; N2Z_inj_mul; }; +subgraph cluster_Relation_Definitions { label="Relation_Definitions"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Relation_Definitions_relation; }; +subgraph cluster_Pos { label="Pos"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Pos_Private_Dec { label="Private_Dec"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Pos_Private_Dec_max_case_strong; }; +subgraph cluster_Pos_Private_Tac { label="Private_Tac"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Pos_Private_Tac_lt_eq; Pos_Private_Tac_eq_le; Pos_Private_Tac_eq_trans; Pos_Private_Tac_not_ge_lt; Pos_Private_Tac_le_neq_lt; Pos_Private_Tac_eq_refl; Pos_Private_Tac_not_neq_eq; Pos_Private_Tac_neq_eq; Pos_Private_Tac_eq_neq; Pos_Private_Tac_le_antisym; Pos_Private_Tac_lt_trans; Pos_Private_Tac_interp_ord; Pos_Private_Tac_trans; Pos_Private_Tac_not_gt_le; Pos_Private_Tac_eq_sym; Pos_Private_Tac_lt_irrefl; Pos_Private_Tac_le_lt_trans; Pos_Private_Tac_eq_lt; }; +Pos_mul_assoc; Pos_eqb_refl; Pos_lt_succ_r; Pos_sub_mask_succ_r; Pos_pred_N; Pos_pred_double_succ; Pos_pred_N_succ; Pos_eqb; Pos_eqb_eq; Pos_add_diag; Pos_add_xO; Pos_mul_succ_l; Pos_of_nat_succ; Pos_of_succ_nat; Pos_iter_op_succ; Pos_iter_op; Pos_le; Pos_le_1_l; Pos_mul_lt_mono_l; Pos_mul_add_distr_l; Pos_mul_sub_distr_l; Pos_mul_xO_r; Pos_mul_xI_r; Pos_mul_1_r; Pos_add_lt_mono; Pos_gt_lt; Pos_mul_compare_mono_l; Pos_mul_comm; Pos_mul_compare_mono_r; Pos_mul_sub_distr_r; Pos_mul_add_distr_r; Pos_succ_pred_or; Pos_eq_equiv; Pos_lt_1_succ; Pos_compare_refl; Pos_gt_lt_iff; Pos_peano_rect; Pos_compare_succ_r; Pos_compare_succ_l; Pos_compare_succ_succ; Pos_add_succ_l; Pos_add_compare_mono_l; Pos_lt_succ_diag_r; Pos_add_lt_mono_l; Pos_peano_ind; Pos_compare_cont_antisym; Pos_compare_antisym; Pos_xI_succ_xO; Pos_compare_lt_iff; Pos_compare_eq_iff; Pos_sub_mask_nul_iff; Pos_compare_cont; Pos_compare_cont_spec; Pos_sub_mask_add_diag_r; Pos_sub_mask_neg_iff; Pos_compare_sub_mask; Pos_mask2cmp; Pos_succ_not_1; Pos_add_carry_add; Pos_succ_inj; Pos_add_reg_r; Pos_add_reg_l; Pos_add_cancel_l; Pos_add_no_neutral; Pos_pred; Pos_double_pred_mask; Pos_SubIsNeg; Pos_SubIsPos; Pos_SubIsNul; Pos_sub_mask_carry; Pos_pred_mask; Pos_add_1_r; Pos_add_1_l; Pos_add_succ_r; Pos_succ_pred_double; Pos_sub_mask_carry_spec; Pos_add_xI_pred_double; Pos_SubMaskSpec; Pos_sub_mask_spec; Pos_sub_mask_add; Pos_sub_mask_add_diag_l; Pos_sub_mask_pos_iff; Pos_lt_iff_add; Pos_sub_mask_pos_; Pos_IsNeg; Pos_IsPos; Pos_double_mask; Pos_sub_mask_pos; Pos_IsNul; Pos_mask; Pos_switch_Eq; Pos_sub_xO_xO; Pos_sub_xO_xI; Pos_sub_xI_xO; Pos_sub_xI_xI; Pos_succ_double_mask; Pos_compare_xO_xO; Pos_compare_xO_xI; Pos_compare_xI_xO; Pos_compare_xI_xI; Pos_pred_double; Pos_sub_mask; Pos_sub_mask_diag; Pos_sub; Pos_lt; Pos_gt; Pos_sub_sub_distr; Pos_compare; Pos_compare_spec; Pos_add_lt_mono_r; Pos_add_sub; Pos_sub_add; Pos_lt_trans; Pos_lt_add_r; Pos_sub_add_distr; Pos_add_sub_assoc; Pos_add_compare_mono_r; Pos_lt_gt; Pos_add_assoc; Pos_add_carry; Pos_add_carry_spec; Pos_add_comm; Pos_to_nat; Pos_succ_of_nat; Pos_eqb_spec; Pos_of_nat; Pos_succ; Pos_add; Pos_mul; Pos_pow_succ_r; Pos_pow_1_r; Pos_iter_ind; Pos_iter_invariant; Pos_iter_swap_gen; Pos_iter_swap; Pos_iter_succ; Pos_iter_add; Pos_iter; Pos_le_lt_trans; Pos_leb_le; Pos_compare_nle_iff; Pos_compare_nge_iff; Pos_leb_spec0; Pos_lt_nle; Pos_max_lub_iff; Pos_max_le_compat_r; Pos_max_case_strong; Pos_lt_le_trans; Pos_le_trans; Pos_add_le_mono_r; Pos_max_mono; Pos_max_monotone; Pos_add_le_mono_l; Pos_add_max_distr_l; Pos_add_max_distr_r; Pos_lt_compat; Pos_ge; Pos_ge_le_iff; Pos_le_nlt; Pos_max_r; Pos_max_l; Pos_lt_total; Pos_max_spec; Pos_le_max_r; Pos_le_max_l; Pos_le_refl; Pos_max; Pos_max_1_l; Pos_compare_le_iff; Pos_lt_eq_cases; Pos_le_lteq; Pos_lt_strorder; Pos_lt_irrefl; Pos_le_antisym; Pos_succ_lt_mono; Pos_le_succ_l; Pos_ggcdn_correct_divisors; Pos_ggcd_correct_divisors; Pos_ggcdn_gcdn; Pos_ggcd_gcd; Pos_ggcdn; Pos_ggcd; Pos_divide_mul_l; Pos_mul_lt_mono_r; Pos_divide_add_cancel_l; Pos_divide_xO_xO; Pos_divide_xO_xI; Pos_divide_mul_r; Pos_size_nat_monotone; Pos_sub_decr; Pos_gcdn_greatest; Pos_gcdn; Pos_size_nat; Pos_divide; Pos_gcd; Pos_gcd_greatest; Pos_eqb_neq; Pos_leb_spec; Pos_leb; Pos_pow; Pos_eq_dec; }; +subgraph cluster_ConstructiveCauchyReals { label="ConstructiveCauchyReals"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ConstructiveCauchyReals_CRealLtProp_morph_Proper; ConstructiveCauchyReals_CReal_appart; ConstructiveCauchyReals_CRealLtEpsilon; ConstructiveCauchyReals_linear_order_T; ConstructiveCauchyReals_CReal_le_lt_trans; ConstructiveCauchyReals_CRealLt_lpo_dec; ConstructiveCauchyReals_CRealLtForget; ConstructiveCauchyReals_CRealLt_above_same; ConstructiveCauchyReals_CReal_plus_proper_l; ConstructiveCauchyReals_CReal_plus_0_l; ConstructiveCauchyReals_CReal_plus_assoc; ConstructiveCauchyReals_CRealLt_aboveSig; ConstructiveCauchyReals_CRealLt_aboveSig_; ConstructiveCauchyReals_CRealLt_above; ConstructiveCauchyReals_CReal_plus_lt_compat_l; ConstructiveCauchyReals_CRealEq_rel; ConstructiveCauchyReals_CReal_plus_opp_l; ConstructiveCauchyReals_CReal_plus_eq_reg_l; ConstructiveCauchyReals_CReal_plus_opp_r; ConstructiveCauchyReals_CReal_plus_morph; ConstructiveCauchyReals_CRealEq_rel_Transitive; ConstructiveCauchyReals_CReal_plus_morph_Proper; ConstructiveCauchyReals_CRealEq_rel_Reflexive; ConstructiveCauchyReals_CRealEq_rel_Symmetric; ConstructiveCauchyReals_CReal_opp_seq; ConstructiveCauchyReals_CReal_opp_cauchy; ConstructiveCauchyReals_CReal_opp_scale; ConstructiveCauchyReals_CReal_opp_bound; ConstructiveCauchyReals_CReal_plus_proper_r; ConstructiveCauchyReals_CRealEq_diff; ConstructiveCauchyReals_bound; ConstructiveCauchyReals_scale; ConstructiveCauchyReals_CReal_plus_seq; ConstructiveCauchyReals_CReal_plus_cauchy; ConstructiveCauchyReals_CReal_plus_scale; ConstructiveCauchyReals_CReal_plus_bound; ConstructiveCauchyReals_CReal_plus_lt_reg_l; ConstructiveCauchyReals_CReal_plus_lt_reg_r; ConstructiveCauchyReals_inject_Q_morph_T; ConstructiveCauchyReals_CReal_plus_comm; ConstructiveCauchyReals_opp_inject_Q; ConstructiveCauchyReals_CReal_plus_morph_T; ConstructiveCauchyReals_CReal_opp; ConstructiveCauchyReals_inject_Z; ConstructiveCauchyReals_CReal_minus; ConstructiveCauchyReals_cauchy; ConstructiveCauchyReals_CRealLt_dec; ConstructiveCauchyReals_CRealLe_refl; ConstructiveCauchyReals_CRealEq_refl; ConstructiveCauchyReals_CRealEq_trans; ConstructiveCauchyReals_CRealEq_sym; ConstructiveCauchyReals_CRealEq_relT; ConstructiveCauchyReals_CRealLt; ConstructiveCauchyReals_CRealLe; ConstructiveCauchyReals_CRealEq; ConstructiveCauchyReals_CRealLe_not_lt; ConstructiveCauchyReals_inject_Q_cauchy; ConstructiveCauchyReals_CRealLt_morph; ConstructiveCauchyReals_inject_Q_plus; ConstructiveCauchyReals_CRealLt_asym; ConstructiveCauchyReals_inject_Q; ConstructiveCauchyReals_CReal_red_seq; ConstructiveCauchyReals_CReal_plus; ConstructiveCauchyReals_seq; ConstructiveCauchyReals_mkCReal; ConstructiveCauchyReals_QBound; ConstructiveCauchyReals_QCauchySeq; ConstructiveCauchyReals_CReal; ConstructiveCauchyReals_CRealLtProp; }; +subgraph cluster_Init { label="Init"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Init_Nat { label="Nat"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Init_Nat_mul; Init_Nat_pred; Init_Nat_add; }; +Init_Unconvertible; }; +subgraph cluster_Qpower { label="Qpower"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Qpower_Qpower_0_r; Qpower_Qinv_power_positive; Qpower_Qinv_power; Qpower_Qpower_minus_pos; Qpower_Qpower_1_le_pos; Qpower_Qpower_1_le; Qpower_Qpower_le_compat_l; Qpower_Qpower_positive_0; Qpower_Qpower_minus_positive; Qpower_Qpower_plus_positive; Qpower_Qpower_plus; Qpower_Qpower_opp; Qpower_Qpower_decomp_positive; Qpower_Qpower_not_0_positive; Qpower_Qpower_pos_positive; Qpower_Qpower_0_le; Qpower_Qpower_not_0; Qpower_Qpower_0_lt; Qpower_Qpower_decomp_pos; Qpower_Qpower_minus; }; +subgraph cluster_ZifyInst { label="ZifyInst"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ZifyInst_Inj_Z_Z; ZifyInst_Inj_pos_Z; }; +subgraph cluster_Ring_polynom { label="Ring_polynom"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Ring_polynom_mkmultm1_ok; Ring_polynom_r_list_pow_rev; Ring_polynom_mkmult_rec_ok; Ring_polynom_mkmult1_ok; Ring_polynom_mkmult_c_pos_ok; Ring_polynom_mkadd_mult_ok; Ring_polynom_add_mult_dev_ok; Ring_polynom_add_pow_list_ok; Ring_polynom_mkmult_c_ok; Ring_polynom_mkadd_mult; Ring_polynom_mkmult1; Ring_polynom_mkmultm1; Ring_polynom_mkmult_c_pos; Ring_polynom_mkmult_rec; Ring_polynom_mkmult_c; Ring_polynom_add_pow_list; Ring_polynom_add_mult_dev; Ring_polynom_r_list_pow; Ring_polynom_mult_dev; Ring_polynom_Pphi_avoid; Ring_polynom_mult_dev_ok; Ring_polynom_local_mkpow_ok; Ring_polynom_Pphi_avoid_ok; Ring_polynom_Pphi_pow_ok; Ring_polynom_ring_rw_pow_correct; Ring_polynom_mkVmon_ok; Ring_polynom_mon_of_pol_ok; Ring_polynom_Mcphi_ok; Ring_polynom_zmon_pred_ok; Ring_polynom_mkZmon_ok; Ring_polynom_Mphi_ok; Ring_polynom_POneSubst_ok; Ring_polynom_PNSubst1_ok; Ring_polynom_PNSubst_ok; Ring_polynom_PSubstL1_ok; Ring_polynom_PSubstL_ok; Ring_polynom_Mphi; Ring_polynom_Ppow_pos_ok; Ring_polynom_Pphi1; Ring_polynom_PmulC_aux_ok; Ring_polynom_PmulI_ok; Ring_polynom_PmulC_ok; Ring_polynom_Pequiv_eq; Ring_polynom_mkPX_ext; Ring_polynom_mkPinj_ext; Ring_polynom_PX_ext; Ring_polynom_PsubC_ok; Ring_polynom_Psub_opp; Ring_polynom_Peq_spec; Ring_polynom_Pequiv; Ring_polynom_ceqb_spec; Ring_polynom_Pphi0; Ring_polynom_Pphi_ext; Ring_polynom_PaddX_ok; Ring_polynom_PaddC_ok; Ring_polynom_jump_add_; Ring_polynom_mkPX_ok; Ring_polynom_pow_pos_add; Ring_polynom_mkPinj_ok; Ring_polynom_Pol_ind; Ring_polynom_PEpow; Ring_polynom_PEopp; Ring_polynom_PEc; Ring_polynom_PEI; Ring_polynom_PEO; Ring_polynom_Padd_ok; Ring_polynom_norm_aux_PEopp; Ring_polynom_norm_aux_PEadd; Ring_polynom_get_PEopp; Ring_polynom_radd_ext_Proper; Ring_polynom_PExpr_ind; Ring_polynom_mkX_ok; Ring_polynom_rmul_ext_Proper; Ring_polynom_ropp_ext_Proper; Ring_polynom_rsub_ext_Proper; Ring_polynom_Psub_ok; Ring_polynom_Popp_ok; Ring_polynom_Pmul_ok; Ring_polynom_Ppow_N_ok; Ring_polynom_norm_aux_spec; Ring_polynom_MPcond; Ring_polynom_PNSubstL_ok; Ring_polynom_norm_subst_spec; Ring_polynom_interp_PElist_ok; Ring_polynom_norm_subst_ok; Ring_polynom_Peq_ok; Ring_polynom_Pphi; Ring_polynom_ring_correct; Ring_polynom_interp_PElist; Ring_polynom_PEmul; Ring_polynom_CFactor; Ring_polynom_MFactor; Ring_polynom_PNSubst1; Ring_polynom_POneSubst; Ring_polynom_PNSubst; Ring_polynom_PSubstL1; Ring_polynom_PSubstL; Ring_polynom_PaddX; Ring_polynom_PaddI; Ring_polynom_PmulC_aux; Ring_polynom_PmulI; Ring_polynom_PmulC; Ring_polynom_mkPinj; Ring_polynom_PsubX; Ring_polynom_PsubI; Ring_polynom_PsubC; Ring_polynom_PaddC; Ring_polynom_mkPX; Ring_polynom_mkXi; Ring_polynom_mkPinj_pred; Ring_polynom_mkX; Ring_polynom_P1; Ring_polynom_Ppow_pos; Ring_polynom_Ppow_N; Ring_polynom_mk_X; Ring_polynom_Psub; Ring_polynom_Popp; Ring_polynom_Pmul; Ring_polynom_Padd; Ring_polynom_norm_aux; Ring_polynom_PNSubstL; Ring_polynom_vmon; Ring_polynom_zmon_pred; Ring_polynom_zmon; Ring_polynom_mon0; Ring_polynom_mkZmon; Ring_polynom_mkVmon; Ring_polynom_Peq; Ring_polynom_P0; Ring_polynom_mon_of_pol; Ring_polynom_mkpow_ok; Ring_polynom_mkopp_pow_ok; Ring_polynom_mkopp_pow; Ring_polynom_mkpow; Ring_polynom_mkmult_pow_ok; Ring_polynom_mkmult_pow; Ring_polynom_Pphi_dev_ok; Ring_polynom_ring_rw_correct; Ring_polynom_PEsub; Ring_polynom_PEadd; Ring_polynom_PEX; Ring_polynom_PX; Ring_polynom_Pinj; Ring_polynom_Pc; Ring_polynom_PExpr; Ring_polynom_Pol; Ring_polynom_Mon; Ring_polynom_Pphi_dev; Ring_polynom_mk_monpol_list; Ring_polynom_norm_subst; Ring_polynom_PEeval; Ring_polynom_Pphi_pow; }; +subgraph cluster_Nat2Z { label="Nat2Z"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Nat2Z_inj_add; Nat2Z_is_nonneg; Nat2Z_inj_mul; Nat2Z_inj_succ; }; +subgraph cluster_Refl { label="Refl"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Refl_make_conj_cons; Refl_make_conj; Refl_make_impl_map; Refl_make_impl; Refl_make_conj_app; Refl_make_conj_rapp; Refl_make_conj_in; Refl_make_conj_impl; }; +subgraph cluster_Z { label="Z"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Z_Private_Tac { label="Private_Tac"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Z_Private_Tac_lt_trans; Z_Private_Tac_interp_ord; Z_Private_Tac_trans; Z_Private_Tac_not_gt_le; Z_Private_Tac_eq_sym; Z_Private_Tac_lt_irrefl; Z_Private_Tac_le_lt_trans; Z_Private_Tac_lt_eq; Z_Private_Tac_le_eq; Z_Private_Tac_eq_lt; Z_Private_Tac_eq_le; }; +subgraph cluster_Z_Private_BootStrap { label="Private_BootStrap"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Z_Private_BootStrap_mul_add_distr_pos; Z_Private_BootStrap_mul_opp_r; Z_Private_BootStrap_mul_0_r; Z_Private_BootStrap_mul_add_distr_r; Z_Private_BootStrap_mul_1_l; Z_Private_BootStrap_add_opp_diag_r; Z_Private_BootStrap_add_0_r; Z_Private_BootStrap_pos_sub_add; Z_Private_BootStrap_opp_add_distr; Z_Private_BootStrap_add_assoc_pos; Z_Private_BootStrap_opp_inj; Z_Private_BootStrap_add_comm; Z_Private_BootStrap_add_assoc; }; +subgraph cluster_Z_Private_NZDiv { label="Private_NZDiv"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Z_Private_NZDiv_div_mod_unique; }; +subgraph cluster_Z_Private_OrderTac { label="Private_OrderTac"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Z_Private_OrderTac_IsTotal { label="IsTotal"; fillcolor="#FFFF83"; labeljust=l; style=filled +Z_Private_OrderTac_IsTotal_lt_compat; Z_Private_OrderTac_IsTotal_lt_strorder; Z_Private_OrderTac_IsTotal_eq_equiv; Z_Private_OrderTac_IsTotal_lt_total; Z_Private_OrderTac_IsTotal_le_lteq; }; +subgraph cluster_Z_Private_OrderTac_Tac { label="Tac"; fillcolor="#FFFF83"; labeljust=l; style=filled +Z_Private_OrderTac_Tac_eq_trans; Z_Private_OrderTac_Tac_not_neq_eq; Z_Private_OrderTac_Tac_eq_sym; Z_Private_OrderTac_Tac_lt_eq; Z_Private_OrderTac_Tac_eq_lt; Z_Private_OrderTac_Tac_not_gt_le; Z_Private_OrderTac_Tac_lt_trans; Z_Private_OrderTac_Tac_interp_ord; Z_Private_OrderTac_Tac_trans; Z_Private_OrderTac_Tac_not_ge_lt; Z_Private_OrderTac_Tac_lt_irrefl; Z_Private_OrderTac_Tac_le_lt_trans; Z_Private_OrderTac_Tac_eq_le; Z_Private_OrderTac_Tac_neq_sym; Z_Private_OrderTac_Tac_le_neq_lt; Z_Private_OrderTac_Tac_neq_eq; Z_Private_OrderTac_Tac_le_eq; Z_Private_OrderTac_Tac_le_refl; Z_Private_OrderTac_Tac_eq_refl; Z_Private_OrderTac_Tac_eq_neq; Z_Private_OrderTac_Tac_le_antisym; }; +}; +Z_add_le_lt_mono; Z_quotrem_eq; Z_pow_pos; Z_eqb_eq; Z_pred_inj; Z_add_pred_l; Z_opp_0; Z_opp_succ; Z_add_pred_r; Z_opp_wd; Z_pred_inj_wd; Z_add_opp_r; Z_sub_succ_l; Z_sub_0_r; Z_sub_wd; Z_sub_diag; Z_mul_1_l; Z_pos_sub_discr; Z_pow; Z_quotrem; Z_mul_cancel_r; Z_mul_reg_r; Z_mul_le_mono_nonneg_r; Z_mul_le_mono_nonneg_l; Z_mul_lt_mono_nonneg; Z_mul_le_mono_nonneg; Z_lt_le_trans; Z_Rgt_wd; Z_gt_wf; Z_eq_le_incl; Z_strong_left_induction; Z_left_induction; Z_order_induction; Z_succ_le_mono; Z_add_le_mono_r; Z_add_le_mono_l; Z_add_le_mono; Z_nlt_ge; Z_le_lt_add_lt; Z_mul_lt_pred; Z_order_induction_0; Z_lt_succ_l; Z_lt_gt_cases; Z_mul_lt_mono_neg_l; Z_mul_cancel_l; Z_mul_le_mono_pos_l; Z_le_trans; Z_le_succ_r; Z_le_le_succ_r; Z_le_preorder; Z_lt_lt_succ_r; Z_Rlt_wd; Z_lt_wf; Z_strong_right_induction; Z_lt_exists_pred; Z_right_induction; Z_succ_lt_mono; Z_add_lt_mono_r; Z_add_lt_mono_l; Z_add_lt_mono; Z_lt_ind; Z_mul_lt_mono_pos_l; Z_mul_add_distr_r; Z_mul_assoc; Z_lt_compat; Z_lt_asymm; Z_lt_trans; Z_lt_strorder; Z_le_lteq; Z_sub_succ_r; Z_sub; Z_compare_sub; Z_lt_succ_diag_r; Z_lt_le_incl; Z_nlt_succ_diag_l; Z_neq_succ_diag_l; Z_nle_succ_diag_l; Z_lt_wd; Z_le_wd; Z_le_refl; Z_central_induction; Z_even; Z_le_succ_l; Z_lt_succ_r; Z_compare_le_iff; Z_lt_eq_cases; Z_le_gt_cases; Z_lt_trichotomy; Z_lt_total; Z_le_lt_trans; Z_mul_shuffle0; Z_mul_lt_mono_pos_r; Z_mul_le_mono_pos_r; Z_compare_refl; Z_lt_irrefl; Z_compare_lt_iff; Z_compare_antisym; Z_compare_spec; Z_compare_eq_iff; Z_eqb; Z_one_succ; Z_add_assoc; Z_peano_ind; Z_succ_pred; Z_add_succ_r; Z_add_cancel_l; Z_add_comm; Z_lt_sub_lt_add_r; Z_pos_sub_diag; Z_eq; Z_pred_wd; Z_pred_succ; Z_pred; Z_succ_inj; Z_succ_wd; Z_le_ngt; Z_le_min_l; Z_max_comm; Z_Proper_instance_0; Z_pos_sub_spec; Z_sub_lt_mono_r; Z_lt_add_lt_sub_r; Z_pos_sub_opp; Z_add_0_l; Z_add_succ_l; Z_succ_inj_wd; Z_add_wd; Z_add_0_r; Z_mul_pos_cancel_l; Z_mul_0_r; Z_mul_0_l; Z_add_cancel_r; Z_to_pos; Z_bi_induction; Z_succ; Z_mul_succ_r; Z_mul_succ_l; Z_mul_wd; Z_eq_equiv; Z_mul_comm; Z_mul_1_r; Z_min_r; Z_min_l; Z_of_nat; Z_min_spec; Z_min; Z_of_N; Z_mul_le_mono_nonpos_l; Z_mul_le_mono_nonpos_r; Z_mul_opp_opp; Z_mul_nonneg_nonpos; Z_eq_refl; Z_abs_opp; Z_abs_wd; Z_opp_nonpos_nonneg; Z_abs_neq; Z_add_nonpos_nonpos; Z_abs_eq; Z_abs_triangle; Z_abs_mul; Z_to_nat; Z_opp; Z_succ_double; Z_double; Z_pred_double; Z_pos_sub; Z_add; Z_lt; Z_abs; Z_mul; Z_add_neg_neg; Z_pow_1_r; Z_pow_twice_r; Z_lt_nge; Z_compare; Z_pow_0_r; Z_pow_succ_r; Z_pow_neg_r; Z_pow_wd; Z_le_ind; Z_leb; Z_geb_leb; Z_gtb_gt; Z_geb_le; Z_le_neq; Z_compare_nle_iff; Z_compare_nge_iff; Z_leb_spec0; Z_opp_le_mono; Z_div_eucl_0_r; Z_div_0_r; Z_eqb_spec; Z_lt_add_pos_l; Z_lt_add_pos_r; Z_le; Z_mul_div_le; Z_sub_le_mono_r; Z_add_simpl_r; Z_le_add_le_sub_r; Z_le_add_le_sub_l; Z_add_nonneg_nonneg; Z_gtb_spec; Z_le_sub_le_add_r; Z_div_wd; Z_sub_move_0_r; Z_div_unique_exact; Z_lt_le_pred; Z_le_ge_cases; Z_divide_opp_r; Z_divide_transitive; Z_gcd_divide_iff; Z_gcd_comm; Z_gcd_opp_l; Z_gtb_ltb; Z_sub_move_r; Z_divide_add_r; Z_max_r; Z_max_l; Z_divide_trans; Z_max_spec; Z_divide_wd; Z_mod_eq; Z_mod_mul; Z_mod_wd; Z_mod_divide; Z_divide_mul_r; Z_div_exact; Z_opp_inj; Z_opp_inj_wd; Z_pos_sub_gt; Z_pos_div_eucl_eq; Z_mul_opp_comm; Z_add_opp_diag_r; Z_mul_add_distr_l; Z_div_eucl_eq; Z_compare_gt_iff; Z_compare_ngt_iff; Z_ltb_spec0; Z_succ_double_spec; Z_ltb_spec; Z_pos_sub_lt; Z_pos_div_eucl_bound; Z_mod_neg_bound; Z_modulo; Z_div_mod; Z_mod_pos_bound; Z_div_mod_unique; Z_div_unique; Z_div_mul; Z_divide_div_mul_exact; Z_div; Z_max; Z_pos_div_eucl; Z_div_eucl; Z_sgn; Z_ggcd; Z_ggcd_gcd; Z_ggcd_correct_divisors; Z_two_succ; Z_lt_1_l; Z_lt_1_mul_pos; Z_lt_1_2; Z_lt_0_1; Z_eq_mul_1_nonneg; Z_lt_ge_cases; Z_mul_id_l; Z_eq_mul_1_nonneg_; Z_mul_opp_r; Z_sub_cancel_r; Z_add_move_l; Z_add_move_r; Z_sub_0_l; Z_add_move_0_r; Z_add_opp_diag_l; Z_mul_opp_l; Z_divide_Zpos; Z_divide_Zpos_Zneg_r; Z_divide_Zpos_Zneg_l; Z_gcd_greatest; Z_gcd_nonneg; Z_divide_antisym_nonneg; Z_gcd_divide_r; Z_gcd_divide_l; Z_gcd_unique; Z_divide_refl; Z_gcd_unique_alt; Z_divide_mul_l; Z_divide; Z_gcd_mul_diag_l; Z_add_move_0_l; Z_gcd; Z_eqb_neq; Z_gtb_lt; Z_gcd_opp_r; Z_opp_nonneg_nonpos; Z_leb_spec; Z_add_opp_l; Z_sub_opp_r; Z_opp_lt_mono; Z_sub_opp_l; Z_opp_pos_neg; Z_sub_1_r; Z_eq_decidable; Z_opp_pred; Z_opp_involutive; Z_opp_add_distr; Z_opp_sub_distr; Z_sub_sub_distr; Z_sub_simpl_r; Z_le_0_sub; Z_gtb; Z_geb; Z_gt_lt_iff; Z_lt_gt; Z_le_ge; Z_gt_lt; Z_gt; Z_add_sub_assoc; Z_lt_0_sub; Z_mul_lt_mono_neg_r; Z_mul_pos_neg; Z_mul_neg_pos; Z_mul_neg_neg; Z_eq_mul_0; Z_mul_nonneg_nonneg; Z_pow_nonneg; Z_pow_pos_nonneg; Z_to_N; Z_add_1_r; Z_pow_add_r; Z_mul_pos_pos; Z_mul_shuffle1; Z_lt_neq; Z_ge_le_iff; Z_ge_le; Z_ge; Z_eq_dec; Z_le_antisymm; Z_nle_gt; Z_ltb_lt; Z_leb_le; Z_ltb; }; +subgraph cluster_RingMicromega { label="RingMicromega"; fillcolor="#FFFFC3"; labeljust=l; style=filled +RingMicromega_micomega_sor_setoid_Symmetric; RingMicromega_micomega_sor_setoid_Transitive; RingMicromega_rplus_morph_Proper; RingMicromega_ropp_morph_Proper; RingMicromega_rtimes_morph_Proper; RingMicromega_SORrm; RingMicromega_Rops_wd; RingMicromega_micomega_sor_setoid_Reflexive; RingMicromega_rlt_morph_Proper; RingMicromega_eval_pol_opp; RingMicromega_rle_morph_Proper; RingMicromega_popp; RingMicromega_micomega_sor_setoid; RingMicromega_SORRing_ring_lemma1; RingMicromega_eq0_cnf; RingMicromega_NonStrict; RingMicromega_Strict; RingMicromega_NonEqual; RingMicromega_Equal; RingMicromega_psub; RingMicromega_norm; RingMicromega_SORaddon; RingMicromega_normalise; RingMicromega_eval_pol; RingMicromega_eval_op1; RingMicromega_cnf_of_list; RingMicromega_cnf_of_list_correct; RingMicromega_xnormalise_correct; RingMicromega_check_inconsistent; RingMicromega_normalise_sound; RingMicromega_xnormalise; RingMicromega_Op1; RingMicromega_cnf_normalise_correct; RingMicromega_cnf_negate_correct; RingMicromega_cnf_negate; RingMicromega_NFormula; RingMicromega_PolEnv; RingMicromega_cnf_normalise; RingMicromega_PolC; RingMicromega_eval_formula; RingMicromega_check_inconsistent_sound; RingMicromega_nformula_plus_nformula_correct; RingMicromega_eval_nformula; RingMicromega_nformula_plus_nformula; RingMicromega_Op2; RingMicromega_Build_Formula; RingMicromega_OpLt; RingMicromega_OpEq; RingMicromega_Formula; RingMicromega_eval_pol_add; RingMicromega_padd; RingMicromega_psubC; RingMicromega_PsubC_ok; RingMicromega_OpAdd; RingMicromega_OpAdd_sound; RingMicromega_mk_SOR_addon; RingMicromega_eval_nformula_dec; RingMicromega_OpMult_sound; RingMicromega_SORcleb_morph; RingMicromega_SORcneqb_morph; RingMicromega_cneqb_sound; RingMicromega_cleb_sound; RingMicromega_PsatzZ; RingMicromega_PsatzC; RingMicromega_PsatzAdd; RingMicromega_PsatzMulE; RingMicromega_PsatzMulC; RingMicromega_PsatzSquare; RingMicromega_PsatzIn; RingMicromega_PsatzLet; RingMicromega_Psatz_ind; RingMicromega_cltb_sound; RingMicromega_pexpr_times_nformula_correct; RingMicromega_nformula_times_nformula_correct; RingMicromega_eval_Psatz_Sound; RingMicromega_checker_nf_sound; RingMicromega_OpMult; RingMicromega_map_option; RingMicromega_nformula_times_nformula; RingMicromega_map_option2; RingMicromega_pexpr_times_nformula; RingMicromega_eval_Psatz; RingMicromega_Psatz; RingMicromega_check_normalised_formulas; RingMicromega_xnegate; RingMicromega_xnegate_correct; RingMicromega_SORpower; RingMicromega_OpGt; RingMicromega_OpGe; RingMicromega_OpLe; RingMicromega_OpNEq; RingMicromega_eval_op2; RingMicromega_eval_pol_sub; RingMicromega_eval_pexpr; RingMicromega_eval_pol_norm; RingMicromega_rminus_morph_Proper; RingMicromega_cneqb; RingMicromega_cltb; }; +subgraph cluster_ConstructiveRcomplete { label="ConstructiveRcomplete"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ConstructiveRcomplete_Qlt_trans_swap_hyp; ConstructiveRcomplete_CRealLtDisjunctEpsilon; ConstructiveRcomplete_Rfloor; }; +subgraph cluster_ZifyClasses { label="ZifyClasses"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ZifyClasses_mkinj; ZifyClasses_mkapp; ZifyClasses_rew_iff_rev; ZifyClasses_InjTyp; ZifyClasses_mkrel; ZifyClasses_inj; ZifyClasses_and_morph; ZifyClasses_mkapp2; ZifyClasses_rew_iff; }; +subgraph cluster_Qfield { label="Qfield"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Qfield_Qsrt; Qfield_Qsft; Qfield_Qpower_theory; Qfield_Qopp_opp; Qfield_Qfield_ring_lemma2; Qfield_Qfield_field_lemma2; Qfield_Qfield_ring_lemma1; Qfield_Qfield_lemma5; Qfield_Qfield_field_lemma1; }; +subgraph cluster_Decidable { label="Decidable"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Decidable_decidable; }; +subgraph cluster_OrdersTac { label="OrdersTac"; fillcolor="#FFFFC3"; labeljust=l; style=filled +OrdersTac_OLE; OrdersTac_ord; OrdersTac_trans_ord; OrdersTac_OLT; OrdersTac_OEQ; }; +subgraph cluster_NatDef { label="NatDef"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_NatDef_N { label="N"; fillcolor="#FFFFA3"; labeljust=l; style=filled +NatDef_N_compare; NatDef_N_succ_double; NatDef_N_double; NatDef_N_sub; NatDef_N_leb; NatDef_N_pos_div_eucl; }; +}; +subgraph cluster_SuccNat2Pos { label="SuccNat2Pos"; fillcolor="#FFFFC3"; labeljust=l; style=filled +SuccNat2Pos_id_succ; SuccNat2Pos_inv; }; +subgraph cluster_Qround { label="Qround"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Qround_Qfloor; Qround_Qfloor_le; Qround_Qlt_floor; }; +subgraph cluster_Qabs { label="Qabs"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Qabs_Qabs_triangle_reverse; Qabs_Qabs_gt; Qabs_Qabs_Qinv; Qabs_Qabs_pos; Qabs_Qabs_Qmult; Qabs_Qabs_nonneg; Qabs_Qabs_Qle_condition; Qabs_Qabs_opp; Qabs_Qle_Qabs; Qabs_Qabs_Qlt_condition; Qabs_Qabs_case_subproof1; Qabs_Qabs_case_subproof0; Qabs_Qabs_case_subproof; Qabs_Qabs_case; Qabs_Qabs_wd_Proper; Qabs_Qabs_triangle; Qabs_Qabs_wd; Qabs_Qabs; }; +subgraph cluster_EnvRing { label="EnvRing"; fillcolor="#FFFFC3"; labeljust=l; style=filled +EnvRing_rmul_ext_Proper; EnvRing_Pol_ind; EnvRing_radd_ext_Proper; EnvRing_Popp_ok; EnvRing_Pphi; EnvRing_PaddX; EnvRing_PaddI; EnvRing_PmulC_aux; EnvRing_PmulI; EnvRing_PmulC; EnvRing_mkXi; EnvRing_mkPinj_pred; EnvRing_mkX; EnvRing_Ppow_pos; EnvRing_P1; EnvRing_Ppow_N; EnvRing_mk_X; EnvRing_Pmul; EnvRing_Padd; EnvRing_norm_aux; EnvRing_Peq; EnvRing_Pc; EnvRing_mkPinj; EnvRing_PX; EnvRing_Pinj; EnvRing_PsubX; EnvRing_PsubI; EnvRing_PsubC; EnvRing_PaddC; EnvRing_mkPX; EnvRing_Popp; EnvRing_P0; EnvRing_Psub; EnvRing_Pol; EnvRing_PExpr; EnvRing_PEmul; EnvRing_PEsub; EnvRing_PEadd; EnvRing_PEX; EnvRing_PEc; EnvRing_Psquare_ok; EnvRing_Psquare; EnvRing_PaddX_ok; EnvRing_Ppow_pos_ok; EnvRing_Pphi1; EnvRing_PmulC_aux_ok; EnvRing_PmulI_ok; EnvRing_PmulC_ok; EnvRing_PEpow; EnvRing_PEopp; EnvRing_Pmul_ok; EnvRing_Ppow_N_ok; EnvRing_Padd_ok; EnvRing_norm_aux_PEopp; EnvRing_norm_aux_PEadd; EnvRing_get_PEopp; EnvRing_PExpr_ind; EnvRing_mkX_ok; EnvRing_norm_aux_spec; EnvRing_PEeval; EnvRing_Peq_ok; EnvRing_Peq_spec; EnvRing_ceqb_spec; EnvRing_Pphi0; EnvRing_env_morph; EnvRing_PsubX_ok; EnvRing_PsubC_ok; EnvRing_mkPinj_ok; EnvRing_ropp_ext_Proper; EnvRing_rsub_ext_Proper; EnvRing_Pjump_pred_double; EnvRing_Pjump_xO_tail; EnvRing_PaddC_ok; EnvRing_mkPX_ok; EnvRing_Pjump_add; EnvRing_pow_pos_add; EnvRing_Psub_ok; }; +subgraph cluster_IntDef { label="IntDef"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_IntDef_Z { label="Z"; fillcolor="#FFFFA3"; labeljust=l; style=filled +IntDef_Z_succ_double; IntDef_Z_double; IntDef_Z_pred_double; IntDef_Z_pos_sub; IntDef_Z_sub; IntDef_Z_opp; IntDef_Z_mul; IntDef_Z_add; }; +}; +subgraph cluster_PosExtra { label="PosExtra"; fillcolor="#FFFFC3"; labeljust=l; style=filled +PosExtra_Pos_pow_1_r; }; +subgraph cluster_Basics { label="Basics"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Basics_impl; Basics_flip; }; +subgraph cluster_RinvImpl { label="RinvImpl"; fillcolor="#FFFFC3"; labeljust=l; style=filled +RinvImpl_Rinv; }; +subgraph cluster_ConstructiveEpsilon { label="ConstructiveEpsilon"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ConstructiveEpsilon_rel_ls_ind; ConstructiveEpsilon_Rnext; ConstructiveEpsilon_Rstop; ConstructiveEpsilon_inv_before_witness; ConstructiveEpsilon_next; ConstructiveEpsilon_stop; ConstructiveEpsilon_before_witness; ConstructiveEpsilon_O_witness; ConstructiveEpsilon_linear_search_conform; ConstructiveEpsilon_rel_ls; ConstructiveEpsilon_linear_search_from_0_conform; ConstructiveEpsilon_rel_ls_post; ConstructiveEpsilon_constructive_indefinite_ground_description_nat; ConstructiveEpsilon_P__decidable; ConstructiveEpsilon_P_; ConstructiveEpsilon_constructive_indefinite_ground_description; }; +subgraph cluster_Nat { label="Nat"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Nat_Private_OrderTac { label="Private_OrderTac"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Nat_Private_OrderTac_IsTotal { label="IsTotal"; fillcolor="#FFFF83"; labeljust=l; style=filled +Nat_Private_OrderTac_IsTotal_le_lteq; Nat_Private_OrderTac_IsTotal_lt_strorder; Nat_Private_OrderTac_IsTotal_eq_equiv; Nat_Private_OrderTac_IsTotal_lt_compat; Nat_Private_OrderTac_IsTotal_lt_total; }; +subgraph cluster_Nat_Private_OrderTac_Tac { label="Tac"; fillcolor="#FFFF83"; labeljust=l; style=filled +Nat_Private_OrderTac_Tac_not_gt_le; Nat_Private_OrderTac_Tac_le_lt_trans; Nat_Private_OrderTac_Tac_not_ge_lt; Nat_Private_OrderTac_Tac_lt_trans; Nat_Private_OrderTac_Tac_interp_ord; Nat_Private_OrderTac_Tac_trans; Nat_Private_OrderTac_Tac_not_neq_eq; Nat_Private_OrderTac_Tac_eq_sym; Nat_Private_OrderTac_Tac_lt_irrefl; Nat_Private_OrderTac_Tac_lt_eq; Nat_Private_OrderTac_Tac_eq_lt; }; +}; +subgraph cluster_Nat_Private_NZPow { label="Private_NZPow"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Nat_Private_NZPow_pow_eq_0; Nat_Private_NZPow_pow_nonzero; }; +Nat_succ_pred; Nat_compare_antisym; Nat_compare_gt_iff; Nat_compare_succ; Nat_induction; Nat_case_analysis; Nat_lt_0_succ; Nat_pred_0; Nat_neq_succ_0; Nat_one_succ; Nat_two_succ; Nat_Rgt_wd; Nat_gt_wf; Nat_eq_le_incl; Nat_strong_left_induction; Nat_left_induction; Nat_order_induction; Nat_succ_le_mono; Nat_add_le_mono_r; Nat_add_le_mono_l; Nat_add_le_mono; Nat_nlt_ge; Nat_le_lt_add_lt; Nat_mul_lt_pred; Nat_order_induction_0; Nat_lt_succ_l; Nat_mul_lt_mono_neg_l; Nat_mul_lt_mono_neg_r; Nat_le_trans; Nat_le_succ_r; Nat_le_le_succ_r; Nat_le_preorder; Nat_Rlt_wd; Nat_lt_lt_succ_r; Nat_lt_wf; Nat_pow_succ_r_; Nat_strong_right_induction; Nat_lt_exists_pred; Nat_right_induction; Nat_succ_lt_mono; Nat_add_lt_mono_r; Nat_add_lt_mono_l; Nat_add_lt_mono; Nat_lt_ind; Nat_add_assoc; Nat_add_0_r; Nat_add_succ_r; Nat_add_0_l; Nat_add_succ_l; Nat_add_wd; Nat_add_cancel_l; Nat_add_comm; Nat_add_cancel_r; Nat_mul_succ_r; Nat_mul_succ_l; Nat_mul_comm; Nat_mul_lt_mono_pos_l; Nat_mul_lt_mono_pos_r; Nat_mul_pos_pos; Nat_mul_pos_neg; Nat_mul_0_r; Nat_mul_0_l; Nat_mul_neg_pos; Nat_mul_neg_neg; Nat_mul_wd; Nat_lt_neq; Nat_le_lteq; Nat_add; Nat_lt_asymm; Nat_lt_trans; Nat_lt_strorder; Nat_compare_refl; Nat_pred_wd; Nat_pred_succ; Nat_succ_inj; Nat_lt_succ_diag_r; Nat_lt_le_incl; Nat_nlt_succ_diag_l; Nat_neq_succ_diag_l; Nat_nle_succ_diag_l; Nat_succ_inj_wd; Nat_lt_irrefl; Nat_bi_induction; Nat_succ_wd; Nat_le_wd; Nat_le_refl; Nat_central_induction; Nat_le_succ_l; Nat_lt_succ_r; Nat_compare_lt_iff; Nat_compare_le_iff; Nat_compare_eq_iff; Nat_compare; Nat_lt_eq_cases; Nat_le_gt_cases; Nat_lt_trichotomy; Nat_lt_total; Nat_lt_wd; Nat_lt_compat; Nat_pow_0_r; Nat_pow_succ_r; Nat_mul; Nat_pow_wd; Nat_eq_mul_0; Nat_eq_equiv; Nat_lt_1_2; Nat_lt_0_1; Nat_le_ind; Nat_le_0_l; Nat_pow_nonzero; Nat_neq_0_lt_0; Nat_pred; Nat_succ_pred_pos; Nat_pow; }; +subgraph cluster_List { label="List"; fillcolor="#FFFFC3"; labeljust=l; style=filled +List_fold_right; List_rev_append; List_rev_; List_tl; List_hd; List_fold_left; List_nth_in_or_default; List_In; }; +subgraph cluster_QMicromega { label="QMicromega"; fillcolor="#FFFFC3"; labeljust=l; style=filled +QMicromega_Qeval_formula_; QMicromega_Qeval_formula_compat; QMicromega_QWeakChecker; QMicromega_QWeakChecker_sound; QMicromega_qunsat; QMicromega_qdeduce; QMicromega_Qnormalise; QMicromega_Qeval_formula; QMicromega_Qeval_nformula_dec; QMicromega_Qsor; QMicromega_QSORaddon; QMicromega_Qeval_nformula; QMicromega_Qnegate; QMicromega_QTautoChecker_sound; QMicromega_QWitness; QMicromega_QTautoChecker; QMicromega_Qlt_bool_iff; QMicromega_pop2_bop2; QMicromega_QNpower; QMicromega_Qlt_bool; QMicromega_Qeval_bop2; QMicromega_Qeval_op2; QMicromega_Qeval_expr_compat; QMicromega_Qeval_expr_; QMicromega_Qeval_op2_hold; QMicromega_Qeval_pop2; QMicromega_Qeval_expr; }; +subgraph cluster_PosDef { label="PosDef"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_PosDef_Pos { label="Pos"; fillcolor="#FFFFA3"; labeljust=l; style=filled +PosDef_Pos_pred_N; PosDef_Pos_iter; PosDef_Pos_eqb; PosDef_Pos_IsPos; PosDef_Pos_succ_double_mask; PosDef_Pos_double_mask; PosDef_Pos_double_pred_mask; PosDef_Pos_mask; PosDef_Pos_sub_mask; PosDef_Pos_IsNeg; PosDef_Pos_IsNul; PosDef_Pos_sub; PosDef_Pos_add_carry; PosDef_Pos_of_succ_nat; PosDef_Pos_iter_op; PosDef_Pos_to_nat; PosDef_Pos_pred_double; PosDef_Pos_succ; PosDef_Pos_add; PosDef_Pos_mul; PosDef_Pos_compare_cont; PosDef_Pos_compare; }; +}; +subgraph cluster_ZMicromega { label="ZMicromega"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ZMicromega_le_neg; ZMicromega_xnormalise_correct; ZMicromega_xnormalise; ZMicromega_pop2_bop2; ZMicromega_Zeval_op2_hold; ZMicromega_narrow_interval_lower_bound; ZMicromega_padd; ZMicromega_makeCuttingPlane_ns_sound; ZMicromega_Zdivide_ceiling; ZMicromega_eval_pol_add; ZMicromega_F; ZMicromega_max_var_acc; ZMicromega_agree_env_tail; ZMicromega_agree_env_jump; ZMicromega_agree_env_eval_nformula; ZMicromega_max_var; ZMicromega_agree_env_subset; ZMicromega_max_var_nformulae_mono_aux; ZMicromega_max_var_nformulae_mono_aux_; ZMicromega_Zgcd_minus; ZMicromega_Zdiv_PX; ZMicromega_Zdiv_Pinj; ZMicromega_Zdiv_Pc; ZMicromega_Zdivide_pol_Zdivide; ZMicromega_Zdivide_pol_sub; ZMicromega_Zdivide_pol_one; ZMicromega_Zdivide_pol; ZMicromega_Zdivide_pol_ind; ZMicromega_Zdiv_pol_correct; ZMicromega_Zgcd_pol_div; ZMicromega_ZgcdM; ZMicromega_ceiling; ZMicromega_makeCuttingPlane; ZMicromega_Zgcd_pol; ZMicromega_Zdiv_pol; ZMicromega_Zgcd_pol_correct_lt; ZMicromega_ExProof; ZMicromega_deprecated_EnumProof; ZMicromega_SplitProof; ZMicromega_ZArithProof_ind; ZMicromega_genCuttingPlaneNone; ZMicromega_agree_env; ZMicromega_eval_nformula_split; ZMicromega_Private_Pos_neq_lt; ZMicromega_eval_Psatz_sound; ZMicromega_eval_nformula_bound_var; ZMicromega_popp; ZMicromega_genCuttingPlane; ZMicromega_agree_env_eval_nformulae; ZMicromega_bound_var; ZMicromega_cutting_plane_sound; ZMicromega_nformula_of_cutting_plane; ZMicromega_eval_nformula_mk_eq_pos; ZMicromega_mk_eq_pos; ZMicromega_max_var_nformulae; ZMicromega_Private_Pos_neq_le_lt; ZMicromega_eval_Psatz; ZMicromega_lt_le_iff; ZMicromega_eq_cnf; ZMicromega_eval_pol_Pc; ZMicromega_ZNpower; ZMicromega_Zeval_bop2; ZMicromega_Zeval_op2; ZMicromega_Zeval_pop2; ZMicromega_Zeval_expr; ZMicromega_Zeval_expr_compat; ZMicromega_eval_expr; ZMicromega_Zeval_formula_; ZMicromega_normZ; ZMicromega_psub; ZMicromega_Zeval_formula_compat_; ZMicromega_eval_pol_norm; ZMicromega_le_0_iff; ZMicromega_eval_pol; ZMicromega_eval_pol_sub; ZMicromega_xnnormalise_correct; ZMicromega_xnegate_correct; ZMicromega_Zunsat_sound; ZMicromega_xnegate; ZMicromega_xnnormalise; ZMicromega_cnf_of_list; ZMicromega_cnf_of_list_correct; ZMicromega_negate_correct; ZMicromega_negate; ZMicromega_ZChecker_sound; ZMicromega_Zunsat; ZMicromega_Zdeduce; ZMicromega_ZChecker; ZMicromega_Zsor; ZMicromega_Zeval_formula_compat; ZMicromega_Zeval_nformula_dec; ZMicromega_eval_nformula; ZMicromega_normalise; ZMicromega_Zeval_formula; ZMicromega_normalise_correct; ZMicromega_ZSORaddon; ZMicromega_ZWitness; ZMicromega_CutProof; ZMicromega_RatProof; ZMicromega_DoneProof; ZMicromega_ZArithProof; ZMicromega_ZTautoChecker_sound; ZMicromega_ZTautoChecker; }; +subgraph cluster_CRelationClasses { label="CRelationClasses"; fillcolor="#FFFFC3"; labeljust=l; style=filled +CRelationClasses_subrelation; CRelationClasses_flip; CRelationClasses_Symmetric; CRelationClasses_crelation; CRelationClasses_Transitive; CRelationClasses_Reflexive; CRelationClasses_Build_Equivalence; CRelationClasses_Equivalence; CRelationClasses_Equivalence_Reflexive; CRelationClasses_symmetry; CRelationClasses_Equivalence_Symmetric; CRelationClasses_arrow; CRelationClasses_iffT; }; +subgraph cluster_Field_theory { label="Field_theory"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Field_theory_radd_ext; Field_theory_rmul_ext; Field_theory_radd_ext_Proper; Field_theory_rsub_ext_Proper; Field_theory_rmul_ext_Proper; Field_theory_ropp_ext_Proper; }; +subgraph cluster_Pos2Nat { label="Pos2Nat"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Pos2Nat_inj_add; Pos2Nat_inj_mul; Pos2Nat_id; Pos2Nat_inj; Pos2Nat_inj_succ; Pos2Nat_is_succ; Pos2Nat_inj_1; Pos2Nat_inj_compare; Pos2Nat_inj_le; Pos2Nat_is_pos; }; +subgraph cluster_Z2N { label="Z2N"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Z2N_id; }; +subgraph cluster_Tauto { label="Tauto"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Tauto_eval_clause; Tauto_eval_cnf_cons_iff; Tauto_cnf_tt; Tauto_clause; Tauto_cnf; Tauto_eval_cnf_ff; Tauto_cnf_ff; Tauto_rtyp; Tauto_hold; Tauto_eNOT; Tauto_eval_tt; Tauto_eval_bf; Tauto_tauto_checker_sound; Tauto_eval_cnf; Tauto_hold_eNOT; Tauto_isBool; Tauto_kind; Tauto_isProp; Tauto_A; Tauto_eKind; Tauto_BFormula; Tauto_hold_eIFF; Tauto_hold_eIFF_IMPL; Tauto_hold_eIMPL; Tauto_add_term_correct; Tauto_eval_opt_clause; Tauto_or_clause_correct; Tauto_or_clause_cnf_correct; Tauto_if_cnf_tt; Tauto_is_cnf_ff_cnf_ff; Tauto_is_cnf_tt_inv; Tauto_is_cnf_tt_cnf_ff; Tauto_is_cnf_ff_inv; Tauto_or_cnf_opt_cnf_ff; Tauto_and_cnf_opt_cnf_ff_r; Tauto_or_cnf_opt_cnf_ff_r; Tauto_and_cnf_opt_cnf_tt; Tauto_EQ; Tauto_IFF; Tauto_IMPL; Tauto_NOT; Tauto_OR; Tauto_AND; Tauto_X; Tauto_FF; Tauto_TT; Tauto_mk_iff_is_bool; Tauto_eval_cnf_and_opt; Tauto_is_bool_inv; Tauto_eval_cnf_app; Tauto_hold_eTT; Tauto_hold_eOR; Tauto_hold_eFF; Tauto_hold_eEQ; Tauto_or_cnf_correct; Tauto_xcnf_impl; Tauto_xcnf_iff; Tauto_hold_eAND; Tauto_GFormula_ind; Tauto_or_cnf_opt_correct; Tauto_add_term; Tauto_or_clause; Tauto_xor_clause_cnf; Tauto_or_clause_cnf; Tauto_or_cnf; Tauto_is_cnf_tt; Tauto_is_cnf_ff; Tauto_and_cnf; Tauto_and_cnf_opt; Tauto_or_cnf_opt; Tauto_mk_or; Tauto_is_bool; Tauto_TFormula; Tauto_mk_iff; Tauto_mk_and; Tauto_mk_impl; Tauto_xcnf; Tauto_cnf_checker; Tauto_xcnf_correct; Tauto_tauto_checker; Tauto_cnf_checker_sound; Tauto_GFormula; Tauto_eIMPL; Tauto_eIFF; Tauto_eAND; Tauto_eTT; Tauto_eOR; Tauto_eFF; Tauto_eval_f; Tauto_e_rtyp; Tauto_eval_cnf_tt; }; +subgraph cluster_Flocq_DOT_Calc_DOT_Div_WRAPPED { label="Flocq_DOT_Calc_DOT_Div_WRAPPED"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Flocq_DOT_Calc_DOT_Div_WRAPPED_Div { label="Div"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_core; Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv; Flocq_DOT_Calc_DOT_Div_WRAPPED_Div_Fdiv_correct; }; +}; +subgraph cluster_Pos2Z { label="Pos2Z"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Pos2Z_is_nonneg; Pos2Z_inj_mul; Pos2Z_pos_le_pos; Pos2Z_add_pos_neg; Pos2Z_neg_is_neg; Pos2Z_inj; Pos2Z_inj_pow_pos; Pos2Z_inj_pow; Pos2Z_pos_is_pos; Pos2Z_inj_succ; }; +subgraph cluster_ConstructiveCauchyRealsMult { label="ConstructiveCauchyRealsMult"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ConstructiveCauchyRealsMult_CReal_inv_pos_cm; ConstructiveCauchyRealsMult_CRealLowerBoundSpec; ConstructiveCauchyRealsMult_CRealLowerBound; ConstructiveCauchyRealsMult_CReal_inv_pos_scale; ConstructiveCauchyRealsMult_CReal_inv_pos_bound; ConstructiveCauchyRealsMult_CReal_inv_pos_seq; ConstructiveCauchyRealsMult_CReal_inv_pos_cauchy; ConstructiveCauchyRealsMult_CReal_neg_lt_pos_subproof; ConstructiveCauchyRealsMult_CReal_neg_lt_pos; ConstructiveCauchyRealsMult_CReal_inv_pos; ConstructiveCauchyRealsMult_CReal_inv; ConstructiveCauchyRealsMult_Weaken_Qle_QpowerRemSubExp; ConstructiveCauchyRealsMult_CReal_mult_assoc; ConstructiveCauchyRealsMult_CReal_mult_1_l; ConstructiveCauchyRealsMult_CReal_red_scale; ConstructiveCauchyRealsMult_Weaken_Qle_QpowerAddExp; ConstructiveCauchyRealsMult_Weaken_Qle_QpowerFac; ConstructiveCauchyRealsMult_CReal_mult_proper_0_l; ConstructiveCauchyRealsMult_CReal_opp_mult_distr_r; ConstructiveCauchyRealsMult_CReal_mult_plus_distr_l; ConstructiveCauchyRealsMult_CReal_mult_comm; ConstructiveCauchyRealsMult_CReal_mult_proper_l; ConstructiveCauchyRealsMult_CReal_isRingExt; ConstructiveCauchyRealsMult_CReal_opp_morph_Proper; ConstructiveCauchyRealsMult_CReal_mult_morph_Proper; ConstructiveCauchyRealsMult_CReal_isRing; ConstructiveCauchyRealsMult_CReal_mult_cauchy; ConstructiveCauchyRealsMult_CReal_mult_scale; ConstructiveCauchyRealsMult_CReal_mult_bound; ConstructiveCauchyRealsMult_CReal_mult_seq; ConstructiveCauchyRealsMult_CReal_mult; ConstructiveCauchyRealsMult_CRealArchimedean; ConstructiveCauchyRealsMult_CRealRing_ring_lemma2; }; +subgraph cluster_Qminmax { label="Qminmax"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Qminmax_Q { label="Q"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Qminmax_Q_Private_Tac { label="Private_Tac"; fillcolor="#FFFF83"; labeljust=l; style=filled +Qminmax_Q_Private_Tac_interp_ord; Qminmax_Q_Private_Tac_trans; Qminmax_Q_Private_Tac_not_gt_le; Qminmax_Q_Private_Tac_eq_sym; Qminmax_Q_Private_Tac_lt_irrefl; Qminmax_Q_Private_Tac_le_lt_trans; Qminmax_Q_Private_Tac_lt_eq; Qminmax_Q_Private_Tac_le_eq; Qminmax_Q_Private_Tac_eq_lt; Qminmax_Q_Private_Tac_eq_le; }; +subgraph cluster_Qminmax_Q_OT { label="OT"; fillcolor="#FFFF83"; labeljust=l; style=filled +Qminmax_Q_OT_lt_strorder; Qminmax_Q_OT_compare_spec; Qminmax_Q_OT_le_lteq; Qminmax_Q_OT_lt_total; Qminmax_Q_OT_eq_equiv; Qminmax_Q_OT_lt_compat; }; +Qminmax_Q_Proper_instance_0; }; +}; +subgraph cluster_Nnat { label="Nnat"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Nnat_N2Nat { label="N2Nat"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Nnat_N2Nat_inj_add; Nnat_N2Nat_id; Nnat_N2Nat_inj; Nnat_N2Nat_inj_mul; }; +subgraph cluster_Nnat_Nat2N { label="Nat2N"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Nnat_Nat2N_inj_add; Nnat_Nat2N_id; Nnat_Nat2N_inj_mul; }; +}; +subgraph cluster_PeanoNat { label="PeanoNat"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_PeanoNat_Nat { label="Nat"; fillcolor="#FFFFA3"; labeljust=l; style=filled +PeanoNat_Nat_mul_wd_obligation_1; PeanoNat_Nat_add_wd_obligation_1; PeanoNat_Nat_pow_wd_obligation_1; PeanoNat_Nat_pred_wd_obligation_1; PeanoNat_Nat_succ_wd_obligation_1; PeanoNat_Nat_lt_wd_obligation_1; }; +}; +subgraph cluster_ListDef { label="ListDef"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ListDef_map; ListDef_nth; }; +subgraph cluster_ZArithRing { label="ZArithRing"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ZArithRing_Private_proj1_eqb_eq; }; +subgraph cluster_VarMap { label="VarMap"; fillcolor="#FFFFC3"; labeljust=l; style=filled +VarMap_Branch; VarMap_Elt; VarMap_Empty; VarMap_t; VarMap_find; }; +subgraph cluster_HLevelsBase { label="HLevelsBase"; fillcolor="#FFFFC3"; labeljust=l; style=filled +HLevelsBase_IsHProp; HLevelsBase_and_hprop; }; +subgraph cluster_Bool { label="Bool"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Bool_diff_false_true; Bool_iff_reflect; Bool_andb_false_iff; Bool_negb_false_iff; Bool_not_true_iff_false; Bool_andb_true_iff; Bool_eqb_true_iff; Bool_orb_true_iff; Bool_orb_comm; Bool_eqb; Bool_negb_true_iff; }; +subgraph cluster_BinList { label="BinList"; fillcolor="#FFFFC3"; labeljust=l; style=filled +BinList_nth_jump; BinList_nth_pred_double; BinList_jump_tl; BinList_jump_succ; BinList_jump_add; BinList_jump_pred_double; BinList_jump; BinList_nth; }; +subgraph cluster_Z2Pos { label="Z2Pos"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Z2Pos_id; }; +subgraph cluster_Morphisms_Prop { label="Morphisms_Prop"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Morphisms_Prop_and_iff_morphism_obligation_1; Morphisms_Prop_and_iff_morphism; Morphisms_Prop_Acc_pt_morphism; Morphisms_Prop_all_iff_morphism_obligation_1; Morphisms_Prop_all_iff_morphism; Morphisms_Prop_not_iff_morphism_obligation_1; Morphisms_Prop_not_iff_morphism; Morphisms_Prop_or_iff_morphism_obligation_1; Morphisms_Prop_or_iff_morphism; Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1; Morphisms_Prop_iff_iff_iff_impl_morphism; Morphisms_Prop_ex_iff_morphism_obligation_1; Morphisms_Prop_ex_iff_morphism; }; +subgraph cluster_Env { label="Env"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Env_nth; Env_tail; Env_jump; Env_Env; Env_hd; Env_nth_spec; Env_nth_jump; Env_nth_pred_double; Env_jump_add; Env_jump_simpl; Env_jump_pred_double; }; +subgraph cluster_QArith_base { label="QArith_base"; fillcolor="#FFFFC3"; labeljust=l; style=filled +QArith_base_Qle_bool; QArith_base_Qmult_assoc; QArith_base_Qmult_plus_distr_l; QArith_base_Qplus_0_l; QArith_base_Qmult_1_l; QArith_base_Qmult_inv_r; QArith_base_Qmult_comm; QArith_base_Qeq_bool_iff; QArith_base_Qeq_bool_eq; QArith_base_Qmult_comp; QArith_base_Qdiv; QArith_base_Qopp_comp; QArith_base_Qplus_lt_le_compat; QArith_base_Qplus_opp_r; QArith_base_Qplus_0_r; QArith_base_Qplus_le_compat; QArith_base_Qplus_comm; QArith_base_Qle_comp; QArith_base_Qinv_plus_distr; QArith_base_Qplus_assoc; QArith_base_Qplus_le_r; QArith_base_Qplus_le_l; QArith_base_Qle_refl; QArith_base_Qcompare_comp; QArith_base_Qlt_compat; QArith_base_Qeq_refl; QArith_base_Qeq_sym; QArith_base_Qeq_trans; QArith_base_Q_Setoid; QArith_base_Qle_lt_trans; QArith_base_Qmult_div_r; QArith_base_Qlt_irrefl; QArith_base_Qle_shift_div_l; QArith_base_Qlt_trans; QArith_base_Qcompare_spec; QArith_base_Qcompare; QArith_base_Qlt_alt; QArith_base_Qle_alt; QArith_base_Qeq_alt; QArith_base_Qle_lteq; QArith_base_Qlt_minus_iff; QArith_base_Qle_not_lt; QArith_base_Qmult_le_compat_nonneg; QArith_base_inject_Z; QArith_base_Qmult_lt_compat_nonneg; QArith_base_Qeq_bool; QArith_base_Qopp_le_compat; QArith_base_Qopp_lt_compat; QArith_base_Qarchimedean; QArith_base_Qeq; QArith_base_Qmult_lt_r; QArith_base_Qmult_lt_l; QArith_base_Qlt_shift_div_r; QArith_base_Qlt_le_weak; QArith_base_Qinv_lt_contravar; QArith_base_Qplus_lt_l; QArith_base_Qplus_comp; QArith_base_Qminus_comp; QArith_base_Qinv_minus_distr; QArith_base_Qlt_le_dec; QArith_base_Qpower_comp; QArith_base_Qinv_pos; QArith_base_Qmult_frac_l; QArith_base_Qmult_le_compat_r; QArith_base_Qmult_le_r; QArith_base_Qmult_le_1_compat; QArith_base_Qmult_le_l; QArith_base_Qlt_le_trans; QArith_base_Qle_minus_iff; QArith_base_Qinv_involutive; QArith_base_Qeq_eq_bool; QArith_base_Qpower_positive_comp; QArith_base_Qeq_dec; QArith_base_Qdiv_comp; QArith_base_Qle; QArith_base_Qinv_comp; QArith_base_Qinv_mult_distr; QArith_base_Qplus; QArith_base_Qopp; QArith_base_Qminus; QArith_base_Qnum; QArith_base_Qden; QArith_base_Qmult; QArith_base_Qpower_positive; QArith_base_Qinv; QArith_base_Qmake; QArith_base_Qpower; QArith_base_Qlt; QArith_base_Q; QArith_base_Qmult_1_r; QArith_base_Qdiv_mult_l; QArith_base_Qlt_not_le; QArith_base_Qmult_lt_0_le_reg_r; QArith_base_Qinv_lt_0_compat; QArith_base_Qmult_integral; QArith_base_Qmult_0_r; QArith_base_Qmult_le_0_compat; QArith_base_Qinv_le_0_compat; QArith_base_Qnot_eq_sym; QArith_base_Qlt_leneq; QArith_base_Qlt_shift_div_l; QArith_base_Qle_bool_imp_le; QArith_base_Qeq_bool_neq; QArith_base_Qnot_le_lt; QArith_base_Qle_antisym; QArith_base_Q_dec; QArith_base_Qlt_not_eq; QArith_base_Qle_trans; QArith_base_Qmult_lt_compat_r; QArith_base_Qmult_0_l; QArith_base_Qle_bool_iff; }; +subgraph cluster_Eqdep_dec { label="Eqdep_dec"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Eqdep_dec_trans_sym_eq; Eqdep_dec_nu_left_inv_on; Eqdep_dec_nu_constant; Eqdep_dec_eq_proofs_unicity_on; }; +subgraph cluster_FunctionalExtensionality { label="FunctionalExtensionality"; fillcolor="#FFFFC3"; labeljust=l; style=filled +FunctionalExtensionality_functional_extensionality_dep; FunctionalExtensionality_functional_extensionality; }; +subgraph cluster_Setoid { label="Setoid"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Setoid_Build_Setoid_Theory; Setoid_Setoid_Theory; Setoid_Seq_refl; Setoid_Seq_trans; Setoid_Seq_sym; }; +subgraph cluster_ClassicalDedekindReals { label="ClassicalDedekindReals"; fillcolor="#FFFFC3"; labeljust=l; style=filled +ClassicalDedekindReals_CReal_of_DReal_seq_bound; ClassicalDedekindReals_sig_forall_dec; ClassicalDedekindReals_DRealAbstrFalse__; ClassicalDedekindReals_DRealAbstrFalse; ClassicalDedekindReals_DRealQuot2; ClassicalDedekindReals_lowerUpper; ClassicalDedekindReals_DRealOpen; ClassicalDedekindReals_isLowerCut_hprop; ClassicalDedekindReals_Rle_antisym; ClassicalDedekindReals_Rle; ClassicalDedekindReals_DRealReprQup; ClassicalDedekindReals_DRealReprQ; ClassicalDedekindReals_DRealQuot1; ClassicalDedekindReals_DRealQlim_rec; ClassicalDedekindReals_lowerCutBelow; ClassicalDedekindReals_lowerCutAbove; ClassicalDedekindReals_Qpower_2_neg_le_one; ClassicalDedekindReals_DRealAbstr_aux; ClassicalDedekindReals_DRealAbstr; ClassicalDedekindReals_Qpower_2_neg_eq_natpow_inv; ClassicalDedekindReals_UpperAboveLower; ClassicalDedekindReals_Qpower_2_invneg_le_pow; ClassicalDedekindReals_CReal_of_DReal_seq_max_prec_1; ClassicalDedekindReals_DRealQlim; ClassicalDedekindReals_DRealQlimExp2; ClassicalDedekindReals_CReal_of_DReal_seq; ClassicalDedekindReals_CReal_of_DReal_scale; ClassicalDedekindReals_CReal_of_DReal_bound; ClassicalDedekindReals_CReal_of_DReal_cauchy; ClassicalDedekindReals_isLowerCut; ClassicalDedekindReals_DReal; ClassicalDedekindReals_DRealRepr; }; +subgraph cluster_HLevels { label="HLevels"; fillcolor="#FFFFC3"; labeljust=l; style=filled +HLevels_not_hprop; HLevels_impl_hprop; HLevels_forall_hprop; }; +subgraph cluster_OrderedRing { label="OrderedRing"; fillcolor="#FFFFC3"; labeljust=l; style=filled +OrderedRing_Rlt_le_trans; OrderedRing_Rlt_neq; OrderedRing_SORle_antisymm; OrderedRing_Rplus_le_mono_r; OrderedRing_rtimes_morph_Proper; OrderedRing_sor_setoid_Symmetric; OrderedRing_ropp_morph_Proper; OrderedRing_SORle_wd; OrderedRing_rle_morph_Proper; OrderedRing_SORplus_le_mono_l; OrderedRing_SORlt_le_neq; OrderedRing_sor_setoid_Transitive; OrderedRing_rplus_morph_Proper; OrderedRing_Rplus_cancel_l; OrderedRing_Rlt_le_neq; OrderedRing_Rplus_le_mono_l; OrderedRing_Rplus_lt_mono_l; OrderedRing_Rplus_comm; OrderedRing_Rplus_lt_mono_r; OrderedRing_sor_setoid; OrderedRing_rlt_morph_Proper; OrderedRing_SOR_ring_lemma1; OrderedRing_sor_setoid_Reflexive; OrderedRing_SORplus_wd; OrderedRing_SORopp_wd; OrderedRing_SORtimes_wd; OrderedRing_SORrt; OrderedRing_SORlt_wd; OrderedRing_SORsetoid; OrderedRing_Rlt_lt_minus; OrderedRing_Rle_le_minus; OrderedRing_Rlt_nge; OrderedRing_Rle_ngt; OrderedRing_SOR; OrderedRing_Rplus_lt_mono; OrderedRing_Rplus_le_lt_mono; OrderedRing_Rplus_le_mono; OrderedRing_Rplus_lt_le_mono; OrderedRing_Rplus_pos_nonneg; OrderedRing_Rplus_nonneg_nonneg; OrderedRing_Rplus_0_r; OrderedRing_Rplus_nonneg_pos; OrderedRing_Rplus_pos_pos; OrderedRing_mk_SOR_theory; OrderedRing_Rtimes_pos_neg; OrderedRing_Rtimes_comm; OrderedRing_Rtimes_nonneg_nonneg; OrderedRing_Rtimes_neq_0; OrderedRing_Rtimes_0_r; OrderedRing_Ropp_lt_mono; OrderedRing_Ropp_pos_neg; OrderedRing_SORtimes_pos_pos; OrderedRing_Rtimes_pos_pos; OrderedRing_Rtimes_0_l; OrderedRing_Rtimes_neg_neg; OrderedRing_Rtimes_square_nonneg; OrderedRing_Req_dne; OrderedRing_rminus_morph; OrderedRing_rminus_morph_Proper; OrderedRing_Rplus_0_l; OrderedRing_Rminus_eq_0; OrderedRing_Rle_lt_trans; OrderedRing_SORle_trans; OrderedRing_Rle_trans; OrderedRing_Rle_antisymm; OrderedRing_Rlt_trans; OrderedRing_SORlt_trichotomy; OrderedRing_Rneq_symm; OrderedRing_SORle_refl; OrderedRing_Rle_refl; OrderedRing_Req_em; OrderedRing_Rle_lt_eq; OrderedRing_Rlt_trichotomy; OrderedRing_Rle_gt_cases; }; +subgraph cluster_SetoidTactics { label="SetoidTactics"; fillcolor="#FFFFC3"; labeljust=l; style=filled +SetoidTactics_Build_DefaultRelation; SetoidTactics_DefaultRelation; SetoidTactics_equivalence_default; SetoidTactics_default_relation; }; +subgraph cluster_Z2Nat { label="Z2Nat"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Z2Nat_id; }; +subgraph cluster_SpecFloat { label="SpecFloat"; fillcolor="#FFFFC3"; labeljust=l; style=filled +SpecFloat_loc_Inexact; SpecFloat_loc_Exact; SpecFloat_location; }; +subgraph cluster_QOrderedType { label="QOrderedType"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_QOrderedType_Q_as_OT { label="Q_as_OT"; fillcolor="#FFFFA3"; labeljust=l; style=filled +QOrderedType_Q_as_OT_lt_compat; QOrderedType_Q_as_OT_eq_equiv; QOrderedType_Q_as_OT_lt_strorder; QOrderedType_Q_as_OT_compare_spec; QOrderedType_Q_as_OT_le_lteq; }; +}; +subgraph cluster_N { label="N"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_N_Private_OrderTac { label="Private_OrderTac"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_N_Private_OrderTac_IsTotal { label="IsTotal"; fillcolor="#FFFF83"; labeljust=l; style=filled +N_Private_OrderTac_IsTotal_lt_total; N_Private_OrderTac_IsTotal_le_lteq; N_Private_OrderTac_IsTotal_eq_equiv; N_Private_OrderTac_IsTotal_lt_compat; N_Private_OrderTac_IsTotal_lt_strorder; }; +subgraph cluster_N_Private_OrderTac_Tac { label="Tac"; fillcolor="#FFFF83"; labeljust=l; style=filled +N_Private_OrderTac_Tac_lt_eq; N_Private_OrderTac_Tac_not_ge_lt; N_Private_OrderTac_Tac_interp_ord; N_Private_OrderTac_Tac_trans; N_Private_OrderTac_Tac_lt_trans; N_Private_OrderTac_Tac_not_gt_le; N_Private_OrderTac_Tac_lt_irrefl; N_Private_OrderTac_Tac_le_lt_trans; }; +}; +N_lt_succ_l; N_lt_ind; N_lt_ind_rel; N_case_analysis; N_add_pred_l; N_add_pred_r; N_sub_gt; N_pred_0; N_eq_le_incl; N_neq_succ_0; N_Rlt_wd; N_lt_lt_succ_r; N_lt_wf; N_le_trans; N_le_gt_cases; N_lt_trichotomy; N_lt_total; N_lt_compat; N_le_lteq; N_neq_succ_diag_l; N_nle_succ_diag_l; N_le_succ_l; N_nlt_succ_diag_l; N_lt_le_incl; N_lt_asymm; N_compare_eq_iff; N_compare_refl; N_lt_irrefl; N_lt_trans; N_lt_strorder; N_le_succ_r; N_le_le_succ_r; N_le_preorder; N_lt_succ_r; N_le_wd; N_central_induction; N_lt_exists_pred; N_strong_right_induction; N_lt_wd; N_lt_eq_cases; N_lt_succ_diag_r; N_right_induction; N_le_0_l; N_sub_succ_r; N_sub_0_r; N_sub_succ; N_induction; N_sub_diag; N_le_refl; N_add_sub; N_sub_wd; N_add_sub_assoc; N_peano_rect; N_pred; N_pred_wd; N_pred_succ; N_succ_inj; N_eq; N_succ_wd; N_add_0_r; N_add_0_l; N_add_succ_r; N_add_succ_l; N_succ_inj_wd; N_eq_equiv; N_add_wd; N_succ; N_bi_induction; N_leb_le; N_compare_le_iff; N_compare_antisym; N_compare_nle_iff; N_compare; N_compare_lt_iff; N_compare_nge_iff; N_leb_spec0; N_succ_double_mul; N_succ_double_add; N_leb_spec; N_succ_double; N_double; N_add_comm; N_sub_add; N_double_mul; N_double_add; N_sub; N_leb; N_add_assoc; N_lt; N_le; N_pos_div_eucl_spec; N_pos_div_eucl; N_add; N_to_nat; N_of_nat; N_mul; N_eqb_spec; N_eqb_eq; N_add_cancel_l; N_mul_succ_r; N_mul_succ_l; N_mul_wd; N_mul_0_r; N_mul_0_l; N_add_cancel_r; N_div_eucl_spec; N_mul_comm; N_div_eucl; N_eqb; }; +subgraph cluster_Datatypes { label="Datatypes"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Datatypes_id; }; +subgraph cluster_Qreduction { label="Qreduction"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Qreduction_Qred; Qreduction_Qred_correct; }; +subgraph cluster_CMorphisms { label="CMorphisms"; fillcolor="#FFFFC3"; labeljust=l; style=filled +CMorphisms_iffT_flip_arrow_subrelation; CMorphisms_Proper; CMorphisms_ProperProxy; CMorphisms_respectful; CMorphisms_Reflexive_partial_app_morphism; CMorphisms_subrelation_refl; CMorphisms_iffT_arrow_subrelation; CMorphisms_subrelation_proper; CMorphisms_subrelation_respectful; CMorphisms_reflexive_proper_proxy; }; +} /* END */ diff --git a/tests/NestedModules.dpd.oracle b/tests/NestedModules.dpd.oracle new file mode 100644 index 000000000..36d71c6b9 --- /dev/null +++ b/tests/NestedModules.dpd.oracle @@ -0,0 +1,46180 @@ +N: 4838 "AF_1_neq_0" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4831 "AF_AR" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4940 "AFdiv_def" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4832 "AFinv_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3564 "ARadd_0_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3559 "ARadd_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3551 "ARadd_assoc" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3560 "ARadd_assoc1" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3561 "ARadd_assoc2" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3532 "ARadd_comm" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3562 "ARdistr_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3604 "ARdistr_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4072 "ARgen_phiPOS_Psucc" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4070 "ARgen_phiPOS_add" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4068 "ARgen_phiPOS_mult" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3571 "ARmul_0_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3605 "ARmul_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3584 "ARmul_1_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3606 "ARmul_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3558 "ARmul_assoc" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3612 "ARmul_assoc1" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3601 "ARmul_assoc2" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3600 "ARmul_comm" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3599 "ARopp_add" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3598 "ARopp_mul_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4060 "ARopp_mul_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4836 "ARopp_zero" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3536 "ARsub_def" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3588 "ARsub_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4890 "ARth_SRth" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3012 "Acc_inv" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3004 "Acc_pt_morphism" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 3015 "Acc_rect" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3874 "BFormula" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3842 "Build_Setoid_Theory" [opaque=no, body=yes, kind=cnst, prop=yes, path="Setoid", ]; +N: 3427 "CFactor" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 5139 "CRealArchimedean" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5093 "CRealEq" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5159 "CRealEq_diff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5102 "CRealEq_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5210 "CRealEq_rel" [opaque=no, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5097 "CRealEq_relT" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5190 "CRealEq_rel_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5188 "CRealEq_rel_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5193 "CRealEq_rel_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5100 "CRealEq_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5101 "CRealEq_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5094 "CRealLe" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5089 "CRealLe_not_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5109 "CRealLe_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5352 "CRealLowerBound" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5353 "CRealLowerBoundSpec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5095 "CRealLt" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5361 "CRealLtDisjunctEpsilon" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveRcomplete", ]; +N: 5318 "CRealLtEpsilon" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5248 "CRealLtForget" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 2728 "CRealLtProp" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5360 "CRealLtProp_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5233 "CRealLt_above" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5235 "CRealLt_aboveSig" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5234 "CRealLt_aboveSig'" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5243 "CRealLt_above_same" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5073 "CRealLt_asym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5110 "CRealLt_dec" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5250 "CRealLt_lpo_dec" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5076 "CRealLt_morph" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5133 "CRealRing_ring_lemma2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5344 "CReal_appart" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5342 "CReal_inv" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5345 "CReal_inv_pos" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5350 "CReal_inv_pos_bound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5348 "CReal_inv_pos_cauchy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5354 "CReal_inv_pos_cm" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5351 "CReal_inv_pos_scale" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5349 "CReal_inv_pos_seq" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5189 "CReal_isRing" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5203 "CReal_isRingExt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5260 "CReal_le_lt_trans" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5134 "CReal_minus" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5142 "CReal_mult" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5239 "CReal_mult_1_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5241 "CReal_mult_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5162 "CReal_mult_bound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5164 "CReal_mult_cauchy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5208 "CReal_mult_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5192 "CReal_mult_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5211 "CReal_mult_plus_distr_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5213 "CReal_mult_proper_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5207 "CReal_mult_proper_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5163 "CReal_mult_scale" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5161 "CReal_mult_seq" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5346 "CReal_neg_lt_pos" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyRealsMult", ]; +N: 5347 "CReal_neg_lt_pos_subproof" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 2775 "CReal_of_DReal_bound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 2774 "CReal_of_DReal_cauchy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 2776 "CReal_of_DReal_scale" [opaque=no, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 2777 "CReal_of_DReal_seq" [opaque=no, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 3876 "CReal_of_DReal_seq_bound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 5007 "CReal_of_DReal_seq_max_prec_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 5138 "CReal_opp" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5182 "CReal_opp_bound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5184 "CReal_opp_cauchy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5194 "CReal_opp_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5212 "CReal_opp_mult_distr_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5183 "CReal_opp_scale" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5185 "CReal_opp_seq" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5062 "CReal_plus" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5238 "CReal_plus_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5237 "CReal_plus_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5148 "CReal_plus_bound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5151 "CReal_plus_cauchy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5143 "CReal_plus_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5206 "CReal_plus_eq_reg_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5232 "CReal_plus_lt_compat_l" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5147 "CReal_plus_lt_reg_l" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5145 "CReal_plus_lt_reg_r" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5204 "CReal_plus_morph" [opaque=no, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5191 "CReal_plus_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5140 "CReal_plus_morph_T" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5209 "CReal_plus_opp_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5205 "CReal_plus_opp_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5240 "CReal_plus_proper_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5173 "CReal_plus_proper_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5149 "CReal_plus_scale" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5154 "CReal_plus_seq" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5230 "CReal_red_scale" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5067 "CReal_red_seq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 2722 "CompOpp" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3209 "CompOpp_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3214 "CompOpp_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3213 "CompOpp_involutive" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4708 "CompSpec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4706 "CompSpec2Type" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4709 "CompSpecT" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4710 "CompareSpec2Type" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 2732 "DReal" [opaque=no, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 5064 "DRealAbstr" [opaque=no, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 5364 "DRealAbstrFalse" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 5368 "DRealAbstrFalse''" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 5066 "DRealAbstr_aux" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 5277 "DRealOpen" [opaque=yes, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 2791 "DRealQlim" [opaque=yes, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 2781 "DRealQlimExp2" [opaque=yes, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 3061 "DRealQlim_rec" [opaque=yes, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 5259 "DRealQuot1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 5363 "DRealQuot2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 2731 "DRealRepr" [opaque=no, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 5261 "DRealReprQ" [opaque=yes, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 5262 "DRealReprQup" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 3995 "Env" [opaque=no, body=yes, kind=cnst, prop=no, path="Env", ]; +N: 3498 "Eq_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3506 "Eqsth" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2832 "Equivalence_PER" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 5092 "Equivalence_Reflexive" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 2839 "Equivalence_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 5086 "Equivalence_Symmetric" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 2855 "Equivalence_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 2854 "Equivalence_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 4704 "F" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4825 "F2AF" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 2700 "F2R" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4799 "FEeval" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4951 "FExpr_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4827 "F_1_neq_0" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3852 "F_R" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 2793 "False_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3788 "False_rec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4806 "Fapp" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4849 "Fcons0" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4841 "Fcons1" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4800 "Fcons2" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 2699 "Fdiv" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5382 "Fdiv" [opaque=no, body=yes, kind=cnst, prop=no, path="Flocq_DOT_Calc_DOT_Div_WRAPPED.Div", ]; +N: 5375 "Fdiv_core" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5383 "Fdiv_core" [opaque=no, body=yes, kind=cnst, prop=no, path="Flocq_DOT_Calc_DOT_Div_WRAPPED.Div", ]; +N: 2694 "Fdiv_correct" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 2698 "Fdiv_correct" [opaque=yes, body=no, kind=cnst, prop=yes, path="Flocq_DOT_Calc_DOT_Div_WRAPPED.Div", ]; +N: 4828 "Fdiv_def" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 5371 "Fexp" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4939 "Field_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5244 "Field_rw_pow_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4826 "Finv_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4795 "Fnorm" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4944 "Fnorm_FEeval_PEeval" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4941 "Fnorm_crossproduct" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5372 "Fnum" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4271 "GFormula_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4785 "ID" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3501 "IDmorph" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3083 "IDphi" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5384 "IPR" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5385 "IPR_2" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 2696 "IZR" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4211 "In" [opaque=no, body=yes, kind=cnst, prop=no, path="List", ]; +N: 5283 "Inj_Z_Z" [opaque=no, body=yes, kind=cnst, prop=no, path="ZifyInst", ]; +N: 4364 "Inj_pos_Z" [opaque=no, body=yes, kind=cnst, prop=no, path="ZifyInst", ]; +N: 2937 "Irreflexive" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 5273 "IsHProp" [opaque=no, body=yes, kind=cnst, prop=no, path="HLevelsBase", ]; +N: 3426 "MFactor" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3520 "MPcond" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3626 "Mcphi_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3613 "Mphi" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3622 "Mphi_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3925 "NFormula" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4843 "NPEadd" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4863 "NPEadd_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4864 "NPEequiv" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4869 "NPEequiv_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4875 "NPEeval_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4844 "NPEmul" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4865 "NPEmul_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4845 "NPEopp" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4866 "NPEopp_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4846 "NPEpow" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4867 "NPEpow_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4847 "NPEsub" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4868 "NPEsub_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4883 "Nopp" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4884 "Nsub" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4991 "NtoZ" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4892 "Ntriv_div_th" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3450 "O_S" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5328 "O_witness" [opaque=no, body=yes, kind=cnst, prop=yes, path="ConstructiveEpsilon", ]; +N: 4354 "OpAdd" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4353 "OpAdd_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4208 "OpMult" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4243 "OpMult_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 5321 "P'" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveEpsilon", ]; +N: 5322 "P'_decidable" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveEpsilon", ]; +N: 3966 "P0" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3270 "P0" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3983 "P1" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3406 "P1" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4796 "PCond" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4945 "PCond_app" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4859 "PCond_cons" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2899 "PER_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 2900 "PER_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 2825 "PER_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2932 "PER_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 4986 "PE_1_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4976 "PE_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4862 "PEadd_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4142 "PEeval" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3069 "PEeval" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4870 "PEmul_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4871 "PEopp_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4980 "PEpow_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4981 "PEpow_1_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4990 "PEpow_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4988 "PEpow_add_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4872 "PEpow_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4978 "PEpow_mul_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4979 "PEpow_mul_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4857 "PEpow_nz" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4842 "PEsimp" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4839 "PEsimp_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4861 "PEsub_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4995 "PExpr_eq" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4998 "PExpr_eq_semi_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4997 "PExpr_eq_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4148 "PExpr_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3535 "PExpr_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4853 "PFcons0_fcons_inv" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4840 "PFcons1_fcons_inv" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4833 "PFcons2_fcons_inv" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3423 "PNSubst" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3425 "PNSubst1" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3620 "PNSubst1_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3397 "PNSubstL" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3519 "PNSubstL_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3619 "PNSubst_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3424 "POneSubst" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3621 "POneSubst_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3421 "PSubstL" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3422 "PSubstL1" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3618 "PSubstL1_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3616 "PSubstL_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3592 "PX_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3979 "Padd" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3399 "Padd" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3969 "PaddC" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3411 "PaddC" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4126 "PaddC_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3556 "PaddC_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3991 "PaddI" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3419 "PaddI" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3992 "PaddX" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3420 "PaddX" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4162 "PaddX_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3557 "PaddX_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4152 "Padd_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3542 "Padd_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4942 "Pcond_Fnorm" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4824 "Pcond_simpl_complete" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3977 "Peq" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3271 "Peq" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4141 "Peq_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3509 "Peq_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4140 "Peq_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3574 "Peq_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3573 "Pequiv" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3596 "Pequiv_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4124 "Pjump_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 4128 "Pjump_pred_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 4127 "Pjump_xO_tail" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3980 "Pmul" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3400 "Pmul" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3988 "PmulC" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3416 "PmulC" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3990 "PmulC_aux" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3418 "PmulC_aux" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4159 "PmulC_aux_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3607 "PmulC_aux_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4157 "PmulC_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3602 "PmulC_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3989 "PmulI" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3417 "PmulI" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4158 "PmulI_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3603 "PmulI_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4154 "Pmul_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3523 "Pmul_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3916 "PolC" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 3922 "PolEnv" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4023 "Pol_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3548 "Pol_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3967 "Popp" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3401 "Popp" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4021 "Popp_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3524 "Popp_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3871 "Pos_log2floor_plus1" [opaque=no, body=yes, kind=cnst, prop=no, path="QExtra", ]; +N: 4372 "Pos_log2floor_plus1_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QExtra", ]; +N: 4377 "Pos_pow_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="PosExtra", ]; +N: 5257 "Pos_pred_double_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveExtra", ]; +N: 3993 "Pphi" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3508 "Pphi" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4138 "Pphi0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3570 "Pphi0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4160 "Pphi1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3610 "Pphi1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3810 "Pphi_avoid" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3807 "Pphi_avoid_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 5132 "Pphi_dev" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 5196 "Pphi_dev_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3569 "Pphi_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3054 "Pphi_pow" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3805 "Pphi_pow_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4686 "Pplus_one_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4669 "Pplus_one_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3982 "Ppow_N" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3404 "Ppow_N" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4153 "Ppow_N_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3522 "Ppow_N_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3984 "Ppow_pos" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3405 "Ppow_pos" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4161 "Ppow_pos_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3611 "Ppow_pos_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3017 "PreOrder_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 5216 "PreOrder_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 4484 "Private_Pos_neq_le_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4501 "Private_Pos_neq_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3502 "Private_proj1_eqb_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZArithRing", ]; +N: 5131 "Proper" [opaque=no, body=yes, kind=cnst, prop=no, path="CMorphisms", ]; +N: 2824 "Proper" [opaque=no, body=yes, kind=cnst, prop=no, path="Morphisms", ]; +N: 5130 "ProperProxy" [opaque=no, body=yes, kind=cnst, prop=no, path="CMorphisms", ]; +N: 2852 "ProperProxy" [opaque=no, body=yes, kind=cnst, prop=no, path="Morphisms", ]; +N: 3080 "Proper_instance_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qminmax.Q", ]; +N: 5217 "Proper_instance_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4221 "Psatz_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4207 "Psquare" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 4216 "Psquare_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3965 "Psub" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3402 "Psub" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3970 "PsubC" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3412 "PsubC" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4132 "PsubC_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 4585 "PsubC_ok" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 3591 "PsubC_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3971 "PsubI" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3413 "PsubI" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3972 "PsubX" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3414 "PsubX" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4133 "PsubX_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 4122 "Psub_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3525 "Psub_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3590 "Psub_opp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 2735 "QBound" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 2734 "QCauchySeq" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 4180 "QNpower" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 3907 "QSORaddon" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 3872 "QTautoChecker" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 3880 "QTautoChecker_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 3926 "QWeakChecker" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 3924 "QWeakChecker_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 3879 "QWitness" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 3458 "Q_Setoid" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4321 "Q_dec" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 2738 "Qabs" [opaque=no, body=yes, kind=cnst, prop=no, path="Qabs", ]; +N: 5355 "Qabs_Qinv" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5160 "Qabs_Qle_condition" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5115 "Qabs_Qlt_condition" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5167 "Qabs_Qmult" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5028 "Qabs_case" [opaque=no, body=yes, kind=cnst, prop=no, path="Qabs", ]; +N: 5039 "Qabs_case_subproof" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5040 "Qabs_case_subproof0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5041 "Qabs_case_subproof1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5357 "Qabs_gt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5165 "Qabs_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5128 "Qabs_opp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5281 "Qabs_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5011 "Qabs_triangle" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 3873 "Qabs_triangle_reverse" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5010 "Qabs_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 5026 "Qabs_wd_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 3078 "Qarchimedean" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 5113 "QarchimedeanExp2_Z" [opaque=no, body=yes, kind=cnst, prop=no, path="QExtra", ]; +N: 5278 "QarchimedeanLowExp2_Z" [opaque=no, body=yes, kind=cnst, prop=no, path="QExtra", ]; +N: 3870 "Qbound_lt_ZExp2" [opaque=no, body=yes, kind=cnst, prop=no, path="QExtra", ]; +N: 3877 "Qbound_lt_ZExp2_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QExtra", ]; +N: 5075 "Qbound_ltabs_ZExp2" [opaque=no, body=yes, kind=cnst, prop=no, path="QExtra", ]; +N: 5087 "Qbound_ltabs_ZExp2_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QExtra", ]; +N: 3298 "Qcompare" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 3486 "Qcompare_comp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3302 "Qcompare_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 2747 "Qden" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 3847 "Qdiv" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 4819 "Qdiv_comp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4778 "Qdiv_mult_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3077 "Qeq" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 3295 "Qeq_alt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3081 "Qeq_bool" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 3851 "Qeq_bool_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3854 "Qeq_bool_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4350 "Qeq_bool_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4820 "Qeq_dec" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 4823 "Qeq_eq_bool" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3461 "Qeq_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3460 "Qeq_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3459 "Qeq_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4177 "Qeval_bop2" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 4171 "Qeval_expr" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 4174 "Qeval_expr'" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 4175 "Qeval_expr_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 3913 "Qeval_formula" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 3935 "Qeval_formula'" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 3930 "Qeval_formula_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 3905 "Qeval_nformula" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 3912 "Qeval_nformula_dec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 4176 "Qeval_op2" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 4173 "Qeval_op2_hold" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 4172 "Qeval_pop2" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 4798 "Qfield_field_lemma1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qfield", ]; +N: 5069 "Qfield_field_lemma2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qfield", ]; +N: 4803 "Qfield_lemma5" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qfield", ]; +N: 4815 "Qfield_ring_lemma1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qfield", ]; +N: 3055 "Qfield_ring_lemma2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qfield", ]; +N: 5178 "Qfloor" [opaque=no, body=yes, kind=cnst, prop=no, path="Qround", ]; +N: 5177 "Qfloor_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qround", ]; +N: 2741 "Qinv" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 4817 "Qinv_comp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4937 "Qinv_involutive" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4398 "Qinv_le_0_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4775 "Qinv_lt_0_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5117 "Qinv_lt_contravar" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5090 "Qinv_minus_distr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4814 "Qinv_mult_distr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3791 "Qinv_plus_distr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5049 "Qinv_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5051 "Qinv_power" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 5052 "Qinv_power_positive" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 2771 "Qle" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 5125 "Qle_Qabs" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qabs", ]; +N: 3296 "Qle_alt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4322 "Qle_antisym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3903 "Qle_bool" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 4184 "Qle_bool_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4351 "Qle_bool_imp_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3795 "Qle_comp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3312 "Qle_lt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3294 "Qle_lteq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5009 "Qle_minus_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5251 "Qle_not_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3785 "Qle_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5356 "Qle_shift_div_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4319 "Qle_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5279 "Qlowbound_lt_ZExp2_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QExtra", ]; +N: 5280 "Qlowbound_ltabs_ZExp2" [opaque=no, body=yes, kind=cnst, prop=no, path="QExtra", ]; +N: 5282 "Qlowbound_ltabs_ZExp2_inv" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QExtra", ]; +N: 2737 "Qlt" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 3297 "Qlt_alt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4178 "Qlt_bool" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 4183 "Qlt_bool_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 3485 "Qlt_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5174 "Qlt_floor" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qround", ]; +N: 3309 "Qlt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5065 "Qlt_le_dec" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 5029 "Qlt_le_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3071 "Qlt_le_weak" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4394 "Qlt_leneq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5287 "Qlt_minus_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4320 "Qlt_not_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4777 "Qlt_not_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4382 "Qlt_shift_div_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5120 "Qlt_shift_div_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3308 "Qlt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3875 "Qlt_trans_swap_hyp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveRcomplete", ]; +N: 2758 "Qminus" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 5096 "Qminus_comp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 2744 "Qmult" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 4317 "Qmult_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4403 "Qmult_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3859 "Qmult_1_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4779 "Qmult_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3862 "Qmult_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3856 "Qmult_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3849 "Qmult_comp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5358 "Qmult_div_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5044 "Qmult_frac_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4405 "Qmult_integral" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3857 "Qmult_inv_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4400 "Qmult_le_0_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5036 "Qmult_le_1_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5214 "Qmult_le_compat_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5038 "Qmult_le_compat_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5032 "Qmult_le_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5037 "Qmult_le_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4776 "Qmult_lt_0_le_reg_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5168 "Qmult_lt_compat_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4318 "Qmult_lt_compat_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5121 "Qmult_lt_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5122 "Qmult_lt_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3861 "Qmult_plus_distr_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3902 "Qnegate" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 3917 "Qnormalise" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 4396 "Qnot_eq_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4323 "Qnot_le_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 2748 "Qnum" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 2759 "Qopp" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 3846 "Qopp_comp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5129 "Qopp_le_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5127 "Qopp_lt_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 5126 "Qopp_opp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qfield", ]; +N: 2760 "Qplus" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 3860 "Qplus_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3798 "Qplus_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3790 "Qplus_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3796 "Qplus_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3056 "Qplus_comp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3797 "Qplus_le_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3786 "Qplus_le_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3787 "Qplus_le_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3057 "Qplus_lt_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3840 "Qplus_lt_le_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3799 "Qplus_opp_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 2739 "Qpower" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 4397 "Qpower_0_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4388 "Qpower_0_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 5166 "Qpower_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 5033 "Qpower_1_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 5034 "Qpower_1_le_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 5027 "Qpower_2_invneg_le_pow" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 5043 "Qpower_2_neg_eq_natpow_inv" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 5098 "Qpower_2_neg_le_one" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 5050 "Qpower_comp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 4374 "Qpower_decomp_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4786 "Qpower_decomp_positive" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 5031 "Qpower_le_compat_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4369 "Qpower_minus" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 5046 "Qpower_minus_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4816 "Qpower_minus_positive" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4395 "Qpower_not_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4404 "Qpower_not_0_positive" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4802 "Qpower_opp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4804 "Qpower_plus" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4813 "Qpower_plus_positive" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4399 "Qpower_pos_positive" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 2742 "Qpower_positive" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 4822 "Qpower_positive_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qpower", ]; +N: 4821 "Qpower_positive_comp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QArith_base", ]; +N: 3843 "Qpower_theory" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qfield", ]; +N: 5152 "Qred" [opaque=no, body=yes, kind=cnst, prop=no, path="Qreduction", ]; +N: 5150 "Qred_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qreduction", ]; +N: 3848 "Qsft" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qfield", ]; +N: 3910 "Qsor" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 3855 "Qsrt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qfield", ]; +N: 2729 "R" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 5343 "R0" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 5362 "R0_def" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5386 "R1" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 3865 "R_set1" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3867 "R_set1_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3864 "R_set1_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4063 "R_setoid3" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4065 "R_setoid3_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4059 "R_setoid3_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4067 "R_setoid3_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4076 "R_setoid3_relation" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4926 "R_setoid4" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4922 "R_setoid4_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4928 "R_setoid4_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 5302 "Rabs" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5063 "Rabst" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 3653 "Radd_0_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3646 "Radd_assoc" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3649 "Radd_comm" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3538 "Radd_ext" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 5304 "Rcase_abs" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 5058 "Rcompare" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3654 "Rdistr_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 2697 "Rdiv" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5105 "Reflexive" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 2844 "Reflexive" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 2851 "ReflexiveProxy" [opaque=no, body=yes, kind=cnst, prop=no, path="Morphisms", ]; +N: 5083 "Reflexive_partial_app_morphism" [opaque=yes, body=yes, kind=cnst, prop=no, path="CMorphisms", ]; +N: 2820 "Reflexive_partial_app_morphism" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 5340 "Req_appart_dec" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 4170 "Req_dne" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4099 "Req_em" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 5079 "Rfloor" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveRcomplete", ]; +N: 5303 "Rge" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5314 "Rge_le" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5313 "Rge_not_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5312 "Rgt" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3040 "Rgt_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3394 "Rgt_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5338 "Rinv" [opaque=yes, body=yes, kind=cnst, prop=no, path="RinvImpl", ]; +N: 5263 "Rle" [opaque=no, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 5300 "Rle" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5264 "Rle_antisym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 4105 "Rle_antisymm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 5308 "Rle_dec" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 5306 "Rle_ge" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4096 "Rle_gt_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4008 "Rle_le_minus" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4098 "Rle_lt_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4108 "Rle_lt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4004 "Rle_ngt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 5315 "Rle_not_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4100 "Rle_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4106 "Rle_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 2703 "Rlt" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 5317 "Rlt_asym" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5311 "Rlt_dec" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 5249 "Rlt_def" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5336 "Rlt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4036 "Rlt_le_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4095 "Rlt_le_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4012 "Rlt_lt_minus" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4094 "Rlt_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4005 "Rlt_nge" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 5316 "Rlt_not_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5309 "Rlt_not_le" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4104 "Rlt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4097 "Rlt_trichotomy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 3773 "Rlt_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3007 "Rlt_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3365 "Rlt_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4114 "Rminus_eq_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 3647 "Rmul_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3648 "Rmul_1_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3652 "Rmul_assoc" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3644 "Rmul_comm" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3579 "Rmul_ext" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 5373 "Rmult" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 4102 "Rneq_symm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 5307 "Rnot_le_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5310 "Rnot_lt_le" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5305 "Ropp" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 3650 "Ropp_add" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3656 "Ropp_def" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3587 "Ropp_ext" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4241 "Ropp_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 3645 "Ropp_mul_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4064 "Ropp_opp" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4240 "Ropp_pos_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4019 "Rops_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 5059 "Rplus" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 4143 "Rplus_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4357 "Rplus_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4037 "Rplus_cancel_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4033 "Rplus_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4362 "Rplus_le_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4361 "Rplus_le_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4035 "Rplus_le_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4086 "Rplus_le_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4360 "Rplus_lt_le_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4363 "Rplus_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4034 "Rplus_lt_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4032 "Rplus_lt_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4358 "Rplus_nonneg_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4356 "Rplus_nonneg_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4359 "Rplus_pos_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4355 "Rplus_pos_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 5247 "Rquot1" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5359 "Rquot2" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2730 "Rrepr" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 5341 "Rrepr_appart_0" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 4880 "Rring_ring_lemma1" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3651 "Rsub_def" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3503 "Rth_ARth" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4237 "Rtimes_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4242 "Rtimes_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4246 "Rtimes_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4236 "Rtimes_neg_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4244 "Rtimes_neq_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4245 "Rtimes_nonneg_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4247 "Rtimes_pos_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4238 "Rtimes_pos_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4217 "Rtimes_square_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 5337 "Rtotal_order" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4007 "SORRing_ring_lemma1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4029 "SOR_ring_lemma1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4234 "SORcleb_morph" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4233 "SORcneqb_morph" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4093 "SORle_antisymm" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4101 "SORle_refl" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4107 "SORle_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4043 "SORle_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4040 "SORlt_le_neq" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4103 "SORlt_trichotomy" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4017 "SORlt_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4026 "SORopp_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4041 "SORplus_le_mono_l" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4027 "SORplus_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4145 "SORpower" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4020 "SORrm" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4018 "SORrt" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4016 "SORsetoid" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4239 "SORtimes_pos_pos" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4025 "SORtimes_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4915 "SRadd_0_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4913 "SRadd_assoc" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4919 "SRadd_comm" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4905 "SRadd_ext" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4917 "SRdistr_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4891 "SReqe_Reqe" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4909 "SRmul_0_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4910 "SRmul_1_l" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4916 "SRmul_assoc" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4918 "SRmul_comm" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4903 "SRmul_ext" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4886 "SRopp" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4911 "SRopp_add" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4904 "SRopp_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4912 "SRopp_mul_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4885 "SRsub" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4914 "SRsub_def" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4889 "SRth_ARth" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3534 "Seq_refl" [opaque=no, body=yes, kind=cnst, prop=yes, path="Setoid", ]; +N: 4835 "Seq_sym" [opaque=no, body=yes, kind=cnst, prop=yes, path="Setoid", ]; +N: 4837 "Seq_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Setoid", ]; +N: 3583 "Setoid_Theory" [opaque=no, body=yes, kind=cnst, prop=no, path="Setoid", ]; +N: 4082 "Smorph0" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4083 "Smorph1" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4077 "Smorph_add" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4081 "Smorph_eq" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4051 "Smorph_morph" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4078 "Smorph_mul" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4079 "Smorph_opp" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4080 "Smorph_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2933 "StrictOrder_Irreflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 2949 "StrictOrder_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 5108 "Symmetric" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 2846 "Symmetric" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 4256 "TFormula" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 5106 "Transitive" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 2847 "Transitive" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 2957 "Unconvertible" [opaque=no, body=yes, kind=cnst, prop=no, path="Init", ]; +N: 5030 "UpperAboveLower" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 5228 "Weaken_Qle_QpowerAddExp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5215 "Weaken_Qle_QpowerFac" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 5242 "Weaken_Qle_QpowerRemSubExp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyRealsMult", ]; +N: 4505 "ZArithProof_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4419 "ZChecker" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4422 "ZChecker_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4459 "ZNpower" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4411 "ZSORaddon" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4381 "ZTautoChecker" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4387 "ZTautoChecker_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4393 "ZWitness" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 5054 "Z_N_nat" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4330 "Z_dec'" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5180 "Z_div_mod_eq_full" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5370 "Z_ge_dec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5365 "Z_ge_lt_dec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5008 "Z_gt_dec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5006 "Z_gt_le_dec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5252 "Z_inj_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveExtra", ]; +N: 5253 "Z_inj_nat_id" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveExtra", ]; +N: 5254 "Z_inj_nat_rev" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveExtra", ]; +N: 5369 "Z_le_dec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5366 "Z_le_gt_dec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4335 "Z_le_lt_eq_dec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4340 "Z_lt_dec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4337 "Z_lt_ge_dec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5245 "Z_lt_le_dec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4987 "Z_pos_sub_gt" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4344 "Z_rec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3489 "Zcompare_mult_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4341 "Zcompare_rec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4342 "Zcompare_rect" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4420 "Zdeduce" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 5374 "Zdigits" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5380 "Zdigits_aux" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4512 "Zdiv_pol" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4588 "Zdiv_pol_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4726 "Zdivide_ceiling" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4638 "Zdivide_pol_Zdivide" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4589 "Zdivide_pol_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4635 "Zdivide_pol_one" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4636 "Zdivide_pol_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4452 "Zeval_bop2" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4445 "Zeval_expr" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4443 "Zeval_expr_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4413 "Zeval_formula" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4440 "Zeval_formula'" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4417 "Zeval_formula_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4437 "Zeval_formula_compat'" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4416 "Zeval_nformula_dec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4447 "Zeval_op2" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4756 "Zeval_op2_hold" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4446 "Zeval_pop2" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4582 "ZgcdM" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4645 "Zgcd_minus" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4513 "Zgcd_pol" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4511 "Zgcd_pol_correct_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4587 "Zgcd_pol_div" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4366 "Zmult_lt_compat2" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4376 "Zmult_lt_reg_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3500 "Zpower_theory" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3487 "Zr_ring_lemma1" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3800 "Zr_ring_lemma2" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4418 "Zsor" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4755 "Zsth" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3505 "Zth" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4992 "ZtoN" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3497 "Ztriv_div_th" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4421 "Zunsat" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4429 "Zunsat_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 2756 "abs" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 5014 "abs_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5012 "abs_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5016 "abs_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5019 "abs_opp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5013 "abs_triangle" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5018 "abs_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4850 "absurd_PCond" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4855 "absurd_PCond_bottom" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2789 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="Init.Nat", ]; +N: 3667 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 2945 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 2754 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2751 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 2761 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4455 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="IntDef.Z", ]; +N: 3705 "add_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2977 "add_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3112 "add_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3706 "add_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2980 "add_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3126 "add_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 3108 "add_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3182 "add_1_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3183 "add_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4370 "add_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3672 "add_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2981 "add_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3124 "add_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3113 "add_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 3248 "add_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3121 "add_assoc_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 4902 "add_cancel_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2974 "add_cancel_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3192 "add_cancel_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3244 "add_cancel_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4896 "add_cancel_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2972 "add_cancel_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3105 "add_cancel_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3119 "add_carry" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3117 "add_carry" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3196 "add_carry_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3118 "add_carry_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3678 "add_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2973 "add_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3115 "add_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3114 "add_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 3243 "add_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3220 "add_compare_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3128 "add_compare_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3483 "add_diag" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3841 "add_le_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3031 "add_le_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3385 "add_le_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3032 "add_le_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4689 "add_le_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3386 "add_le_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3033 "add_le_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4700 "add_le_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3387 "add_le_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2987 "add_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3260 "add_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3355 "add_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2993 "add_lt_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3218 "add_lt_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3357 "add_lt_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2994 "add_lt_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3138 "add_lt_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3358 "add_lt_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4688 "add_max_distr_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4687 "add_max_distr_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4516 "add_move_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4539 "add_move_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4542 "add_move_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4541 "add_move_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3813 "add_mult_dev" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3825 "add_mult_dev_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4791 "add_neg_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3191 "add_no_neutral" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4738 "add_nonneg_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5015 "add_nonpos_nonpos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4538 "add_opp_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3239 "add_opp_diag_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 4612 "add_opp_diag_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4481 "add_opp_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3636 "add_opp_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5284 "add_pos_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Z", ]; +N: 3814 "add_pow_list" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3824 "add_pow_list_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3780 "add_pred_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3642 "add_pred_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3779 "add_pred_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3639 "add_pred_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3193 "add_reg_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3194 "add_reg_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4741 "add_simpl_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3720 "add_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3137 "add_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3718 "add_sub_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3129 "add_sub_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4441 "add_sub_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3703 "add_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2976 "add_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3221 "add_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3111 "add_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3704 "add_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2979 "add_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3181 "add_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3245 "add_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4269 "add_term" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4310 "add_term_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 3700 "add_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2975 "add_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3109 "add_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2978 "add_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="PeanoNat.Nat", ]; +N: 3178 "add_xI_pred_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3482 "add_xO" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4503 "agree_env" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4662 "agree_env_eval_nformula" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4495 "agree_env_eval_nformulae" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4664 "agree_env_jump" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4658 "agree_env_subset" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4665 "agree_env_tail" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 2990 "all" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 2988 "all_iff_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 2991 "all_iff_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 4946 "and_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4261 "and_cnf" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4260 "and_cnf_opt" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4295 "and_cnf_opt_cnf_ff_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4293 "and_cnf_opt_cnf_tt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4561 "and_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5272 "and_hprop" [opaque=yes, body=yes, kind=cnst, prop=yes, path="HLevelsBase", ]; +N: 4661 "and_iff_compat_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3010 "and_iff_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 3011 "and_iff_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 2849 "and_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4371 "and_morph" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZifyClasses", ]; +N: 3694 "and_rec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4111 "andb" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4730 "andb_false_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Bool", ]; +N: 4232 "andb_prop" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4315 "andb_true_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Bool", ]; +N: 4303 "app" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5081 "arrow" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 3698 "bi_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2910 "bi_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3104 "bi_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5158 "bound" [opaque=no, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 4494 "bound_var" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 5301 "bpow" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3781 "case_analysis" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3052 "case_analysis" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 5112 "cauchy" [opaque=no, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 4578 "ceiling" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 3735 "central_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2905 "central_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3330 "central_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4139 "ceqb_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 4876 "ceqb_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3572 "ceqb_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4854 "ceqb_spec'" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 2701 "cexp" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3946 "check_inconsistent" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 3909 "check_inconsistent_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4199 "check_normalised_formulas" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4209 "checker_nf_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 3957 "clause" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4230 "cleb_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4109 "cltb" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4219 "cltb_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4110 "cneqb" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4231 "cneqb_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 3954 "cnf" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4251 "cnf_checker" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4248 "cnf_checker_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 3943 "cnf_ff" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3927 "cnf_negate" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 3932 "cnf_negate_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 3921 "cnf_normalise" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 3933 "cnf_normalise_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 3950 "cnf_of_list" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4426 "cnf_of_list" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 3949 "cnf_of_list_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4425 "cnf_of_list_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3999 "cnf_tt" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3687 "compare" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3496 "compare" [opaque=no, body=yes, kind=cnst, prop=no, path="NatDef.N", ]; +N: 2881 "compare" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 3141 "compare" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2723 "compare" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 2720 "compare" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3690 "compare_antisym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 5295 "compare_antisym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3208 "compare_antisym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3304 "compare_antisym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3204 "compare_cont" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2727 "compare_cont" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3215 "compare_cont_antisym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3203 "compare_cont_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3748 "compare_eq_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2882 "compare_eq_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3206 "compare_eq_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3299 "compare_eq_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5294 "compare_gt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4609 "compare_gt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3691 "compare_le_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2883 "compare_le_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4620 "compare_le_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3327 "compare_le_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3686 "compare_lt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2884 "compare_lt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3207 "compare_lt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3305 "compare_lt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3685 "compare_nge_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 4720 "compare_nge_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4751 "compare_nge_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4608 "compare_ngt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3689 "compare_nle_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 4721 "compare_nle_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4752 "compare_nle_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3747 "compare_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2928 "compare_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3241 "compare_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3311 "compare_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3300 "compare_spec" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.OT", ]; +N: 3140 "compare_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3301 "compare_spec" [opaque=no, body=yes, kind=cnst, prop=yes, path="QOrderedType.Q_as_OT", ]; +N: 3303 "compare_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3339 "compare_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3200 "compare_sub_mask" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 5292 "compare_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3223 "compare_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3224 "compare_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3222 "compare_succ_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3153 "compare_xI_xI" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3154 "compare_xI_xO" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3155 "compare_xO_xI" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3156 "compare_xO_xO" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 2938 "complement" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 4801 "condition" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5320 "constructive_indefinite_ground_description" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveEpsilon", ]; +N: 5319 "constructive_indefinite_ground_description_Z" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveExtra", ]; +N: 5323 "constructive_indefinite_ground_description_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveEpsilon", ]; +N: 5107 "crelation" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 4943 "cross_product_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4492 "cutting_plane_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4482 "decidable" [opaque=no, body=yes, kind=cnst, prop=no, path="Decidable", ]; +N: 4994 "default_isIn" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4996 "default_isIn_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3060 "default_relation" [opaque=no, body=yes, kind=cnst, prop=no, path="SetoidTactics", ]; +N: 4797 "denum" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3695 "diff_false_true" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Bool", ]; +N: 5381 "digits2_Pnat" [opaque=yes, body=no, kind=cnst, prop=no, ]; +N: 5082 "display_pow_linear" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4584 "div" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4747 "div_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4882 "div_eucl" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 4579 "div_eucl" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4748 "div_eucl_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4610 "div_eucl_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4895 "div_eucl_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3623 "div_eucl_th" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4625 "div_exact" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4598 "div_mod" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4622 "div_mod_unique" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_NZDiv", ]; +N: 4595 "div_mod_unique" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4591 "div_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4594 "div_unique" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4729 "div_unique_exact" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4734 "div_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4534 "divide" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4519 "divide" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4532 "divide_Zpos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4530 "divide_Zpos_Zneg_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4531 "divide_Zpos_Zneg_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4553 "divide_add_cancel_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4646 "divide_add_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4526 "divide_antisym_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4590 "divide_div_mul_exact" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4555 "divide_mul_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4520 "divide_mul_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4550 "divide_mul_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4626 "divide_mul_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4653 "divide_opp_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4522 "divide_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4642 "divide_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4652 "divide_transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4631 "divide_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4551 "divide_xO_xI" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4552 "divide_xO_xO" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3679 "double" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3494 "double" [opaque=no, body=yes, kind=cnst, prop=no, path="NatDef.N", ]; +N: 2765 "double" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4463 "double" [opaque=no, body=yes, kind=cnst, prop=no, path="IntDef.Z", ]; +N: 3675 "double_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3166 "double_mask" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3229 "double_mask" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3676 "double_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3189 "double_pred_mask" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3228 "double_pred_mask" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 4192 "eAND" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4189 "eFF" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4193 "eIFF" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4194 "eIMPL" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3881 "eKind" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3936 "eNOT" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4190 "eOR" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4191 "eTT" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4187 "e_rtyp" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4134 "env_morph" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3708 "eq" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3238 "eq" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4006 "eq0_cnf" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 3044 "eq_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 3046 "eq_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 3045 "eq_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 2895 "eq_add_S" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4474 "eq_cnf" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4343 "eq_dec" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4331 "eq_dec" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4472 "eq_decidable" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3759 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.IsTotal", ]; +N: 2861 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.IsTotal", ]; +N: 3322 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.IsTotal", ]; +N: 3701 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2809 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3066 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.OT", ]; +N: 3242 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3457 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="QOrderedType.Q_as_OT", ]; +N: 3099 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3043 "eq_equivalence" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 2795 "eq_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 2866 "eq_ind_r" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4716 "eq_le" [opaque=no, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 3283 "eq_le" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.Private_Tac", ]; +N: 5218 "eq_le" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_Tac", ]; +N: 5025 "eq_le" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 3775 "eq_le_incl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3038 "eq_le_incl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3392 "eq_le_incl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4670 "eq_lt" [opaque=no, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 3284 "eq_lt" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.Private_Tac", ]; +N: 5219 "eq_lt" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_Tac", ]; +N: 2813 "eq_lt" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 3373 "eq_lt" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 2810 "eq_mul_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4406 "eq_mul_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4562 "eq_mul_1_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4556 "eq_mul_1_nonneg'" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4693 "eq_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 4328 "eq_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 5269 "eq_proofs_unicity_on" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Eqdep_dec", ]; +N: 2830 "eq_proper_proxy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 5084 "eq_rec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5176 "eq_rec_r" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4220 "eq_rect" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4696 "eq_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 4329 "eq_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 5020 "eq_refl" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3452 "eq_rewrite_relation" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2867 "eq_sym" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4674 "eq_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 3289 "eq_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.Private_Tac", ]; +N: 5224 "eq_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_Tac", ]; +N: 2822 "eq_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 3375 "eq_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 2983 "eq_trans" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4699 "eq_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 3379 "eq_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 4197 "eqb" [opaque=no, body=yes, kind=cnst, prop=no, path="Bool", ]; +N: 4848 "eqb" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3659 "eqb" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3282 "eqb" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3281 "eqb" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4923 "eqb_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3658 "eqb_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3657 "eqb_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4497 "eqb_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4514 "eqb_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3833 "eqb_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4935 "eqb_spec" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 4931 "eqb_spec" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4746 "eqb_spec" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4314 "eqb_true_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Bool", ]; +N: 3074 "equivalence_default" [opaque=no, body=yes, kind=cnst, prop=yes, path="SetoidTactics", ]; +N: 3133 "equivalence_rewrite_relation" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 4201 "eval_Psatz" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4483 "eval_Psatz" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4210 "eval_Psatz_Sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4500 "eval_Psatz_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3928 "eval_bf" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4003 "eval_clause" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3918 "eval_cnf" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4282 "eval_cnf_and_opt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4280 "eval_cnf_app" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4001 "eval_cnf_cons_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 3948 "eval_cnf_ff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4168 "eval_cnf_tt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4442 "eval_expr" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4188 "eval_f" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3914 "eval_formula" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 3904 "eval_nformula" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4415 "eval_nformula" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4499 "eval_nformula_bound_var" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4316 "eval_nformula_dec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4489 "eval_nformula_mk_eq_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4502 "eval_nformula_split" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3951 "eval_op1" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4117 "eval_op2" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4309 "eval_opt_clause" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4115 "eval_pexpr" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 3952 "eval_pol" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4434 "eval_pol" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4473 "eval_pol_Pc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4732 "eval_pol_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4723 "eval_pol_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4113 "eval_pol_norm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4436 "eval_pol_norm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4013 "eval_pol_opp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4116 "eval_pol_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4433 "eval_pol_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3929 "eval_tt" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 5377 "even" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4632 "ex_iff_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 4633 "ex_iff_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 4634 "ex_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 2896 "f_equal" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4460 "f_equal2" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2894 "f_equal_nat" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4834 "fcons_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4851 "field_is_integral_domain" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3878 "find" [opaque=no, body=yes, kind=cnst, prop=no, path="VarMap", ]; +N: 2811 "flip" [opaque=no, body=yes, kind=cnst, prop=no, path="Basics", ]; +N: 5137 "flip" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 5171 "flip_Reflexive" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 4267 "fold_left" [opaque=no, body=yes, kind=cnst, prop=no, path="List", ]; +N: 4000 "fold_right" [opaque=no, body=yes, kind=cnst, prop=no, path="List", ]; +N: 5268 "forall_hprop" [opaque=yes, body=yes, kind=cnst, prop=yes, path="HLevels", ]; +N: 3614 "fst" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5266 "functional_extensionality" [opaque=yes, body=yes, kind=cnst, prop=yes, path="FunctionalExtensionality", ]; +N: 5267 "functional_extensionality_dep" [opaque=yes, body=no, kind=cnst, prop=yes, path="FunctionalExtensionality", ]; +N: 4533 "gcd" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4515 "gcd" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4650 "gcd_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4651 "gcd_divide_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4524 "gcd_divide_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4525 "gcd_divide_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4529 "gcd_greatest" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4528 "gcd_greatest" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4518 "gcd_mul_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4527 "gcd_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4649 "gcd_opp_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4509 "gcd_opp_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4523 "gcd_unique" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4521 "gcd_unique_alt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4536 "gcdn" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4546 "gcdn_greatest" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4681 "ge" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4336 "ge" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4338 "ge_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4680 "ge_le_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4339 "ge_le_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4453 "geb" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4758 "geb_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4760 "geb_leb" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4496 "genCuttingPlane" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4504 "genCuttingPlaneNone" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4052 "gen_Zeqb_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4888 "gen_phiN" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4925 "gen_phiN1" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4920 "gen_phiN_add" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4887 "gen_phiN_morph" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4924 "gen_phiN_mult" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4921 "gen_phiN_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4074 "gen_phiPOS" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4062 "gen_phiPOS1" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4046 "gen_phiZ" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4061 "gen_phiZ1" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4075 "gen_phiZ1_pos_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4053 "gen_phiZ_add" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4054 "gen_phiZ_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4047 "gen_phiZ_morph" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4055 "gen_phiZ_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4149 "get_PEopp" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3539 "get_PEopp" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3801 "get_signZ" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3803 "get_signZ_th" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3063 "get_sign_None" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3844 "get_sign_None_th" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4572 "ggcd" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4570 "ggcd" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4576 "ggcd_correct_divisors" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4568 "ggcd_correct_divisors" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4574 "ggcd_gcd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4569 "ggcd_gcd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4573 "ggcdn" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4577 "ggcdn_correct_divisors" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4575 "ggcdn_gcdn" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3145 "gt" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4444 "gt" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3259 "gt_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4448 "gt_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3232 "gt_lt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4451 "gt_lt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3039 "gt_wf" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3393 "gt_wf" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4454 "gtb" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4759 "gtb_gt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4510 "gtb_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4648 "gtb_ltb" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4737 "gtb_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3994 "hd" [opaque=no, body=yes, kind=cnst, prop=no, path="Env", ]; +N: 3454 "hd" [opaque=no, body=yes, kind=cnst, prop=no, path="List", ]; +N: 3937 "hold" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4272 "hold_eAND" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4276 "hold_eEQ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4277 "hold_eFF" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4313 "hold_eIFF" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4312 "hold_eIFF_IMPL" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4311 "hold_eIMPL" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 3915 "hold_eNOT" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4278 "hold_eOR" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4279 "hold_eTT" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4782 "id" [opaque=no, body=yes, kind=cnst, prop=no, path="Datatypes", ]; +N: 3474 "id" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nnat.N2Nat", ]; +N: 3470 "id" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nnat.Nat2N", ]; +N: 3449 "id" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat2Pos", ]; +N: 3451 "id" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Nat", ]; +N: 5053 "id" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z2N", ]; +N: 5042 "id" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z2Nat", ]; +N: 5155 "id" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z2Pos", ]; +N: 4050 "id_phi_N" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3446 "id_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="SuccNat2Pos", ]; +N: 4302 "if_cnf_tt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4999 "if_true" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2823 "iff" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5080 "iffT" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 5077 "iffT_arrow_subrelation" [opaque=yes, body=yes, kind=cnst, prop=no, path="CMorphisms", ]; +N: 5135 "iffT_flip_arrow_subrelation" [opaque=yes, body=yes, kind=cnst, prop=no, path="CMorphisms", ]; +N: 2833 "iff_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 2879 "iff_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 2831 "iff_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 2877 "iff_equivalence" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 2834 "iff_flip_impl_subrelation" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2836 "iff_iff_iff_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 2848 "iff_iff_iff_impl_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 2862 "iff_impl_subrelation" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2853 "iff_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3692 "iff_reflect" [opaque=no, body=yes, kind=cnst, prop=no, path="Bool", ]; +N: 4543 "iff_stepl" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2897 "iff_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2858 "iff_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2812 "impl" [opaque=no, body=yes, kind=cnst, prop=no, path="Basics", ]; +N: 5169 "impl_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 5172 "impl_Reflexive_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 5270 "impl_hprop" [opaque=yes, body=yes, kind=cnst, prop=yes, path="HLevels", ]; +N: 2941 "impl_pars" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 4196 "implb" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 2702 "inbetween_float" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3723 "induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3053 "induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4383 "inj" [opaque=no, body=yes, kind=cnst, prop=no, path="ZifyClasses", ]; +N: 3472 "inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nnat.N2Nat", ]; +N: 3445 "inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Nat", ]; +N: 4788 "inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Z", ]; +N: 5293 "inj_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Nat", ]; +N: 3794 "inj_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nnat.N2Nat", ]; +N: 3792 "inj_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N2Z", ]; +N: 3793 "inj_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nnat.Nat2N", ]; +N: 3789 "inj_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat2Z", ]; +N: 3481 "inj_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Nat", ]; +N: 5289 "inj_compare" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Nat", ]; +N: 5285 "inj_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Nat", ]; +N: 3471 "inj_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nnat.N2Nat", ]; +N: 3468 "inj_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N2Z", ]; +N: 3469 "inj_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nnat.Nat2N", ]; +N: 5045 "inj_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat2Pos", ]; +N: 3065 "inj_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat2Z", ]; +N: 3478 "inj_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Nat", ]; +N: 3431 "inj_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Z", ]; +N: 4380 "inj_pow" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Z", ]; +N: 4781 "inj_pow_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Z", ]; +N: 5048 "inj_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat2Z", ]; +N: 3441 "inj_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Nat", ]; +N: 4373 "inj_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Z", ]; +N: 5071 "inject_Q" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5085 "inject_Q_cauchy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5144 "inject_Q_morph_T" [opaque=yes, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5074 "inject_Q_plus" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 5136 "inject_Z" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5175 "inject_Z" [opaque=no, body=yes, kind=cnst, prop=no, path="QArith_base", ]; +N: 3504 "interp_PElist" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3517 "interp_PElist_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4684 "interp_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos.Private_Tac", ]; +N: 3396 "interp_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="Qminmax.Q.Private_Tac", ]; +N: 5227 "interp_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="Z.Private_Tac", ]; +N: 3760 "interp_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="N.Private_OrderTac.Tac", ]; +N: 2951 "interp_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat.Private_OrderTac.Tac", ]; +N: 3349 "interp_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="Z.Private_OrderTac.Tac", ]; +N: 3439 "inv" [opaque=yes, body=yes, kind=cnst, prop=yes, path="SuccNat2Pos", ]; +N: 5332 "inv_before_witness" [opaque=no, body=yes, kind=cnst, prop=yes, path="ConstructiveEpsilon", ]; +N: 5170 "inverse_impl_rewrite_relation" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 4993 "isIn" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4989 "isIn_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2768 "isLowerCut" [opaque=no, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 5265 "isLowerCut_hprop" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 4257 "is_bool" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4281 "is_bool_inv" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4262 "is_cnf_ff" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4301 "is_cnf_ff_cnf_ff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4297 "is_cnf_ff_inv" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4263 "is_cnf_tt" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4298 "is_cnf_tt_cnf_ff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4299 "is_cnf_tt_inv" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 5367 "is_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat2Z", ]; +N: 3802 "is_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Z", ]; +N: 5255 "is_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Nat", ]; +N: 3440 "is_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Nat", ]; +N: 3939 "is_true" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4769 "iter" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3661 "iter" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 4770 "iter_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4784 "iter_ind" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4783 "iter_invariant" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3442 "iter_op" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2788 "iter_op" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3443 "iter_op_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4771 "iter_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4772 "iter_swap" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4773 "iter_swap_gen" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3456 "jump" [opaque=no, body=yes, kind=cnst, prop=no, path="BinList", ]; +N: 3996 "jump" [opaque=no, body=yes, kind=cnst, prop=no, path="Env", ]; +N: 3566 "jump_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="BinList", ]; +N: 4137 "jump_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Env", ]; +N: 3555 "jump_add'" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3552 "jump_pred_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="BinList", ]; +N: 4135 "jump_pred_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Env", ]; +N: 4136 "jump_simpl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Env", ]; +N: 3567 "jump_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="BinList", ]; +N: 3568 "jump_tl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="BinList", ]; +N: 3670 "le" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3436 "le" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2695 "le" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4435 "le_0_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3728 "le_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2802 "le_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 2886 "le_0_n" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4465 "le_0_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3429 "le_1_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 2887 "le_S_n" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4739 "le_add_le_sub_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4740 "le_add_le_sub_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4615 "le_antisym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4692 "le_antisym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 4327 "le_antisym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 4326 "le_antisymm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3285 "le_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.Private_Tac", ]; +N: 5220 "le_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_Tac", ]; +N: 4557 "le_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 4449 "le_ge" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4654 "le_ge_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3767 "le_gt_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2871 "le_gt_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3325 "le_gt_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2889 "le_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 2806 "le_ind" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4764 "le_ind" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3740 "le_le_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3018 "le_le_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3368 "le_le_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3029 "le_lt_add_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3383 "le_lt_add_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4753 "le_lt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4671 "le_lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 3287 "le_lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.Private_Tac", ]; +N: 5222 "le_lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_Tac", ]; +N: 3739 "le_lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.Tac", ]; +N: 3000 "le_lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 3317 "le_lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 3316 "le_lt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3761 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.IsTotal", ]; +N: 2950 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.IsTotal", ]; +N: 3320 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.IsTotal", ]; +N: 3762 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2955 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3292 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.OT", ]; +N: 4618 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3293 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="QOrderedType.Q_as_OT", ]; +N: 3342 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4667 "le_max_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4668 "le_max_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 5236 "le_min_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2888 "le_n_S" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4763 "le_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4754 "le_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4697 "le_neq_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 4593 "le_neq_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 5258 "le_ngt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4679 "le_nlt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 2892 "le_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3738 "le_preorder" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3016 "le_preorder" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3367 "le_preorder" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3721 "le_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2906 "le_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4663 "le_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4402 "le_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 3331 "le_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4735 "le_sub_le_add_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3752 "le_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2904 "le_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4605 "le_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3329 "le_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3741 "le_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3019 "le_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3369 "le_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3768 "le_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3022 "le_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4701 "le_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3370 "le_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3736 "le_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2907 "le_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3332 "le_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3673 "leb" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3492 "leb" [opaque=no, body=yes, kind=cnst, prop=no, path="NatDef.N", ]; +N: 4485 "leb" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2713 "leb" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3693 "leb_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 4722 "leb_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4185 "leb_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3681 "leb_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 4493 "leb_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4488 "leb_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3684 "leb_spec0" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 4719 "leb_spec0" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4750 "leb_spec0" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3036 "left_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3390 "left_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5296 "linear_order_T" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5327 "linear_search_conform" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveEpsilon", ]; +N: 5325 "linear_search_from_0_conform" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveEpsilon", ]; +N: 3617 "list_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4235 "list_rec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3808 "local_mkpow_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3058 "lowerCutAbove" [opaque=yes, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 3059 "lowerCutBelow" [opaque=yes, body=yes, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 5286 "lowerUpper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ClassicalDedekindReals", ]; +N: 2794 "lt" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3671 "lt" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3146 "lt" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2757 "lt" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 2807 "lt_0_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4563 "lt_0_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4432 "lt_0_sub" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3051 "lt_0_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 2808 "lt_1_2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4564 "lt_1_2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4566 "lt_1_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4565 "lt_1_mul_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5290 "lt_1_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 5179 "lt_add_lt_sub_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4745 "lt_add_pos_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4744 "lt_add_pos_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3132 "lt_add_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3749 "lt_asymm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2942 "lt_asymm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3346 "lt_asymm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3758 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.IsTotal", ]; +N: 2860 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.IsTotal", ]; +N: 3348 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.IsTotal", ]; +N: 3763 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2863 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3064 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.OT", ]; +N: 4683 "lt_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3484 "lt_compat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QOrderedType.Q_as_OT", ]; +N: 3350 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4717 "lt_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 3286 "lt_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.Private_Tac", ]; +N: 5221 "lt_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_Tac", ]; +N: 3776 "lt_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.Tac", ]; +N: 2816 "lt_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 3374 "lt_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 3731 "lt_eq_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2872 "lt_eq_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4619 "lt_eq_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3326 "lt_eq_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3734 "lt_exists_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2997 "lt_exists_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3361 "lt_exists_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4560 "lt_ge_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3127 "lt_gt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4450 "lt_gt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3377 "lt_gt_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3170 "lt_iff_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3783 "lt_ind" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2985 "lt_ind" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3354 "lt_ind" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3782 "lt_ind_rel" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3746 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2911 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4616 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4673 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 3288 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.Private_Tac", ]; +N: 5223 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_Tac", ]; +N: 3742 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.Tac", ]; +N: 2821 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 3318 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 3310 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4475 "lt_le_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3750 "lt_le_incl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2919 "lt_le_incl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3337 "lt_le_incl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4727 "lt_le_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4702 "lt_le_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3428 "lt_le_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3772 "lt_lt_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3006 "lt_lt_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3366 "lt_lt_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2959 "lt_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4347 "lt_neq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4780 "lt_nge" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4718 "lt_nle" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3743 "lt_strorder" [opaque=no, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.IsTotal", ]; +N: 2934 "lt_strorder" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.IsTotal", ]; +N: 3343 "lt_strorder" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.IsTotal", ]; +N: 3744 "lt_strorder" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2935 "lt_strorder" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3306 "lt_strorder" [opaque=no, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.OT", ]; +N: 4617 "lt_strorder" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3307 "lt_strorder" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QOrderedType.Q_as_OT", ]; +N: 3344 "lt_strorder" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5288 "lt_sub_lt_add_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3730 "lt_succ_diag_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2920 "lt_succ_diag_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3219 "lt_succ_diag_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3338 "lt_succ_diag_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3784 "lt_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3026 "lt_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3380 "lt_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3737 "lt_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2903 "lt_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3769 "lt_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3328 "lt_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3764 "lt_total" [opaque=no, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.IsTotal", ]; +N: 2859 "lt_total" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.IsTotal", ]; +N: 3321 "lt_total" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.IsTotal", ]; +N: 3765 "lt_total" [opaque=no, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2868 "lt_total" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3291 "lt_total" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.OT", ]; +N: 4676 "lt_total" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3323 "lt_total" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3745 "lt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2939 "lt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3134 "lt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4685 "lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 5231 "lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_Tac", ]; +N: 3756 "lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.Tac", ]; +N: 2986 "lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 3356 "lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 3345 "lt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3766 "lt_trichotomy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2869 "lt_trichotomy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3324 "lt_trichotomy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3732 "lt_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2864 "lt_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3333 "lt_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2865 "lt_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="PeanoNat.Nat", ]; +N: 3770 "lt_wf" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3003 "lt_wf" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3364 "lt_wf" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4179 "ltb" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4186 "ltb_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4603 "ltb_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4607 "ltb_spec0" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 5297 "mag" [opaque=yes, body=no, kind=cnst, prop=no, ]; +N: 5298 "mag_val" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4517 "makeCuttingPlane" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4728 "makeCuttingPlane_ns_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3944 "make_conj" [opaque=no, body=yes, kind=cnst, prop=no, path="Refl", ]; +N: 4305 "make_conj_app" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Refl", ]; +N: 4002 "make_conj_cons" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Refl", ]; +N: 4212 "make_conj_impl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Refl", ]; +N: 4213 "make_conj_in" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Refl", ]; +N: 4304 "make_conj_rapp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Refl", ]; +N: 3911 "make_impl" [opaque=no, body=yes, kind=cnst, prop=no, path="Refl", ]; +N: 3934 "make_impl_map" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Refl", ]; +N: 3908 "map" [opaque=no, body=yes, kind=cnst, prop=no, path="ListDef", ]; +N: 4206 "map_option" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4203 "map_option2" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 3199 "mask2cmp" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4659 "max" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4583 "max" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4655 "max_1_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4703 "max_case_strong" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4705 "max_case_strong" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos.Private_Dec", ]; +N: 5229 "max_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4677 "max_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4643 "max_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4714 "max_le_compat_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4715 "max_lub_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4691 "max_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4690 "max_monotone" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4678 "max_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4644 "max_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4672 "max_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4637 "max_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4660 "max_var" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4666 "max_var_acc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4486 "max_var_nformulae" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4657 "max_var_nformulae_mono_aux" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4656 "max_var_nformulae_mono_aux'" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4009 "micomega_sor_setoid" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4015 "micomega_sor_setoid_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4091 "micomega_sor_setoid_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4090 "micomega_sor_setoid_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 5114 "min" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 5123 "min_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5124 "min_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5116 "min_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3968 "mkPX" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3410 "mkPX" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3595 "mkPX_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4125 "mkPX_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3553 "mkPX_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3975 "mkPinj" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3415 "mkPinj" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3593 "mkPinj_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4131 "mkPinj_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3549 "mkPinj_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3986 "mkPinj_pred" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3408 "mkPinj_pred" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3272 "mkVmon" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3628 "mkVmon_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3985 "mkX" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3407 "mkX" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4147 "mkX_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3533 "mkX_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3987 "mkXi" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3409 "mkXi" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3273 "mkZmon" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3624 "mkZmon_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3981 "mk_X" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3403 "mk_X" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4254 "mk_and" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4487 "mk_eq_pos" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4255 "mk_iff" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4283 "mk_iff_is_bool" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4253 "mk_impl" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3084 "mk_monpol_list" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4258 "mk_or" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3822 "mkadd_mult" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3826 "mkadd_mult_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4794 "mkapp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZifyClasses", ]; +N: 4367 "mkapp2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZifyClasses", ]; +N: 3821 "mkmult1" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3829 "mkmult1_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3815 "mkmult_c" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3823 "mkmult_c_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3817 "mkmult_c_pos" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3827 "mkmult_c_pos_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 5197 "mkmult_pow" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 5198 "mkmult_pow_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3816 "mkmult_rec" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3830 "mkmult_rec_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3819 "mkmultm1" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3832 "mkmultm1_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 5200 "mkopp_pow" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 5201 "mkopp_pow_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 5199 "mkpow" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 5202 "mkpow_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4384 "mkrel" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZifyClasses", ]; +N: 4627 "mod_divide" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4630 "mod_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4629 "mod_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4600 "mod_neg_bound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4596 "mod_pos_bound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4628 "mod_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4599 "modulo" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3267 "mon_of_pol" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3627 "mon_of_pol_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3529 "morph0" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3530 "morph1" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3565 "morph_add" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3578 "morph_eq" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3608 "morph_mul" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3594 "morph_opp" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3597 "morph_sub" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3041 "mul" [opaque=no, body=yes, kind=cnst, prop=no, path="Init.Nat", ]; +N: 3465 "mul" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 2819 "mul" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 2745 "mul" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2749 "mul" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 2746 "mul" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4456 "mul" [opaque=no, body=yes, kind=cnst, prop=no, path="IntDef.Z", ]; +N: 4897 "mul_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2963 "mul_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3106 "mul_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4898 "mul_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2964 "mul_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3251 "mul_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 3107 "mul_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3249 "mul_1_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 3629 "mul_1_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3261 "mul_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3082 "mul_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3265 "mul_add_distr_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4611 "mul_add_distr_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3253 "mul_add_distr_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 3254 "mul_add_distr_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3250 "mul_add_distr_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 3352 "mul_add_distr_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3863 "mul_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3351 "mul_assoc" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3372 "mul_cancel_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3463 "mul_cancel_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4894 "mul_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2969 "mul_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3257 "mul_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3085 "mul_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3258 "mul_compare_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3256 "mul_compare_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4743 "mul_div_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4559 "mul_id_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3432 "mul_le_mono_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3434 "mul_le_mono_nonneg_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3435 "mul_le_mono_nonneg_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5024 "mul_le_mono_nonpos_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5023 "mul_le_mono_nonpos_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3371 "mul_le_mono_pos_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3313 "mul_le_mono_pos_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3266 "mul_lt_mono_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3025 "mul_lt_mono_neg_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3376 "mul_lt_mono_neg_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3024 "mul_lt_mono_neg_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4410 "mul_lt_mono_neg_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3433 "mul_lt_mono_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2968 "mul_lt_mono_pos_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3353 "mul_lt_mono_pos_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2967 "mul_lt_mono_pos_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3314 "mul_lt_mono_pos_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4554 "mul_lt_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3028 "mul_lt_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3382 "mul_lt_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2961 "mul_neg_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4407 "mul_neg_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2962 "mul_neg_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4408 "mul_neg_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4401 "mul_nonneg_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5021 "mul_nonneg_nonpos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4613 "mul_opp_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4537 "mul_opp_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5022 "mul_opp_opp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3252 "mul_opp_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 4545 "mul_opp_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5156 "mul_pos_cancel_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2965 "mul_pos_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4409 "mul_pos_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2966 "mul_pos_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4349 "mul_pos_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3462 "mul_reg_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3315 "mul_shuffle0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4348 "mul_shuffle1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3264 "mul_sub_distr_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3255 "mul_sub_distr_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4900 "mul_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2970 "mul_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3480 "mul_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3101 "mul_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4901 "mul_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2971 "mul_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3102 "mul_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4899 "mul_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2960 "mul_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3100 "mul_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3042 "mul_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="PeanoNat.Nat", ]; +N: 3262 "mul_xI_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3263 "mul_xO_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3811 "mult_dev" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3809 "mult_dev_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3479 "mult_n_O" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4736 "narrow_interval_lower_bound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3466 "nat_N_Z" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2885 "nat_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 5035 "neg_is_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Z", ]; +N: 4423 "negate" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4424 "negate_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3941 "negb" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4724 "negb_false_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Bool", ]; +N: 4182 "negb_true_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Bool", ]; +N: 2796 "neq_0_lt_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3447 "neq_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 4694 "neq_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 4558 "neq_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 3774 "neq_succ_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3049 "neq_succ_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3754 "neq_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2917 "neq_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3335 "neq_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4597 "neq_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 5376 "new_location" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5379 "new_location_even" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5378 "new_location_odd" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4490 "nformula_of_cutting_plane" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 3901 "nformula_plus_nformula" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 3906 "nformula_plus_nformula_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4205 "nformula_times_nformula" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4214 "nformula_times_nformula_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4325 "nle_gt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3753 "nle_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2914 "nle_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3334 "nle_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3030 "nlt_ge" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3384 "nlt_ge" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3751 "nlt_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2918 "nlt_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3336 "nlt_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3958 "norm" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4439 "normZ" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 3978 "norm_aux" [opaque=no, body=yes, kind=cnst, prop=no, path="EnvRing", ]; +N: 3398 "norm_aux" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 4150 "norm_aux_PEadd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3540 "norm_aux_PEadd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4151 "norm_aux_PEopp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3541 "norm_aux_PEopp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4146 "norm_aux_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3521 "norm_aux_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3079 "norm_subst" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3510 "norm_subst_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3518 "norm_subst_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3953 "normalise" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4414 "normalise" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4412 "normalise_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3945 "normalise_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 2770 "not" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4332 "not_Zeq_inf" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3197 "not_eq_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4698 "not_ge_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 3771 "not_ge_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.Tac", ]; +N: 2989 "not_ge_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 3319 "not_ge_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 4675 "not_gt_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 3290 "not_gt_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.Private_Tac", ]; +N: 5225 "not_gt_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_Tac", ]; +N: 3755 "not_gt_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.Tac", ]; +N: 3002 "not_gt_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 3363 "not_gt_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 5271 "not_hprop" [opaque=yes, body=yes, kind=cnst, prop=yes, path="HLevels", ]; +N: 2929 "not_iff_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 2930 "not_iff_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 4695 "not_neq_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 2828 "not_neq_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 3378 "not_neq_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 4581 "not_true_iff_false" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Bool", ]; +N: 3453 "nth" [opaque=no, body=yes, kind=cnst, prop=no, path="BinList", ]; +N: 3998 "nth" [opaque=no, body=yes, kind=cnst, prop=no, path="Env", ]; +N: 4204 "nth" [opaque=no, body=yes, kind=cnst, prop=no, path="ListDef", ]; +N: 4218 "nth_in_or_default" [opaque=yes, body=yes, kind=cnst, prop=no, path="List", ]; +N: 3586 "nth_jump" [opaque=yes, body=yes, kind=cnst, prop=yes, path="BinList", ]; +N: 4164 "nth_jump" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Env", ]; +N: 3585 "nth_pred_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="BinList", ]; +N: 4163 "nth_pred_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Env", ]; +N: 4165 "nth_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Env", ]; +N: 5274 "nu_constant" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Eqdep_dec", ]; +N: 5275 "nu_left_inv_on" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Eqdep_dec", ]; +N: 4805 "num" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3062 "of_N" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3467 "of_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3475 "of_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="BinNatDef.N", ]; +N: 2783 "of_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3073 "of_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3448 "of_nat_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3444 "of_succ_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3075 "of_succ_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3048 "one_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3280 "one_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2767 "opp" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4457 "opp" [opaque=no, body=yes, kind=cnst, prop=no, path="IntDef.Z", ]; +N: 3641 "opp_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3122 "opp_add_distr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 4469 "opp_add_distr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3120 "opp_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 4624 "opp_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4623 "opp_inj_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5141 "opp_inject_Q" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveCauchyReals", ]; +N: 4470 "opp_involutive" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4749 "opp_le_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4479 "opp_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4491 "opp_nonneg_nonpos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5017 "opp_nonpos_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4477 "opp_pos_neg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4471 "opp_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4468 "opp_sub_distr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3640 "opp_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3638 "opp_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2915 "or_cancel_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4268 "or_clause" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4265 "or_clause_cnf" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4307 "or_clause_cnf_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4308 "or_clause_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4264 "or_cnf" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4275 "or_cnf_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4259 "or_cnf_opt" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4296 "or_cnf_opt_cnf_ff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4294 "or_cnf_opt_cnf_ff_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4270 "or_cnf_opt_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 2916 "or_iff_compat_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2873 "or_iff_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 2876 "or_iff_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 2870 "or_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4198 "orb" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4300 "orb_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Bool", ]; +N: 4306 "orb_true_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Bool", ]; +N: 3035 "order_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3389 "order_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3027 "order_induction_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3381 "order_induction_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4725 "padd" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4731 "padd" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 3217 "peano_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3247 "peano_ind" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3717 "peano_rect" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3225 "peano_rect" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2913 "per_partial_app_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2921 "per_partial_app_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 4202 "pexpr_times_nformula" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4215 "pexpr_times_nformula_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4084 "phi_ext1_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4548 "plus_Sn_m" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2984 "plus_n_O" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2982 "plus_n_Sm" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2992 "pointwise_relation" [opaque=no, body=yes, kind=cnst, prop=no, path="Morphisms", ]; +N: 4181 "pop2_bop2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="QMicromega", ]; +N: 4757 "pop2_bop2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4010 "popp" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4498 "popp" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 3668 "pos_div_eucl" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3491 "pos_div_eucl" [opaque=no, body=yes, kind=cnst, prop=no, path="NatDef.N", ]; +N: 4580 "pos_div_eucl" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4601 "pos_div_eucl_bound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4614 "pos_div_eucl_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3669 "pos_div_eucl_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 4379 "pos_is_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Z", ]; +N: 3430 "pos_le_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos2Z", ]; +N: 2762 "pos_sub" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4461 "pos_sub" [opaque=no, body=yes, kind=cnst, prop=no, path="IntDef.Z", ]; +N: 3125 "pos_sub_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_BootStrap", ]; +N: 3240 "pos_sub_diag" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3554 "pos_sub_discr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4621 "pos_sub_gt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4602 "pos_sub_lt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3123 "pos_sub_opp" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3144 "pos_sub_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3116 "positive_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 3072 "positive_nat_Z" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4346 "positive_rec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 2780 "pow" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 4378 "pow" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3499 "pow" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 2838 "pow_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4768 "pow_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4787 "pow_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4790 "pow_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3516 "pow_N" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4873 "pow_N_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4085 "pow_N_pow_N" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4045 "pow_N_th" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4368 "pow_add_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2804 "pow_eq_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_NZPow", ]; +N: 4874 "pow_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4766 "pow_neg_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4386 "pow_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2797 "pow_nonzero" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 2803 "pow_nonzero" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_NZPow", ]; +N: 2743 "pow_pos" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3662 "pow_pos" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4932 "pow_pos_0" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4933 "pow_pos_1" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4123 "pow_pos_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 3550 "pow_pos_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3580 "pow_pos_add" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4984 "pow_pos_add_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4934 "pow_pos_cst" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4963 "pow_pos_div" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4936 "pow_pos_mul_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4983 "pow_pos_mul_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4385 "pow_pos_nonneg" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4858 "pow_pos_nz" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3581 "pow_pos_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3582 "pow_pos_swap" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2837 "pow_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4792 "pow_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4767 "pow_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5047 "pow_succ_r'" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4789 "pow_twice_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2815 "pow_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4765 "pow_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2956 "pow_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="PeanoNat.Nat", ]; +N: 2893 "pred" [opaque=no, body=yes, kind=cnst, prop=no, path="Init.Nat", ]; +N: 3712 "pred" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 2792 "pred" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 3190 "pred" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3235 "pred" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3777 "pred_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3050 "pred_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3716 "pred_N" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3713 "pred_N" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3714 "pred_N_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3152 "pred_double" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2763 "pred_double" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 2764 "pred_double" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4462 "pred_double" [opaque=no, body=yes, kind=cnst, prop=no, path="IntDef.Z", ]; +N: 3715 "pred_double_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3643 "pred_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3637 "pred_inj_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3184 "pred_mask" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3710 "pred_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2924 "pred_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3236 "pred_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3711 "pred_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2925 "pred_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3237 "pred_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2926 "pred_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="PeanoNat.Nat", ]; +N: 3931 "prod_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 5187 "prod_rect" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3464 "proj1" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 2779 "proj1_sig" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4092 "proj2" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3850 "proper_prf" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 3013 "proper_sym_impl_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 3959 "psub" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4438 "psub" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4586 "psubC" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 3919 "qdeduce" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 3923 "qunsat" [opaque=no, body=yes, kind=cnst, prop=no, path="QMicromega", ]; +N: 3488 "quotrem" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3665 "quotrem_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3812 "r_list_pow" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3831 "r_list_pow_rev" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 5002 "radd_ext" [opaque=no, body=yes, kind=cnst, prop=yes, path="Field_theory", ]; +N: 3563 "radd_ext2_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4071 "radd_ext3_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4930 "radd_ext4_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4022 "radd_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 4881 "radd_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Field_theory", ]; +N: 3866 "radd_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3537 "radd_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 5339 "radix_val" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4947 "rdiv1" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4952 "rdiv2b" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4953 "rdiv3b" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4970 "rdiv4" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4954 "rdiv4b" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4948 "rdiv5" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4949 "rdiv6" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5000 "rdiv7" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4955 "rdiv7b" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4957 "rdiv_ext" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5001 "rdiv_r_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4972 "rdiv_simpl" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3143 "reflexive_eq_dom_reflexive" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 3139 "reflexive_proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 5068 "reflexive_proper_proxy" [opaque=yes, body=yes, kind=cnst, prop=no, path="CMorphisms", ]; +N: 2835 "reflexive_proper_proxy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2817 "reflexive_reflexive_proxy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2829 "reflexivity" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 5335 "rel_ls_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="ConstructiveEpsilon", ]; +N: 5324 "rel_ls_post" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ConstructiveEpsilon", ]; +N: 2842 "relation" [opaque=no, body=yes, kind=cnst, prop=no, path="Relation_Definitions", ]; +N: 5091 "respectful" [opaque=no, body=yes, kind=cnst, prop=no, path="CMorphisms", ]; +N: 2826 "respectful" [opaque=no, body=yes, kind=cnst, prop=no, path="Morphisms", ]; +N: 3818 "rev'" [opaque=no, body=yes, kind=cnst, prop=no, path="List", ]; +N: 3820 "rev_append" [opaque=no, body=yes, kind=cnst, prop=no, path="List", ]; +N: 4365 "rew_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZifyClasses", ]; +N: 4793 "rew_iff_rev" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZifyClasses", ]; +N: 3136 "rewrite_relation_eq_dom" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 3729 "right_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2996 "right_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3360 "right_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3507 "ring_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 5195 "ring_rw_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3804 "ring_rw_pow_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3068 "ring_subst_niter" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4958 "rinv_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4042 "rle_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4011 "rle_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4030 "rlt_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4014 "rlt_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4166 "rminus_morph" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4144 "rminus_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4112 "rminus_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4985 "rmul_ext" [opaque=no, body=yes, kind=cnst, prop=yes, path="Field_theory", ]; +N: 3609 "rmul_ext2_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4058 "rmul_ext3_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4929 "rmul_ext4_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4024 "rmul_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 4860 "rmul_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Field_theory", ]; +N: 3868 "rmul_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3528 "rmul_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4971 "rmul_reg_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3589 "ropp_ext2_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4069 "ropp_ext3_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4130 "ropp_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 4856 "ropp_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Field_theory", ]; +N: 3527 "ropp_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4044 "ropp_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4088 "ropp_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4852 "ropp_neq_0" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4038 "rplus_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4089 "rplus_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 3531 "rpow_pow_N" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4956 "rsplit_common" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4962 "rsplit_left" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4961 "rsplit_right" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4877 "rsub_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4878 "rsub_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4129 "rsub_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="EnvRing", ]; +N: 4879 "rsub_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Field_theory", ]; +N: 3526 "rsub_ext_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 4049 "rtimes_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4087 "rtimes_morph_Proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 3940 "rtyp" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4073 "same_gen" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4927 "same_genN" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4066 "same_genZ" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5157 "scale" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 5055 "seq" [opaque=no, body=yes, kind=cnst, prop=no, path="ConstructiveCauchyReals", ]; +N: 4571 "sgn" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3835 "sig_forall_dec" [opaque=yes, body=no, kind=cnst, prop=no, path="ClassicalDedekindReals", ]; +N: 3828 "sign_spec" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 4535 "size_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 4549 "size_nat_monotone" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3615 "snd" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4031 "sor_setoid" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4028 "sor_setoid_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4048 "sor_setoid_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4039 "sor_setoid_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="OrderedRing", ]; +N: 4950 "split" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4974 "split_aux" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 4975 "split_aux_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4977 "split_aux_ok1" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5003 "split_nz_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 5004 "split_nz_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4959 "split_ok_l" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 4960 "split_ok_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3037 "strong_left_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3391 "strong_left_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3733 "strong_right_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2998 "strong_right_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3362 "strong_right_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3674 "sub" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3493 "sub" [opaque=no, body=yes, kind=cnst, prop=no, path="NatDef.N", ]; +N: 3149 "sub" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3130 "sub" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3340 "sub" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4458 "sub" [opaque=no, body=yes, kind=cnst, prop=no, path="IntDef.Z", ]; +N: 4540 "sub_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3725 "sub_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3634 "sub_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4476 "sub_1_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3677 "sub_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3135 "sub_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3131 "sub_add_distr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4544 "sub_cancel_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4547 "sub_decr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3722 "sub_diag" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3630 "sub_diag" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3778 "sub_gt" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 4742 "sub_le_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 5181 "sub_lt_mono_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3151 "sub_mask" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3226 "sub_mask" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3173 "sub_mask_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3172 "sub_mask_add_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3202 "sub_mask_add_diag_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3185 "sub_mask_carry" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3179 "sub_mask_carry_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3150 "sub_mask_diag" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3201 "sub_mask_neg_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3205 "sub_mask_nul_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3165 "sub_mask_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3169 "sub_mask_pos'" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3171 "sub_mask_pos_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3174 "sub_mask_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3727 "sub_mask_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4733 "sub_move_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4647 "sub_move_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4478 "sub_opp_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4480 "sub_opp_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 4466 "sub_simpl_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3142 "sub_sub_distr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4467 "sub_sub_distr" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3724 "sub_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3635 "sub_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3726 "sub_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3341 "sub_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3719 "sub_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3633 "sub_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3158 "sub_xI_xI" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3159 "sub_xI_xO" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3160 "sub_xO_xI" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3161 "sub_xO_xO" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 5186 "subrelation" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 2843 "subrelation" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 5072 "subrelation_proper" [opaque=yes, body=yes, kind=cnst, prop=no, path="CMorphisms", ]; +N: 2814 "subrelation_proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 5078 "subrelation_refl" [opaque=yes, body=yes, kind=cnst, prop=no, path="CMorphisms", ]; +N: 2818 "subrelation_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 5070 "subrelation_respectful" [opaque=yes, body=yes, kind=cnst, prop=no, path="CMorphisms", ]; +N: 2840 "subrelation_respectful" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 3699 "succ" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 2755 "succ" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2752 "succ" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3103 "succ" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3680 "succ_double" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3495 "succ_double" [opaque=no, body=yes, kind=cnst, prop=no, path="NatDef.N", ]; +N: 2766 "succ_double" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 4464 "succ_double" [opaque=no, body=yes, kind=cnst, prop=no, path="IntDef.Z", ]; +N: 3682 "succ_double_add" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 3157 "succ_double_mask" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 3230 "succ_double_mask" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 3683 "succ_double_mul" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 4604 "succ_double_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3709 "succ_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2922 "succ_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3195 "succ_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3234 "succ_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3702 "succ_inj_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2912 "succ_inj_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3110 "succ_inj_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3034 "succ_le_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3388 "succ_le_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2995 "succ_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4606 "succ_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3359 "succ_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3198 "succ_not_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3067 "succ_of_nat" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 3869 "succ_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3246 "succ_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3180 "succ_pred_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 5291 "succ_pred_or" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 2790 "succ_pred_pos" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3707 "succ_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="N", ]; +N: 2908 "succ_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 3233 "succ_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 2909 "succ_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="PeanoNat.Nat", ]; +N: 4345 "sumbool_rec" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3162 "switch_Eq" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 5088 "symmetry" [opaque=no, body=yes, kind=cnst, prop=no, path="CRelationClasses", ]; +N: 2880 "symmetry" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 3997 "tail" [opaque=no, body=yes, kind=cnst, prop=no, path="Env", ]; +N: 4249 "tauto_checker" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3920 "tauto_checker_sound" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 3455 "tl" [opaque=no, body=yes, kind=cnst, prop=no, path="List", ]; +N: 4375 "to_N" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 3473 "to_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="N", ]; +N: 3070 "to_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="Pos", ]; +N: 2787 "to_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="PosDef.Pos", ]; +N: 2782 "to_nat" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 5153 "to_pos" [opaque=no, body=yes, kind=cnst, prop=no, path="Z", ]; +N: 5246 "total_order_T" [opaque=yes, body=yes, kind=cnst, prop=no, ]; +N: 4682 "trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos.Private_Tac", ]; +N: 3395 "trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Qminmax.Q.Private_Tac", ]; +N: 5226 "trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_Tac", ]; +N: 3757 "trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="N.Private_OrderTac.Tac", ]; +N: 2946 "trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 3347 "trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z.Private_OrderTac.Tac", ]; +N: 2827 "trans_co_eq_inv_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2931 "trans_co_eq_inv_impl_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2923 "trans_co_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2927 "trans_co_impl_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2952 "trans_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="OrdersTac", ]; +N: 2878 "trans_sym_co_inv_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 2898 "trans_sym_co_inv_impl_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 5276 "trans_sym_eq" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Eqdep_dec", ]; +N: 2901 "transitivity" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 3076 "triv_div" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3845 "triv_div_th" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 3047 "two_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 4567 "two_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Z", ]; +N: 3005 "well_founded" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3001 "well_founded_induction" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 3014 "well_founded_induction_type" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 5256 "xI_succ_xO" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Pos", ]; +N: 4252 "xcnf" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 4250 "xcnf_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4273 "xcnf_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4274 "xcnf_impl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Tauto", ]; +N: 4169 "xnegate" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4428 "xnegate" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4167 "xnegate_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4430 "xnegate_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4427 "xnnormalise" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 4431 "xnnormalise_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 3942 "xnormalise" [opaque=no, body=yes, kind=cnst, prop=no, path="RingMicromega", ]; +N: 4761 "xnormalise" [opaque=no, body=yes, kind=cnst, prop=no, path="ZMicromega", ]; +N: 3947 "xnormalise_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="RingMicromega", ]; +N: 4762 "xnormalise_correct" [opaque=yes, body=yes, kind=cnst, prop=yes, path="ZMicromega", ]; +N: 4266 "xor_clause_cnf" [opaque=no, body=yes, kind=cnst, prop=no, path="Tauto", ]; +N: 3278 "zmon_pred" [opaque=no, body=yes, kind=cnst, prop=no, path="Ring_polynom", ]; +N: 3625 "zmon_pred_ok" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Ring_polynom", ]; +N: 3008 "Acc" [kind=inductive, prop=no, ]; +N: 3575 "BoolSpec" [kind=inductive, prop=no, ]; +N: 2733 "CReal" [kind=inductive, prop=no, path="ConstructiveCauchyReals", ]; +N: 3147 "CompareSpec" [kind=inductive, prop=no, ]; +N: 4707 "CompareSpecT" [kind=inductive, prop=no, ]; +N: 3437 "DefaultRelation" [kind=inductive, prop=no, path="SetoidTactics", ]; +N: 5103 "Equivalence" [kind=inductive, prop=no, path="CRelationClasses", ]; +N: 2845 "Equivalence" [kind=inductive, prop=no, path="RelationClasses", ]; +N: 4938 "FExpr" [kind=inductive, prop=no, ]; +N: 2773 "False" [kind=inductive, prop=no, ]; +N: 3883 "Formula" [kind=inductive, prop=no, path="RingMicromega", ]; +N: 4195 "GFormula" [kind=inductive, prop=no, path="Tauto", ]; +N: 4774 "InjTyp" [kind=inductive, prop=no, path="ZifyClasses", ]; +N: 3086 "Mon" [kind=inductive, prop=no, path="Ring_polynom", ]; +N: 3098 "N" [kind=inductive, prop=no, ]; +N: 3938 "Op1" [kind=inductive, prop=no, path="RingMicromega", ]; +N: 3898 "Op2" [kind=inductive, prop=no, path="RingMicromega", ]; +N: 2856 "PER" [kind=inductive, prop=no, path="RelationClasses", ]; +N: 3897 "PExpr" [kind=inductive, prop=no, path="EnvRing", ]; +N: 3088 "PExpr" [kind=inductive, prop=no, path="Ring_polynom", ]; +N: 2943 "Params" [kind=inductive, prop=no, path="Morphisms", ]; +N: 3960 "Pol" [kind=inductive, prop=no, path="EnvRing", ]; +N: 3087 "Pol" [kind=inductive, prop=no, path="Ring_polynom", ]; +N: 3021 "PreOrder" [kind=inductive, prop=no, path="RelationClasses", ]; +N: 4200 "Psatz" [kind=inductive, prop=no, path="RingMicromega", ]; +N: 2736 "Q" [kind=inductive, prop=no, path="QArith_base", ]; +N: 3148 "RewriteRelation" [kind=inductive, prop=no, path="RelationClasses", ]; +N: 3956 "SOR" [kind=inductive, prop=no, path="OrderedRing", ]; +N: 3955 "SORaddon" [kind=inductive, prop=no, path="RingMicromega", ]; +N: 2936 "StrictOrder" [kind=inductive, prop=no, path="RelationClasses", ]; +N: 3175 "SubMaskSpec" [kind=inductive, prop=no, path="Pos", ]; +N: 2798 "True" [kind=inductive, prop=no, ]; +N: 2706 "Z" [kind=inductive, prop=no, ]; +N: 4389 "ZArithProof" [kind=inductive, prop=no, path="ZMicromega", ]; +N: 4592 "Zdivide_pol" [kind=inductive, prop=no, path="ZMicromega", ]; +N: 4829 "almost_field_theory" [kind=inductive, prop=no, ]; +N: 3515 "almost_ring_theory" [kind=inductive, prop=no, ]; +N: 2705 "and" [kind=inductive, prop=no, ]; +N: 5329 "before_witness" [kind=inductive, prop=no, path="ConstructiveEpsilon", ]; +N: 2714 "bool" [kind=inductive, prop=no, ]; +N: 2712 "comparison" [kind=inductive, prop=no, ]; +N: 3511 "div_theory" [kind=inductive, prop=no, ]; +N: 2715 "eq" [kind=inductive, prop=no, ]; +N: 2999 "ex" [kind=inductive, prop=no, ]; +N: 3853 "field_theory" [kind=inductive, prop=no, ]; +N: 2707 "float" [kind=inductive, prop=no, ]; +N: 5056 "inbetween" [kind=inductive, prop=no, ]; +N: 3899 "kind" [kind=inductive, prop=no, path="Tauto", ]; +N: 2805 "le" [kind=inductive, prop=no, ]; +N: 4807 "linear" [kind=inductive, prop=no, ]; +N: 3089 "list" [kind=inductive, prop=no, ]; +N: 2709 "location" [kind=inductive, prop=no, path="SpecFloat", ]; +N: 5299 "mag_prop" [kind=inductive, prop=no, ]; +N: 3163 "mask" [kind=inductive, prop=no, path="Pos", ]; +N: 3227 "mask" [kind=inductive, prop=no, path="PosDef.Pos", ]; +N: 2786 "nat" [kind=inductive, prop=no, ]; +N: 3268 "option" [kind=inductive, prop=no, ]; +N: 2772 "or" [kind=inductive, prop=no, ]; +N: 2953 "ord" [kind=inductive, prop=no, path="OrdersTac", ]; +N: 2711 "positive" [kind=inductive, prop=no, ]; +N: 3514 "power_theory" [kind=inductive, prop=no, ]; +N: 2704 "prod" [kind=inductive, prop=no, ]; +N: 2708 "radix" [kind=inductive, prop=no, ]; +N: 3688 "reflect" [kind=inductive, prop=no, ]; +N: 5326 "rel_ls" [kind=inductive, prop=no, path="ConstructiveEpsilon", ]; +N: 3513 "ring_eq_ext" [kind=inductive, prop=no, ]; +N: 3512 "ring_morph" [kind=inductive, prop=no, ]; +N: 3631 "ring_theory" [kind=inductive, prop=no, ]; +N: 4973 "rsplit" [kind=inductive, prop=no, ]; +N: 4056 "semi_morph" [kind=inductive, prop=no, ]; +N: 4907 "semi_ring_theory" [kind=inductive, prop=no, ]; +N: 2769 "sig" [kind=inductive, prop=no, ]; +N: 5099 "sigT" [kind=inductive, prop=no, ]; +N: 3806 "sign_theory" [kind=inductive, prop=no, ]; +N: 4906 "sring_eq_ext" [kind=inductive, prop=no, ]; +N: 5111 "sum" [kind=inductive, prop=no, ]; +N: 3837 "sumbool" [kind=inductive, prop=no, ]; +N: 3836 "sumor" [kind=inductive, prop=no, ]; +N: 3882 "t" [kind=inductive, prop=no, path="VarMap", ]; +N: 2958 "unit" [kind=inductive, prop=no, ]; +N: 3009 "Acc_intro" [kind=construct, prop=yes, ]; +N: 3576 "BoolSpecT" [kind=construct, prop=yes, ]; +N: 2778 "mkCReal" [kind=construct, prop=no, path="ConstructiveCauchyReals", ]; +N: 3210 "CompEq" [kind=construct, prop=yes, ]; +N: 4711 "CompEqT" [kind=construct, prop=no, ]; +N: 3438 "Build_DefaultRelation" [kind=construct, prop=yes, path="SetoidTactics", ]; +N: 5104 "Build_Equivalence" [kind=construct, prop=no, path="CRelationClasses", ]; +N: 2902 "Build_Equivalence" [kind=construct, prop=yes, path="RelationClasses", ]; +N: 4964 "FEO" [kind=construct, prop=no, ]; +N: 3895 "Build_Formula" [kind=construct, prop=no, path="RingMicromega", ]; +N: 4284 "TT" [kind=construct, prop=no, path="Tauto", ]; +N: 5005 "mkinj" [kind=construct, prop=no, path="ZifyClasses", ]; +N: 3274 "mon0" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 3476 "N0" [kind=construct, prop=no, ]; +N: 3961 "Equal" [kind=construct, prop=no, path="RingMicromega", ]; +N: 3889 "OpEq" [kind=construct, prop=no, path="RingMicromega", ]; +N: 2857 "Build_PER" [kind=construct, prop=yes, path="RelationClasses", ]; +N: 3884 "PEc" [kind=construct, prop=no, path="EnvRing", ]; +N: 3543 "PEO" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 2944 "Build_Params" [kind=construct, prop=yes, path="Morphisms", ]; +N: 3976 "Pc" [kind=construct, prop=no, path="EnvRing", ]; +N: 3090 "Pc" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 3023 "Build_PreOrder" [kind=construct, prop=yes, path="RelationClasses", ]; +N: 4222 "PsatzLet" [kind=construct, prop=no, path="RingMicromega", ]; +N: 2740 "Qmake" [kind=construct, prop=no, path="QArith_base", ]; +N: 3216 "Build_RewriteRelation" [kind=construct, prop=yes, path="RelationClasses", ]; +N: 4324 "mk_SOR_theory" [kind=construct, prop=yes, path="OrderedRing", ]; +N: 4352 "mk_SOR_addon" [kind=construct, prop=yes, path="RingMicromega", ]; +N: 2940 "Build_StrictOrder" [kind=construct, prop=yes, path="RelationClasses", ]; +N: 3186 "SubIsNul" [kind=construct, prop=yes, path="Pos", ]; +N: 2800 "I" [kind=construct, prop=yes, ]; +N: 2710 "Z0" [kind=construct, prop=no, ]; +N: 4390 "DoneProof" [kind=construct, prop=no, path="ZMicromega", ]; +N: 4639 "Zdiv_Pc" [kind=construct, prop=yes, path="ZMicromega", ]; +N: 4830 "mk_afield" [kind=construct, prop=yes, ]; +N: 3655 "mk_art" [kind=construct, prop=yes, ]; +N: 2850 "conj" [kind=construct, prop=yes, ]; +N: 5330 "stop" [kind=construct, prop=yes, path="ConstructiveEpsilon", ]; +N: 2716 "true" [kind=construct, prop=no, ]; +N: 2724 "Eq" [kind=construct, prop=no, ]; +N: 3666 "mkdiv_th" [kind=construct, prop=yes, ]; +N: 2799 "eq_refl" [kind=construct, prop=yes, ]; +N: 3020 "ex_intro" [kind=construct, prop=yes, ]; +N: 3858 "mk_field" [kind=construct, prop=yes, ]; +N: 5057 "Float" [kind=construct, prop=no, ]; +N: 3896 "isProp" [kind=construct, prop=no, path="Tauto", ]; +N: 2890 "le_n" [kind=construct, prop=yes, ]; +N: 4812 "mk_linear" [kind=construct, prop=no, ]; +N: 3096 "nil" [kind=construct, prop=no, ]; +N: 5060 "loc_Exact" [kind=construct, prop=no, path="SpecFloat", ]; +N: 3164 "IsNul" [kind=construct, prop=no, path="Pos", ]; +N: 3176 "IsNul" [kind=construct, prop=no, path="PosDef.Pos", ]; +N: 2784 "O" [kind=construct, prop=no, ]; +N: 3275 "Some" [kind=construct, prop=no, ]; +N: 2874 "or_introl" [kind=construct, prop=yes, ]; +N: 2947 "OEQ" [kind=construct, prop=no, path="OrdersTac", ]; +N: 2753 "xI" [kind=construct, prop=no, ]; +N: 3663 "mkpow_th" [kind=construct, prop=yes, ]; +N: 3269 "pair" [kind=construct, prop=no, ]; +N: 3696 "ReflectT" [kind=construct, prop=no, ]; +N: 5333 "Rstop" [kind=construct, prop=yes, path="ConstructiveEpsilon", ]; +N: 3664 "mk_reqe" [kind=construct, prop=yes, ]; +N: 3660 "mkmorph" [kind=construct, prop=yes, ]; +N: 3632 "mk_rt" [kind=construct, prop=yes, ]; +N: 4982 "mk_rsplit" [kind=construct, prop=no, ]; +N: 4057 "mkRmorph" [kind=construct, prop=yes, ]; +N: 4908 "mk_srt" [kind=construct, prop=yes, ]; +N: 2801 "exist" [kind=construct, prop=no, ]; +N: 5146 "existT" [kind=construct, prop=no, ]; +N: 3834 "mksign_th" [kind=construct, prop=yes, ]; +N: 4893 "mk_seqe" [kind=construct, prop=yes, ]; +N: 5118 "inl" [kind=construct, prop=no, ]; +N: 3838 "left" [kind=construct, prop=no, ]; +N: 4333 "inleft" [kind=construct, prop=no, ]; +N: 3891 "Empty" [kind=construct, prop=no, path="VarMap", ]; +N: 2841 "tt" [kind=construct, prop=no, ]; +N: 3577 "BoolSpecF" [kind=construct, prop=yes, ]; +N: 3211 "CompLt" [kind=construct, prop=yes, ]; +N: 4712 "CompLtT" [kind=construct, prop=no, ]; +N: 4965 "FEI" [kind=construct, prop=no, ]; +N: 4285 "FF" [kind=construct, prop=no, path="Tauto", ]; +N: 3277 "zmon" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 3477 "Npos" [kind=construct, prop=no, ]; +N: 3962 "NonEqual" [kind=construct, prop=no, path="RingMicromega", ]; +N: 4118 "OpNEq" [kind=construct, prop=no, path="RingMicromega", ]; +N: 3885 "PEX" [kind=construct, prop=no, path="EnvRing", ]; +N: 3544 "PEI" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 3973 "Pinj" [kind=construct, prop=no, path="EnvRing", ]; +N: 3091 "Pinj" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 4223 "PsatzIn" [kind=construct, prop=no, path="RingMicromega", ]; +N: 3187 "SubIsPos" [kind=construct, prop=yes, path="Pos", ]; +N: 2717 "Zpos" [kind=construct, prop=no, ]; +N: 4391 "RatProof" [kind=construct, prop=no, path="ZMicromega", ]; +N: 4640 "Zdiv_Pinj" [kind=construct, prop=yes, path="ZMicromega", ]; +N: 5331 "next" [kind=construct, prop=yes, path="ConstructiveEpsilon", ]; +N: 2721 "false" [kind=construct, prop=no, ]; +N: 2725 "Lt" [kind=construct, prop=no, ]; +N: 3900 "isBool" [kind=construct, prop=no, path="Tauto", ]; +N: 2891 "le_S" [kind=construct, prop=yes, ]; +N: 3097 "cons" [kind=construct, prop=no, ]; +N: 5061 "loc_Inexact" [kind=construct, prop=no, path="SpecFloat", ]; +N: 3167 "IsPos" [kind=construct, prop=no, path="Pos", ]; +N: 3231 "IsPos" [kind=construct, prop=no, path="PosDef.Pos", ]; +N: 2785 "S" [kind=construct, prop=no, ]; +N: 3276 "None" [kind=construct, prop=no, ]; +N: 2875 "or_intror" [kind=construct, prop=yes, ]; +N: 2948 "OLT" [kind=construct, prop=no, path="OrdersTac", ]; +N: 2718 "xO" [kind=construct, prop=no, ]; +N: 3697 "ReflectF" [kind=construct, prop=no, ]; +N: 5334 "Rnext" [kind=construct, prop=yes, path="ConstructiveEpsilon", ]; +N: 5119 "inr" [kind=construct, prop=no, ]; +N: 3839 "right" [kind=construct, prop=no, ]; +N: 4334 "inright" [kind=construct, prop=no, ]; +N: 3892 "Elt" [kind=construct, prop=no, path="VarMap", ]; +N: 3212 "CompGt" [kind=construct, prop=yes, ]; +N: 4713 "CompGtT" [kind=construct, prop=no, ]; +N: 4818 "FEc" [kind=construct, prop=no, ]; +N: 4286 "X" [kind=construct, prop=no, path="Tauto", ]; +N: 3279 "vmon" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 3963 "Strict" [kind=construct, prop=no, path="RingMicromega", ]; +N: 4119 "OpLe" [kind=construct, prop=no, path="RingMicromega", ]; +N: 3886 "PEadd" [kind=construct, prop=no, path="EnvRing", ]; +N: 3545 "PEc" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 3974 "PX" [kind=construct, prop=no, path="EnvRing", ]; +N: 3092 "PX" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 4224 "PsatzSquare" [kind=construct, prop=no, path="RingMicromega", ]; +N: 3188 "SubIsNeg" [kind=construct, prop=yes, path="Pos", ]; +N: 2750 "Zneg" [kind=construct, prop=no, ]; +N: 4392 "CutProof" [kind=construct, prop=no, path="ZMicromega", ]; +N: 4641 "Zdiv_PX" [kind=construct, prop=yes, path="ZMicromega", ]; +N: 2726 "Gt" [kind=construct, prop=no, ]; +N: 3168 "IsNeg" [kind=construct, prop=no, path="Pos", ]; +N: 3177 "IsNeg" [kind=construct, prop=no, path="PosDef.Pos", ]; +N: 2954 "OLE" [kind=construct, prop=no, path="OrdersTac", ]; +N: 2719 "xH" [kind=construct, prop=no, ]; +N: 3893 "Branch" [kind=construct, prop=no, path="VarMap", ]; +N: 4808 "FEX" [kind=construct, prop=no, ]; +N: 3894 "A" [kind=construct, prop=no, path="Tauto", ]; +N: 3964 "NonStrict" [kind=construct, prop=no, path="RingMicromega", ]; +N: 4120 "OpGe" [kind=construct, prop=no, path="RingMicromega", ]; +N: 3887 "PEsub" [kind=construct, prop=no, path="EnvRing", ]; +N: 3093 "PEX" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 4225 "PsatzMulC" [kind=construct, prop=no, path="RingMicromega", ]; +N: 4506 "SplitProof" [kind=construct, prop=no, path="ZMicromega", ]; +N: 4966 "FEadd" [kind=construct, prop=no, ]; +N: 4287 "AND" [kind=construct, prop=no, path="Tauto", ]; +N: 3890 "OpLt" [kind=construct, prop=no, path="RingMicromega", ]; +N: 3888 "PEmul" [kind=construct, prop=no, path="EnvRing", ]; +N: 3094 "PEadd" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 4226 "PsatzMulE" [kind=construct, prop=no, path="RingMicromega", ]; +N: 4507 "deprecated_EnumProof" [kind=construct, prop=no, path="ZMicromega", ]; +N: 4967 "FEsub" [kind=construct, prop=no, ]; +N: 4288 "OR" [kind=construct, prop=no, path="Tauto", ]; +N: 4121 "OpGt" [kind=construct, prop=no, path="RingMicromega", ]; +N: 4155 "PEopp" [kind=construct, prop=no, path="EnvRing", ]; +N: 3095 "PEsub" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 4227 "PsatzAdd" [kind=construct, prop=no, path="RingMicromega", ]; +N: 4508 "ExProof" [kind=construct, prop=no, path="ZMicromega", ]; +N: 4809 "FEmul" [kind=construct, prop=no, ]; +N: 4289 "NOT" [kind=construct, prop=no, path="Tauto", ]; +N: 4156 "PEpow" [kind=construct, prop=no, path="EnvRing", ]; +N: 3490 "PEmul" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 4228 "PsatzC" [kind=construct, prop=no, path="RingMicromega", ]; +N: 4968 "FEopp" [kind=construct, prop=no, ]; +N: 4290 "IMPL" [kind=construct, prop=no, path="Tauto", ]; +N: 3546 "PEopp" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 4229 "PsatzZ" [kind=construct, prop=no, path="RingMicromega", ]; +N: 4810 "FEinv" [kind=construct, prop=no, ]; +N: 4291 "IFF" [kind=construct, prop=no, path="Tauto", ]; +N: 3547 "PEpow" [kind=construct, prop=no, path="Ring_polynom", ]; +N: 4811 "FEdiv" [kind=construct, prop=no, ]; +N: 4292 "EQ" [kind=construct, prop=no, path="Tauto", ]; +N: 4969 "FEpow" [kind=construct, prop=no, ]; +E: 2694 2695 [weight=1, ]; +E: 2694 2696 [weight=2, ]; +E: 2694 2697 [weight=2, ]; +E: 2694 2698 [weight=1, ]; +E: 2694 2699 [weight=1, ]; +E: 2694 2700 [weight=6, ]; +E: 2694 2701 [weight=1, ]; +E: 2694 2702 [weight=1, ]; +E: 2694 2703 [weight=2, ]; +E: 2694 2704 [weight=3, ]; +E: 2694 2705 [weight=1, ]; +E: 2694 2706 [weight=6, ]; +E: 2694 2707 [weight=2, ]; +E: 2694 2708 [weight=1, ]; +E: 2694 2709 [weight=1, ]; +E: 2694 2710 [weight=2, ]; +E: 2695 2706 [weight=4, ]; +E: 2695 2712 [weight=1, ]; +E: 2695 2715 [weight=1, ]; +E: 2695 2720 [weight=1, ]; +E: 2695 2726 [weight=1, ]; +E: 2695 2770 [weight=1, ]; +E: 2696 2706 [weight=3, ]; +E: 2696 2729 [weight=2, ]; +E: 2696 5305 [weight=1, ]; +E: 2696 5343 [weight=1, ]; +E: 2696 5384 [weight=2, ]; +E: 2697 2729 [weight=5, ]; +E: 2697 5338 [weight=1, ]; +E: 2697 5373 [weight=1, ]; +E: 2698 2695 [weight=1, ]; 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+E: 5385 5059 [weight=4, ]; +E: 5385 5373 [weight=2, ]; +E: 5385 5386 [weight=7, ]; +E: 5386 2717 [weight=1, ]; +E: 5386 2719 [weight=2, ]; +E: 5386 2729 [weight=1, ]; +E: 5386 2740 [weight=1, ]; +E: 5386 5063 [weight=1, ]; +E: 5386 5071 [weight=1, ]; diff --git a/tests/NestedModules.v b/tests/NestedModules.v new file mode 100644 index 000000000..3d076fcd7 --- /dev/null +++ b/tests/NestedModules.v @@ -0,0 +1,198 @@ +(* -*- mode: coq; coq-prog-args: ("-emacs" "-w" "-deprecated-native-compiler-option,-native-compiler-disabled" "-native-compiler" "ondemand" "-R" "." "Top" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/Bignums" "Bignums" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/Cheerios" "Cheerios" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/CoqEAL" "CoqEAL" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/Coqprime" "Coqprime" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/Coquelicot" "Coquelicot" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/ExtLib" "ExtLib" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/Flocq" "Flocq" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/HB" "HB" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/ITree" "ITree" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/InfSeqExt" "InfSeqExt" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/Interval" "Interval" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/LF" "LF" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/LeanImport" "LeanImport" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/Ltac2" "Ltac2" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/MenhirLib" "MenhirLib" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/Paco" "Paco" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/QuickChick" "QuickChick" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/RecordUpdate" "RecordUpdate" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/Rewriter" "Rewriter" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/SimpleIO" "SimpleIO" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/StructTact" "StructTact" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/VST" "VST" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/Verdi" "Verdi" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/compcert" "compcert" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/coqutil" "coqutil" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/deriving" "deriving" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/dpdgraph" "dpdgraph" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/elpi" "elpi" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/elpi_elpi" "elpi_elpi" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/elpi_examples" "elpi_examples" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/extructures" "extructures" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/iris" "iris" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/iris_ora" "iris_ora" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/mathcomp" "mathcomp" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/riscv" "riscv" "-Q" "/mnt/disks/data/jason/.opam/4.14.2/lib/coq/user-contrib/stdpp" "stdpp" "-top" "Top.make_dpd") -*- *) +(* File reduced by coq-bug-minimizer from original input, then from 21 lines to 5 lines, then from 19 lines to 204 lines, then from 211 lines to 59 lines, then from 73 lines to 2518 lines, then from 2521 lines to 80 lines, then from 94 lines to 809 lines, then from 816 lines to 164 lines, then from 178 lines to 286 lines, then from 293 lines to 196 lines, then from 210 lines to 2673 lines, then from 2675 lines to 262 lines, then from 276 lines to 1462 lines, then from 1469 lines to 306 lines, then from 320 lines to 1362 lines, then from 1369 lines to 359 lines, then from 373 lines to 383 lines, then from 390 lines to 359 lines, then from 374 lines to 361 lines, then from 376 lines to 188 lines, then from 203 lines to 188 lines *) +(* coqc version 9.1+alpha compiled with OCaml 4.14.2 + coqtop version 9.1+alpha + Expected coqc runtime on this file: 0.592 sec + Expected coqc peak memory usage on this file: 454800.0 kb *) +Require Stdlib.Floats.SpecFloat. +Require Stdlib.Reals.Reals. +Import Stdlib.ZArith.ZArith. + +Record radix := { radix_val :> Z ; radix_prop : Zle_bool 2 radix_val = true }. +Fixpoint digits2_Pnat (n : positive) : nat. +Admitted. + +Section Fcore_digits. + +Variable beta : radix. + +Section digits_aux. + +Variable p : Z. + +Fixpoint Zdigits_aux (nb pow : Z) (n : nat) { struct n } : Z := + match n with + | O => nb + | S n => if Zlt_bool p pow then nb else Zdigits_aux (nb + 1) (Zmult beta pow) n + end. + +End digits_aux. + +Definition Zdigits n := + match n with + | Z0 => Z0 + | Zneg p => Zdigits_aux (Zpos p) 1 beta (digits2_Pnat p) + | Zpos p => Zdigits_aux n 1 beta (digits2_Pnat p) + end. + +End Fcore_digits. +Import Stdlib.Reals.Reals. + +Definition Rcompare x y := + match total_order_T x y with + | inleft (left _) => Lt + | inleft (right _) => Eq + | inright _ => Gt + end. + +Section pow. + +Variable r : radix. + +Definition bpow e := + match e with + | Zpos p => IZR (Zpower_pos r p) + | Zneg p => Rinv (IZR (Zpower_pos r p)) + | Z0 => 1%R + end. + +Record mag_prop x := { + mag_val :> Z ; + _ : (x <> 0)%R -> (bpow (mag_val - 1)%Z <= Rabs x < bpow mag_val)%R +}. + +Definition mag : + forall x : R, mag_prop x. +Admitted. + +End pow. + +Section Def. + +Record float (beta : radix) := Float { Fnum : Z ; Fexp : Z }. + +Arguments Fnum {beta}. +Arguments Fexp {beta}. + +Variable beta : radix. + +Definition F2R (f : float beta) := + (IZR (Fnum f) * bpow beta (Fexp f))%R. + +End Def. +Arguments F2R {beta}. + +Notation location := SpecFloat.location (only parsing). +Notation loc_Exact := SpecFloat.loc_Exact (only parsing). +Notation loc_Inexact := SpecFloat.loc_Inexact (only parsing). + +Section Fcalc_bracket. + +Variable d u : R. + +Variable x : R. + +Inductive inbetween : location -> Prop := + | inbetween_Exact : x = d -> inbetween loc_Exact + | inbetween_Inexact l : (d < x < u)%R -> Rcompare x ((d + u) / 2)%R = l -> inbetween (loc_Inexact l). + +End Fcalc_bracket. + +Section Fcalc_bracket_step. +Variable nb_steps : Z. + +Definition new_location_even k l := + if Zeq_bool k 0 then + match l with loc_Exact => l | _ => loc_Inexact Lt end + else + loc_Inexact + match Z.compare (2 * k) nb_steps with + | Lt => Lt + | Eq => match l with loc_Exact => Eq | _ => Gt end + | Gt => Gt + end. + +Definition new_location_odd k l := + if Zeq_bool k 0 then + match l with loc_Exact => l | _ => loc_Inexact Lt end + else + loc_Inexact + match Z.compare (2 * k + 1) nb_steps with + | Lt => Lt + | Eq => match l with loc_Inexact l => l | loc_Exact => Lt end + | Gt => Gt + end. + +Definition new_location := + if Z.even nb_steps then new_location_even else new_location_odd. + +End Fcalc_bracket_step. + +Section Fcalc_bracket_generic. + +Variable beta : radix. + +Definition inbetween_float m e x l := + inbetween (F2R (Float beta m e)) (F2R (Float beta (m + 1) e)) x l. + +End Fcalc_bracket_generic. + +Section Generic. + +Variable beta : radix. + +Variable fexp : Z -> Z. + +Definition cexp x := + fexp (mag beta x). + +End Generic. + +Module Export Flocq_DOT_Calc_DOT_Div_WRAPPED. +Module Export Div. + +Section Fcalc_div. + +Variable beta : radix. + +Variable fexp : Z -> Z. + +Definition Fdiv_core m1 e1 m2 e2 e := + let (m1', m2') := + if Zle_bool e (e1 - e2)%Z + then (m1 * Zpower beta (e1 - e2 - e), m2)%Z + else (m1, m2 * Zpower beta (e - (e1 - e2)))%Z in + let '(q, r) := Z.div_eucl m1' m2' in + (q, new_location m2' r loc_Exact). + +Definition Fdiv (x y : float beta) := + let (m1, e1) := x in + let (m2, e2) := y in + let e' := ((Zdigits beta m1 + e1) - (Zdigits beta m2 + e2))%Z in + let e := Z.min (Z.min (fexp e') (fexp (e' + 1))) (e1 - e2) in + let '(m, l) := Fdiv_core m1 e1 m2 e2 e in + (m, e, l). + +Theorem Fdiv_correct : + forall x y, + (0 < F2R x)%R -> (0 < F2R y)%R -> + let '(m, e, l) := Fdiv x y in + (e <= cexp beta fexp (F2R x / F2R y))%Z /\ + inbetween_float beta m e (F2R x / F2R y) l. +Admitted. + +End Fcalc_div. + +End Div. +End Flocq_DOT_Calc_DOT_Div_WRAPPED. +Module Export Flocq. +Module Export Calc. +Module Export Div. +Include Flocq_DOT_Calc_DOT_Div_WRAPPED.Div. +End Div. +End Calc. +End Flocq. + +Require Import dpdgraph.dpdgraph. +Set DependGraph File "NestedModules.dpd". +Print DependGraph Flocq.Calc.Div.Fdiv_correct. diff --git a/tests/PeanoNatBitwise.cmd b/tests/PeanoNatBitwise.cmd new file mode 100644 index 000000000..dd6b20075 --- /dev/null +++ b/tests/PeanoNatBitwise.cmd @@ -0,0 +1,4 @@ +Load "PeanoNatBitwise.v". +Require Import dpdgraph.dpdgraph. +Set DependGraph File "PeanoNatBitwise.dpd". +Print DependGraph Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec.land_spec. diff --git a/tests/PeanoNatBitwise.dot.oracle b/tests/PeanoNatBitwise.dot.oracle new file mode 100644 index 000000000..4e5afdfd8 --- /dev/null +++ b/tests/PeanoNatBitwise.dot.oracle @@ -0,0 +1,871 @@ +digraph tests/PeanoNatBitwise { + graph [ratio=0.5] + node [style=filled] +Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 [label="iff_iff_iff_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Nat_even_spec [label="even_spec", URL=, fillcolor="#7FFFD4"] ; +Nat_neq_succ_diag_l [label="neq_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +_negb [label="negb", URL=<.html#negb>, fillcolor="#F070D1"] ; +Nat_nlt_succ_diag_l [label="nlt_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +Nat_add_0_l [label="add_0_l", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_le_incl [label="lt_le_incl", URL=, fillcolor="#7FFFD4"] ; +Nat_Odd [label="Odd", URL=, fillcolor="#F070D1"] ; +Morphisms_iff_flip_impl_subrelation [label="iff_flip_impl_subrelation", URL=, fillcolor="#7FFFD4"] ; +Nat_Even [label="Even", URL=, fillcolor="#F070D1"] ; +Nat_odd_spec [label="odd_spec", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_succ_diag_r [label="lt_succ_diag_r", URL=, fillcolor="#7FFFD4"] ; +_and [label="and", URL=<.html#and>, fillcolor="#E2CDFA"] ; +Nat_le_refl [label="le_refl", URL=, fillcolor="#7FFFD4"] ; +_true [label="true", URL=<.html#true>, fillcolor="#7FAAFF"] ; +Nat_compare_refl [label="compare_refl", URL=, fillcolor="#7FFFD4"] ; +_ex_intro [label="ex_intro", URL=<.html#ex_intro>, fillcolor="#7FAAFF"] ; +Morphisms_Prop_not_iff_morphism [label="not_iff_morphism", URL=, fillcolor="#7FFFD4"] ; +_iff [label="iff", URL=<.html#iff>, fillcolor="#F070D1"] ; +Nat_compare [label="compare", URL=, fillcolor="#F070D1"] ; +Nat_compare_lt_iff [label="compare_lt_iff", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_Parity_Odd_0 [label="Odd_0", URL=, fillcolor="#7FFFD4"] ; +_comparison [label="comparison", URL=<.html#comparison>, fillcolor="#E2CDFA"] ; +Nat_Private_Parity_Odd_1 [label="Odd_1", URL=, fillcolor="#7FFFD4"] ; +_Eq [label="Eq", URL=<.html#Eq>, fillcolor="#7FAAFF"] ; +Nat_Private_Parity_Odd_2 [label="Odd_2", URL=, fillcolor="#7FFFD4"] ; +_Lt [label="Lt", URL=<.html#Lt>, fillcolor="#7FAAFF"] ; +Morphisms_trans_co_eq_inv_impl_morphism [label="trans_co_eq_inv_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +_le_0_n [label="le_0_n", URL=<.html#le_0_n>, fillcolor="#7FFFD4"] ; +Morphisms_eq_proper_proxy [label="eq_proper_proxy", URL=, fillcolor="#7FFFD4"] ; +_le_n_S [label="le_n_S", URL=<.html#le_n_S>, fillcolor="#7FFFD4"] ; +RelationClasses_iff_Transitive [label="iff_Transitive", URL=, fillcolor="#7FFFD4"] ; +_Gt [label="Gt", URL=<.html#Gt>, fillcolor="#7FAAFF"] ; +_conj [label="conj", URL=<.html#conj>, fillcolor="#7FAAFF"] ; +Morphisms_Prop_not_iff_morphism_obligation_1 [label="not_iff_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_Transitive [label="Transitive", URL=, fillcolor="#F070D1"] ; +_iff_trans [label="iff_trans", URL=<.html#iff_trans>, fillcolor="#7FFFD4"] ; +Nat_compare_eq_iff [label="compare_eq_iff", URL=, fillcolor="#7FFFD4"] ; +Relation_Definitions_relation [label="relation", URL=, fillcolor="#F070D1"] ; +_eq_add_S [label="eq_add_S", URL=<.html#eq_add_S>, fillcolor="#7FFFD4"] ; +Nat_compare_le_iff [label="compare_le_iff", URL=, fillcolor="#7FFFD4"] ; +Morphisms_ProperProxy [label="ProperProxy", URL=, fillcolor="#F070D1"] ; +Morphisms_impl_pars [label="impl_pars", URL=, fillcolor="#7FFFD4"] ; +Basics_flip [label="flip", URL=, fillcolor="#F070D1"] ; +Nat_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +Basics_impl [label="impl", URL=, fillcolor="#F070D1"] ; +Morphisms_Params [label="Params", URL=, fillcolor="#E2CDFA"] ; +Morphisms_Proper [label="Proper", URL=, fillcolor="#F070D1"] ; +Morphisms_respectful [label="respectful", URL=, fillcolor="#F070D1"] ; +Nat_lt_asymm [label="lt_asymm", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Build_Params [label="Build_Params", URL=, fillcolor="#7FAAFF"] ; +Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 [label="trans_co_eq_inv_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_transitivity [label="transitivity", URL=, fillcolor="#7FFFD4"] ; +Nat_eq_le_incl [label="eq_le_incl", URL=, fillcolor="#7FFFD4"] ; +_plus_n_Sm [label="plus_n_Sm", URL=<.html#plus_n_Sm>, fillcolor="#7FFFD4"] ; +Nat_le_le_succ_r [label="le_le_succ_r", URL=, fillcolor="#7FFFD4"] ; +_plus_n_O [label="plus_n_O", URL=<.html#plus_n_O>, fillcolor="#7FFFD4"] ; +Nat_le_succ_r [label="le_succ_r", URL=, fillcolor="#7FFFD4"] ; +Nat_neq_succ_0 [label="neq_succ_0", URL=, fillcolor="#7FFFD4"] ; +_f_equal [label="f_equal", URL=<.html#f_equal>, fillcolor="#7FFFD4"] ; +_ex [label="ex", URL=<.html#ex>, fillcolor="#E2CDFA"] ; +Nat_pred_0 [label="pred_0", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +Init_Nat_add [label="add", URL=, fillcolor="#F070D1"] ; +Nat_Private_OrderTac_Tac_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +_f_equal_nat [label="f_equal_nat", URL=<.html#f_equal_nat>, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_not_gt_le [label="not_gt_le", URL=, fillcolor="#7FFFD4"] ; +_not [label="not", URL=<.html#not>, fillcolor="#F070D1"] ; +Nat_Private_OrderTac_IsTotal_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_Parity_Even_0 [label="Even_0", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_IsTotal_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_Parity_Even_1 [label="Even_1", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_Parity_Even_2 [label="Even_2", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_trichotomy [label="lt_trichotomy", URL=, fillcolor="#7FFFD4"] ; +Nat_add_wd [label="add_wd", URL=, fillcolor="#7FFFD4"] ; +Nat_le_gt_cases [label="le_gt_cases", URL=, fillcolor="#7FFFD4"] ; +Nat_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +Morphisms_reflexive_reflexive_proxy [label="reflexive_reflexive_proxy", URL=, fillcolor="#7FFFD4"] ; +Nat_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +Nat_succ_inj_wd [label="succ_inj_wd", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_StrictOrder_Irreflexive [label="StrictOrder_Irreflexive", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_IsTotal_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Reflexive_partial_app_morphism [label="Reflexive_partial_app_morphism", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +Nat_add_succ_l [label="add_succ_l", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_StrictOrder [label="StrictOrder", URL=, fillcolor="#E2CDFA"] ; +Nat_add_succ_r [label="add_succ_r", URL=, fillcolor="#7FFFD4"] ; +Nat_add_0_r [label="add_0_r", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_Irreflexive [label="Irreflexive", URL=, fillcolor="#F070D1"] ; +RelationClasses_iff_equivalence [label="iff_equivalence", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_complement [label="complement", URL=, fillcolor="#F070D1"] ; +RelationClasses_Build_StrictOrder [label="Build_StrictOrder", URL=, fillcolor="#7FAAFF"] ; +Morphisms_per_partial_app_morphism [label="per_partial_app_morphism", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_trans [label="trans", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_Equivalence_Transitive [label="Equivalence_Transitive", URL=, fillcolor="#7FFFD4"] ; +OrdersTac_OLT [label="OLT", URL=, fillcolor="#7FAAFF"] ; +Morphisms_trans_sym_co_inv_impl_morphism [label="trans_sym_co_inv_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_StrictOrder_Transitive [label="StrictOrder_Transitive", URL=, fillcolor="#7FFFD4"] ; +Morphisms_PER_morphism [label="PER_morphism", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_IsTotal_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +Nat_bi_induction [label="bi_induction", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_reflexivity [label="reflexivity", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_IsTotal_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_interp_ord [label="interp_ord", URL=, fillcolor="#F070D1"] ; +RelationClasses_Equivalence_PER [label="Equivalence_PER", URL=, fillcolor="#7FFFD4"] ; +OrdersTac_trans_ord [label="trans_ord", URL=, fillcolor="#F070D1"] ; +RelationClasses_iff_Reflexive [label="iff_Reflexive", URL=, fillcolor="#7FFFD4"] ; +OrdersTac_ord [label="ord", URL=, fillcolor="#E2CDFA"] ; +Morphisms_reflexive_proper_proxy [label="reflexive_proper_proxy", URL=, fillcolor="#7FFFD4"] ; +OrdersTac_OEQ [label="OEQ", URL=, fillcolor="#7FAAFF"] ; +RelationClasses_Equivalence_Reflexive [label="Equivalence_Reflexive", URL=, fillcolor="#7FFFD4"] ; +OrdersTac_OLE [label="OLE", URL=, fillcolor="#7FAAFF"] ; +RelationClasses_Reflexive [label="Reflexive", URL=, fillcolor="#F070D1"] ; +RelationClasses_Equivalence [label="Equivalence", URL=, fillcolor="#E2CDFA"] ; +Nat_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +Nat_Private_OrderTac_Tac_lt_eq [label="lt_eq", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_Symmetric [label="Symmetric", URL=, fillcolor="#F070D1"] ; +Morphisms_ReflexiveProxy [label="ReflexiveProxy", URL=, fillcolor="#F070D1"] ; +_iff_refl [label="iff_refl", URL=<.html#iff_refl>, fillcolor="#7FFFD4"] ; +RelationClasses_Equivalence_Symmetric [label="Equivalence_Symmetric", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_PER [label="PER", URL=, fillcolor="#E2CDFA"] ; +RelationClasses_Build_PER [label="Build_PER", URL=, fillcolor="#7FAAFF"] ; +Morphisms_PER_morphism_obligation_1 [label="PER_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_PER_Symmetric [label="PER_Symmetric", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_symmetry [label="symmetry", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_PER_Transitive [label="PER_Transitive", URL=, fillcolor="#7FFFD4"] ; +Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 [label="trans_sym_co_inv_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Morphisms_per_partial_app_morphism_obligation_1 [label="per_partial_app_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_iff_Symmetric [label="iff_Symmetric", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_Build_Equivalence [label="Build_Equivalence", URL=, fillcolor="#7FAAFF"] ; +_iff_sym [label="iff_sym", URL=<.html#iff_sym>, fillcolor="#7FFFD4"] ; +Nat_succ_wd [label="succ_wd", URL=, fillcolor="#7FFFD4"] ; +PeanoNat_Nat_succ_wd_obligation_1 [label="succ_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Nat_succ_inj [label="succ_inj", URL=, fillcolor="#7FFFD4"] ; +Morphisms_subrelation_proper [label="subrelation_proper", URL=, fillcolor="#7FFFD4"] ; +Morphisms_subrelation_refl [label="subrelation_refl", URL=, fillcolor="#7FFFD4"] ; +Nat_pred [label="pred", URL=, fillcolor="#F070D1"] ; +Morphisms_trans_co_impl_morphism [label="trans_co_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +Morphisms_iff_impl_subrelation [label="iff_impl_subrelation", URL=, fillcolor="#7FFFD4"] ; +Nat_pred_succ [label="pred_succ", URL=, fillcolor="#7FFFD4"] ; +Nat_pred_wd [label="pred_wd", URL=, fillcolor="#7FFFD4"] ; +Morphisms_subrelation_respectful [label="subrelation_respectful", URL=, fillcolor="#7FFFD4"] ; +_tt [label="tt", URL=<.html#tt>, fillcolor="#7FAAFF"] ; +RelationClasses_subrelation [label="subrelation", URL=, fillcolor="#F070D1"] ; +PeanoNat_Nat_pred_wd_obligation_1 [label="pred_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_and_ind [label="and_ind", URL=<.html#and_ind>, fillcolor="#7FFFD4"] ; +Morphisms_trans_co_impl_morphism_obligation_1 [label="trans_co_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Init_Unconvertible [label="Unconvertible", URL=, fillcolor="#F070D1"] ; +_unit [label="unit", URL=<.html#unit>, fillcolor="#E2CDFA"] ; +RelationClasses_eq_equivalence [label="eq_equivalence", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_eq_Reflexive [label="eq_Reflexive", URL=, fillcolor="#7FFFD4"] ; +RelationClasses_eq_Transitive [label="eq_Transitive", URL=, fillcolor="#7FFFD4"] ; +Nat_PrivateImplementsBitwiseSpec_land_spec [label="land_spec", URL=, peripheries=3, fillcolor="#7FFFD4"] ; +RelationClasses_eq_Symmetric [label="eq_Symmetric", URL=, fillcolor="#7FFFD4"] ; +Nat_land [label="land", URL=, fillcolor="#F070D1"] ; +_eq_trans [label="eq_trans", URL=<.html#eq_trans>, fillcolor="#7FFFD4"] ; +_andb [label="andb", URL=<.html#andb>, fillcolor="#F070D1"] ; +PeanoNat_Nat_add_wd_obligation_1 [label="add_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Nat_testbit [label="testbit", URL=, fillcolor="#F070D1"] ; +Nat_PrivateImplementsBitwiseSpec_div2_succ_double [label="div2_succ_double", URL=, fillcolor="#7FFFD4"] ; +Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 [label="testbit_bitwise_1", URL=, fillcolor="#7FFFD4"] ; +Nat_PrivateImplementsBitwiseSpec_div2_double [label="div2_double", URL=, fillcolor="#7FFFD4"] ; +_nat [label="nat", URL=<.html#nat>, fillcolor="#E2CDFA"] ; +Nat_le_0_l [label="le_0_l", URL=, fillcolor="#7FFFD4"] ; +_bool [label="bool", URL=<.html#bool>, fillcolor="#E2CDFA"] ; +Nat_le_trans [label="le_trans", URL=, fillcolor="#7FFFD4"] ; +_eq [label="eq", URL=<.html#eq>, fillcolor="#E2CDFA"] ; +Nat_succ_le_mono [label="succ_le_mono", URL=, fillcolor="#7FFFD4"] ; +_false [label="false", URL=<.html#false>, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_le_div2 [label="le_div2", URL=, fillcolor="#F070D1"] ; +_eq_refl [label="eq_refl", URL=<.html#eq_refl>, fillcolor="#7FAAFF"] ; +Nat_lt_succ_r [label="lt_succ_r", URL=, fillcolor="#7FFFD4"] ; +_le_n [label="le_n", URL=<.html#le_n>, fillcolor="#7FAAFF"] ; +_lt [label="lt", URL=<.html#lt>, fillcolor="#F070D1"] ; +_S [label="S", URL=<.html#S>, fillcolor="#7FAAFF"] ; +_le_S [label="le_S", URL=<.html#le_S>, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l [label="testbit_0_l", URL=, fillcolor="#F070D1"] ; +_le_S_n [label="le_S_n", URL=<.html#le_S_n>, fillcolor="#7FFFD4"] ; +Nat_odd [label="odd", URL=, fillcolor="#F070D1"] ; +_le_ind [label="le_ind", URL=<.html#le_ind>, fillcolor="#7FFFD4"] ; +_le_pred [label="le_pred", URL=<.html#le_pred>, fillcolor="#7FFFD4"] ; +Nat_div2 [label="div2", URL=, fillcolor="#F070D1"] ; +Init_Nat_pred [label="pred", URL=, fillcolor="#F070D1"] ; +_False_ind [label="False_ind", URL=<.html#False_ind>, fillcolor="#7FFFD4"] ; +Nat_lt_eq_cases [label="lt_eq_cases", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr [label="div2_decr", URL=, fillcolor="#F070D1"] ; +Nat_succ_lt_mono [label="succ_lt_mono", URL=, fillcolor="#7FFFD4"] ; +Nat_PrivateImplementsBitwiseSpec_div2_bitwise [label="div2_bitwise", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Prop_or_iff_morphism [label="or_iff_morphism", URL=, fillcolor="#7FFFD4"] ; +_nat_ind [label="nat_ind", URL=<.html#nat_ind>, fillcolor="#7FFFD4"] ; +_or [label="or", URL=<.html#or>, fillcolor="#E2CDFA"] ; +_eq_ind [label="eq_ind", URL=<.html#eq_ind>, fillcolor="#7FFFD4"] ; +Morphisms_Prop_or_iff_morphism_obligation_1 [label="or_iff_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +_eq_sym [label="eq_sym", URL=<.html#eq_sym>, fillcolor="#7FFFD4"] ; +_or_ind [label="or_ind", URL=<.html#or_ind>, fillcolor="#7FFFD4"] ; +_eq_ind_r [label="eq_ind_r", URL=<.html#eq_ind_r>, fillcolor="#7FFFD4"] ; +_or_introl [label="or_introl", URL=<.html#or_introl>, fillcolor="#7FAAFF"] ; +Nat_bitwise [label="bitwise", URL=, fillcolor="#F070D1"] ; +_or_intror [label="or_intror", URL=<.html#or_intror>, fillcolor="#7FAAFF"] ; +Nat_PrivateImplementsBitwiseSpec_odd_bitwise [label="odd_bitwise", URL=, fillcolor="#7FFFD4"] ; +_True [label="True", URL=<.html#True>, fillcolor="#E2CDFA"] ; +Nat_le_succ_l [label="le_succ_l", URL=, fillcolor="#7FFFD4"] ; +_False [label="False", URL=<.html#False>, fillcolor="#E2CDFA"] ; +Nat_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +_le [label="le", URL=<.html#le>, fillcolor="#E2CDFA"] ; +Nat_nle_succ_diag_l [label="nle_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +_O [label="O", URL=<.html#O>, fillcolor="#7FAAFF"] ; +Nat_central_induction [label="central_induction", URL=, fillcolor="#7FFFD4"] ; +_I [label="I", URL=<.html#I>, fillcolor="#7FAAFF"] ; +Nat_le_wd [label="le_wd", URL=, fillcolor="#7FFFD4"] ; +Bool_negb_false_iff [label="negb_false_iff", URL=, fillcolor="#7FFFD4"] ; +Nat_lt_wd [label="lt_wd", URL=, fillcolor="#7FFFD4"] ; +_or_cancel_r [label="or_cancel_r", URL=<.html#or_cancel_r>, fillcolor="#7FFFD4"] ; +Nat_add_comm [label="add_comm", URL=, fillcolor="#7FFFD4"] ; +_or_iff_compat_r [label="or_iff_compat_r", URL=<.html#or_iff_compat_r>, fillcolor="#7FFFD4"] ; +Nat_add [label="add", URL=, fillcolor="#F070D1"] ; +Nat_mul [label="mul", URL=, fillcolor="#F070D1"] ; +PeanoNat_Nat_lt_wd_obligation_1 [label="lt_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Morphisms_Prop_iff_iff_iff_impl_morphism [label="iff_iff_iff_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +Nat_even [label="even", URL=, fillcolor="#F070D1"] ; + Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> _iff [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> _conj [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> Basics_impl [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> _and_ind [] ; + Nat_even_spec -> Nat_even [] ; + Nat_even_spec -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_even_spec -> Morphisms_eq_proper_proxy [] ; + Nat_even_spec -> RelationClasses_iff_Transitive [] ; + Nat_even_spec -> Nat_Private_Parity_Even_0 [] ; + Nat_even_spec -> Nat_Private_Parity_Even_1 [] ; + Nat_even_spec -> Nat_Private_Parity_Even_2 [] ; + Nat_neq_succ_diag_l -> Nat_lt_irrefl [] ; + Nat_neq_succ_diag_l -> Nat_lt_wd [] ; + Nat_neq_succ_diag_l -> Nat_lt_succ_diag_r [] ; + _negb -> _bool [] ; + _negb -> _false [] ; + _negb -> _true [] ; + Nat_nlt_succ_diag_l -> Nat_lt_succ_r [] ; + Nat_nlt_succ_diag_l -> Nat_lt_irrefl [] ; + Nat_nlt_succ_diag_l -> Nat_lt_le_incl [] ; + Nat_add_0_l -> _eq [] ; + Nat_add_0_l -> _eq_refl [] ; + Nat_add_0_l -> _O [] ; + Nat_add_0_l -> Nat_add [] ; + Nat_lt_le_incl -> Nat_lt_eq_cases [] ; + Nat_Odd -> _eq [] ; + Nat_Odd -> Nat_mul [] ; + Nat_Odd -> _ex [] ; + Morphisms_iff_flip_impl_subrelation -> _iff [] ; + Morphisms_iff_flip_impl_subrelation -> Basics_flip [] ; + Morphisms_iff_flip_impl_subrelation -> Basics_impl [] ; + Morphisms_iff_flip_impl_subrelation -> RelationClasses_subrelation [] ; + Morphisms_iff_flip_impl_subrelation -> _and_ind [] ; + Nat_Even -> _eq [] ; + Nat_Even -> Nat_mul [] ; + Nat_Even -> _ex [] ; + Nat_odd_spec -> Nat_odd [] ; + Nat_odd_spec -> Nat_Private_Parity_Odd_0 [] ; + Nat_odd_spec -> Nat_Private_Parity_Odd_1 [] ; + Nat_odd_spec -> Nat_Private_Parity_Odd_2 [] ; + Nat_odd_spec -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_odd_spec -> Morphisms_eq_proper_proxy [] ; + Nat_odd_spec -> RelationClasses_iff_Transitive [] ; + Nat_lt_succ_diag_r -> Nat_lt_succ_r [] ; + Nat_lt_succ_diag_r -> Morphisms_iff_flip_impl_subrelation [] ; + Nat_lt_succ_diag_r -> Nat_le_refl [] ; + Nat_le_refl -> Nat_eq_equiv [] ; + Nat_le_refl -> RelationClasses_reflexivity [] ; + Nat_le_refl -> RelationClasses_Equivalence_Reflexive [] ; + Nat_le_refl -> Nat_lt_eq_cases [] ; + Nat_compare_refl -> Nat_eq_equiv [] ; + Nat_compare_refl -> RelationClasses_reflexivity [] ; + Nat_compare_refl -> RelationClasses_Equivalence_Reflexive [] ; + Nat_compare_refl -> Nat_compare_eq_iff [] ; + Morphisms_Prop_not_iff_morphism -> Morphisms_Proper [] ; + Morphisms_Prop_not_iff_morphism -> Morphisms_Prop_not_iff_morphism_obligation_1 [] ; + _iff -> _and [] ; + Nat_compare -> _nat [] ; + Nat_compare -> _comparison [] ; + Nat_compare -> _Eq [] ; + Nat_compare -> _Lt [] ; + Nat_compare -> _Gt [] ; + Nat_compare_lt_iff -> _False_ind [] ; + Nat_compare_lt_iff -> _eq_ind [] ; + Nat_compare_lt_iff -> _True [] ; + Nat_compare_lt_iff -> _I [] ; + Nat_compare_lt_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_compare_lt_iff -> Morphisms_eq_proper_proxy [] ; + Nat_compare_lt_iff -> RelationClasses_iff_Transitive [] ; + Nat_compare_lt_iff -> _lt [] ; + Nat_compare_lt_iff -> _le_S_n [] ; + Nat_compare_lt_iff -> Nat_compare [] ; + Nat_compare_lt_iff -> _le_0_n [] ; + Nat_compare_lt_iff -> _le_n_S [] ; + Nat_Private_Parity_Odd_0 -> _eq_refl [] ; + Nat_Private_Parity_Odd_0 -> _False_ind [] ; + Nat_Private_Parity_Odd_0 -> _eq_ind [] ; + Nat_Private_Parity_Odd_0 -> _True [] ; + Nat_Private_Parity_Odd_0 -> _I [] ; + Nat_Private_Parity_Odd_0 -> Nat_Odd [] ; + Nat_Private_Parity_Odd_0 -> _not [] ; + Nat_Private_Parity_Odd_1 -> _eq_refl [] ; + Nat_Private_Parity_Odd_1 -> Nat_Odd [] ; + Nat_Private_Parity_Odd_1 -> _ex_intro [] ; + Nat_Private_Parity_Odd_2 -> _False_ind [] ; + Nat_Private_Parity_Odd_2 -> _eq_ind_r [] ; + Nat_Private_Parity_Odd_2 -> _True [] ; + Nat_Private_Parity_Odd_2 -> _I [] ; + Nat_Private_Parity_Odd_2 -> Nat_Odd [] ; + Nat_Private_Parity_Odd_2 -> _ex_intro [] ; + Nat_Private_Parity_Odd_2 -> _iff [] ; + Nat_Private_Parity_Odd_2 -> _conj [] ; + Nat_Private_Parity_Odd_2 -> _plus_n_Sm [] ; + Nat_Private_Parity_Odd_2 -> _plus_n_O [] ; + Morphisms_trans_co_eq_inv_impl_morphism -> Morphisms_Proper [] ; + Morphisms_trans_co_eq_inv_impl_morphism -> Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 [] ; + _le_0_n -> _le_n [] ; + _le_0_n -> _nat_ind [] ; + _le_0_n -> _le [] ; + _le_0_n -> _le_S [] ; + Morphisms_eq_proper_proxy -> _eq [] ; + Morphisms_eq_proper_proxy -> _eq_refl [] ; + Morphisms_eq_proper_proxy -> Morphisms_ProperProxy [] ; + _le_n_S -> _le_n [] ; + _le_n_S -> _le_S [] ; + _le_n_S -> _le_ind [] ; + RelationClasses_iff_Transitive -> RelationClasses_Transitive [] ; + RelationClasses_iff_Transitive -> _iff_trans [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> _False_ind [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> _iff [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> _conj [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> _not [] ; + Morphisms_Prop_not_iff_morphism_obligation_1 -> _and_ind [] ; + RelationClasses_Transitive -> Relation_Definitions_relation [] ; + _iff_trans -> _iff [] ; + _iff_trans -> _conj [] ; + Nat_compare_eq_iff -> _False_ind [] ; + Nat_compare_eq_iff -> _nat_ind [] ; + Nat_compare_eq_iff -> _eq_ind [] ; + Nat_compare_eq_iff -> _True [] ; + Nat_compare_eq_iff -> _I [] ; + Nat_compare_eq_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_compare_eq_iff -> Morphisms_eq_proper_proxy [] ; + Nat_compare_eq_iff -> RelationClasses_iff_Transitive [] ; + Nat_compare_eq_iff -> _f_equal_nat [] ; + Nat_compare_eq_iff -> Nat_compare [] ; + Nat_compare_eq_iff -> _eq_add_S [] ; + _eq_add_S -> _S [] ; + _eq_add_S -> _f_equal [] ; + _eq_add_S -> Init_Nat_pred [] ; + Nat_compare_le_iff -> _False_ind [] ; + Nat_compare_le_iff -> _eq_ind [] ; + Nat_compare_le_iff -> _True [] ; + Nat_compare_le_iff -> _I [] ; + Nat_compare_le_iff -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_compare_le_iff -> Morphisms_eq_proper_proxy [] ; + Nat_compare_le_iff -> RelationClasses_iff_Transitive [] ; + Nat_compare_le_iff -> _not [] ; + Nat_compare_le_iff -> _le_S_n [] ; + Nat_compare_le_iff -> Nat_compare [] ; + Nat_compare_le_iff -> _le_0_n [] ; + Nat_compare_le_iff -> _le_n_S [] ; + Morphisms_ProperProxy -> Relation_Definitions_relation [] ; + Morphisms_impl_pars -> _O [] ; + Morphisms_impl_pars -> Basics_impl [] ; + Morphisms_impl_pars -> Morphisms_Params [] ; + Morphisms_impl_pars -> Morphisms_Build_Params [] ; + Nat_lt_trans -> Morphisms_impl_pars [] ; + Nat_lt_trans -> Nat_lt_asymm [] ; + Morphisms_Params -> _nat [] ; + Morphisms_Proper -> Relation_Definitions_relation [] ; + Morphisms_respectful -> Relation_Definitions_relation [] ; + Nat_lt_asymm -> Nat_le_succ_l [] ; + Morphisms_Build_Params -> _nat [] ; + Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> _eq [] ; + Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Basics_flip [] ; + Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Basics_impl [] ; + Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> RelationClasses_transitivity [] ; + RelationClasses_transitivity -> RelationClasses_Transitive [] ; + Nat_eq_le_incl -> Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Nat_eq_le_incl -> Nat_Private_OrderTac_Tac_not_gt_le [] ; + Nat_eq_le_incl -> Nat_Private_OrderTac_Tac_lt_eq [] ; + _plus_n_Sm -> _nat_ind [] ; + _plus_n_Sm -> Init_Nat_add [] ; + _plus_n_Sm -> _f_equal_nat [] ; + Nat_le_le_succ_r -> Nat_Private_OrderTac_Tac_lt_trans [] ; + Nat_le_le_succ_r -> Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Nat_le_le_succ_r -> Nat_Private_OrderTac_Tac_not_gt_le [] ; + _plus_n_O -> _nat_ind [] ; + _plus_n_O -> Init_Nat_add [] ; + _plus_n_O -> _f_equal_nat [] ; + Nat_le_succ_r -> RelationClasses_reflexivity [] ; + Nat_le_succ_r -> Nat_lt_succ_r [] ; + Nat_le_succ_r -> Nat_lt_eq_cases [] ; + Nat_neq_succ_0 -> Morphisms_PER_morphism [] ; + Nat_neq_succ_0 -> Nat_succ_wd [] ; + Nat_neq_succ_0 -> Morphisms_iff_impl_subrelation [] ; + Nat_neq_succ_0 -> Nat_pred_succ [] ; + Nat_neq_succ_0 -> Nat_pred_wd [] ; + Nat_neq_succ_0 -> Nat_neq_succ_diag_l [] ; + Nat_neq_succ_0 -> Nat_pred_0 [] ; + _f_equal -> _eq [] ; + _f_equal -> _eq_refl [] ; + Nat_pred_0 -> _eq [] ; + Nat_pred_0 -> _eq_refl [] ; + Nat_pred_0 -> _O [] ; + Nat_pred_0 -> Nat_pred [] ; + Nat_Private_OrderTac_Tac_lt_trans -> Nat_Private_OrderTac_Tac_trans [] ; + Init_Nat_add -> _nat [] ; + Init_Nat_add -> _S [] ; + Nat_Private_OrderTac_Tac_lt_irrefl -> RelationClasses_StrictOrder_Irreflexive [] ; + Nat_Private_OrderTac_Tac_lt_irrefl -> Nat_Private_OrderTac_IsTotal_lt_strorder [] ; + _f_equal_nat -> _nat [] ; + _f_equal_nat -> _f_equal [] ; + Nat_Private_OrderTac_Tac_not_gt_le -> Nat_Private_OrderTac_IsTotal_le_lteq [] ; + Nat_Private_OrderTac_Tac_not_gt_le -> Nat_Private_OrderTac_IsTotal_lt_total [] ; + _not -> _False [] ; + Nat_Private_OrderTac_IsTotal_le_lteq -> Nat_le_lteq [] ; + Nat_Private_Parity_Even_0 -> _eq_refl [] ; + Nat_Private_Parity_Even_0 -> Nat_Even [] ; + Nat_Private_Parity_Even_0 -> _ex_intro [] ; + Nat_Private_OrderTac_IsTotal_lt_total -> Nat_lt_total [] ; + Nat_Private_Parity_Even_1 -> _False_ind [] ; + Nat_Private_Parity_Even_1 -> _eq_ind_r [] ; + Nat_Private_Parity_Even_1 -> _True [] ; + Nat_Private_Parity_Even_1 -> _I [] ; + Nat_Private_Parity_Even_1 -> Nat_Even [] ; + Nat_Private_Parity_Even_1 -> _plus_n_Sm [] ; + Nat_Private_Parity_Even_1 -> _not [] ; + Nat_lt_total -> Nat_lt_trichotomy [] ; + Nat_Private_Parity_Even_2 -> _False_ind [] ; + Nat_Private_Parity_Even_2 -> _eq_ind_r [] ; + Nat_Private_Parity_Even_2 -> _True [] ; + Nat_Private_Parity_Even_2 -> _I [] ; + Nat_Private_Parity_Even_2 -> Nat_Even [] ; + Nat_Private_Parity_Even_2 -> _ex_intro [] ; + Nat_Private_Parity_Even_2 -> _iff [] ; + Nat_Private_Parity_Even_2 -> _conj [] ; + Nat_Private_Parity_Even_2 -> _plus_n_Sm [] ; + Nat_lt_trichotomy -> Nat_le_gt_cases [] ; + Nat_add_wd -> Morphisms_Proper [] ; + Nat_add_wd -> PeanoNat_Nat_add_wd_obligation_1 [] ; + Nat_le_gt_cases -> Nat_le_succ_l [] ; + Nat_eq_equiv -> _nat [] ; + Nat_eq_equiv -> RelationClasses_eq_equivalence [] ; + Morphisms_reflexive_reflexive_proxy -> RelationClasses_Reflexive [] ; + Morphisms_reflexive_reflexive_proxy -> Morphisms_ReflexiveProxy [] ; + Nat_le_lteq -> Nat_lt_eq_cases [] ; + Nat_succ_inj_wd -> Nat_succ_wd [] ; + Nat_succ_inj_wd -> Nat_succ_inj [] ; + RelationClasses_StrictOrder_Irreflexive -> RelationClasses_StrictOrder [] ; + Nat_Private_OrderTac_IsTotal_lt_strorder -> Nat_lt_strorder [] ; + Morphisms_Reflexive_partial_app_morphism -> Morphisms_ProperProxy [] ; + Morphisms_Reflexive_partial_app_morphism -> Morphisms_Proper [] ; + Morphisms_Reflexive_partial_app_morphism -> Morphisms_respectful [] ; + Nat_lt_strorder -> Nat_lt_trans [] ; + Nat_lt_strorder -> RelationClasses_StrictOrder [] ; + Nat_lt_strorder -> RelationClasses_Build_StrictOrder [] ; + Nat_add_succ_l -> _eq [] ; + Nat_add_succ_l -> _eq_refl [] ; + Nat_add_succ_l -> Nat_add [] ; + RelationClasses_StrictOrder -> RelationClasses_Transitive [] ; + RelationClasses_StrictOrder -> RelationClasses_Irreflexive [] ; + Nat_add_succ_r -> Nat_add_0_l [] ; + Nat_add_succ_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_add_succ_r -> Morphisms_eq_proper_proxy [] ; + Nat_add_succ_r -> Nat_add_wd [] ; + Nat_add_succ_r -> Nat_succ_inj_wd [] ; + Nat_add_succ_r -> Nat_add_succ_l [] ; + Nat_add_succ_r -> RelationClasses_iff_equivalence [] ; + Nat_add_succ_r -> Morphisms_per_partial_app_morphism [] ; + Nat_add_succ_r -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_add_succ_r -> Nat_bi_induction [] ; + Nat_add_succ_r -> RelationClasses_reflexivity [] ; + Nat_add_0_r -> Nat_add_0_l [] ; + Nat_add_0_r -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_add_0_r -> Morphisms_eq_proper_proxy [] ; + Nat_add_0_r -> Nat_add_wd [] ; + Nat_add_0_r -> Nat_succ_inj_wd [] ; + Nat_add_0_r -> Nat_add_succ_l [] ; + Nat_add_0_r -> RelationClasses_iff_equivalence [] ; + Nat_add_0_r -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_add_0_r -> Nat_bi_induction [] ; + Nat_add_0_r -> RelationClasses_reflexivity [] ; + RelationClasses_Irreflexive -> RelationClasses_Reflexive [] ; + RelationClasses_Irreflexive -> RelationClasses_complement [] ; + RelationClasses_iff_equivalence -> RelationClasses_iff_Transitive [] ; + RelationClasses_iff_equivalence -> RelationClasses_iff_Reflexive [] ; + RelationClasses_iff_equivalence -> RelationClasses_Equivalence [] ; + RelationClasses_iff_equivalence -> RelationClasses_iff_Symmetric [] ; + RelationClasses_iff_equivalence -> RelationClasses_Build_Equivalence [] ; + RelationClasses_complement -> _False [] ; + RelationClasses_complement -> Relation_Definitions_relation [] ; + RelationClasses_Build_StrictOrder -> RelationClasses_Transitive [] ; + RelationClasses_Build_StrictOrder -> RelationClasses_Irreflexive [] ; + Morphisms_per_partial_app_morphism -> Morphisms_Proper [] ; + Morphisms_per_partial_app_morphism -> Morphisms_per_partial_app_morphism_obligation_1 [] ; + Nat_Private_OrderTac_Tac_trans -> Nat_Private_OrderTac_IsTotal_le_lteq [] ; + Nat_Private_OrderTac_Tac_trans -> Nat_Private_OrderTac_IsTotal_lt_strorder [] ; + Nat_Private_OrderTac_Tac_trans -> RelationClasses_StrictOrder_Transitive [] ; + Nat_Private_OrderTac_Tac_trans -> Nat_Private_OrderTac_IsTotal_lt_compat [] ; + Nat_Private_OrderTac_Tac_trans -> Nat_Private_OrderTac_IsTotal_eq_equiv [] ; + Nat_Private_OrderTac_Tac_trans -> Nat_Private_OrderTac_Tac_interp_ord [] ; + Nat_Private_OrderTac_Tac_trans -> OrdersTac_trans_ord [] ; + Nat_Private_OrderTac_Tac_trans -> OrdersTac_OEQ [] ; + RelationClasses_Equivalence_Transitive -> RelationClasses_Equivalence [] ; + Morphisms_trans_sym_co_inv_impl_morphism -> Morphisms_Proper [] ; + Morphisms_trans_sym_co_inv_impl_morphism -> Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 [] ; + RelationClasses_StrictOrder_Transitive -> RelationClasses_StrictOrder [] ; + Morphisms_PER_morphism -> Morphisms_Proper [] ; + Morphisms_PER_morphism -> Morphisms_PER_morphism_obligation_1 [] ; + Nat_Private_OrderTac_IsTotal_lt_compat -> Nat_lt_compat [] ; + Nat_bi_induction -> _eq [] ; + Nat_bi_induction -> _nat_ind [] ; + Nat_bi_induction -> _iff [] ; + Nat_bi_induction -> Morphisms_Proper [] ; + Nat_bi_induction -> Morphisms_respectful [] ; + RelationClasses_reflexivity -> RelationClasses_Reflexive [] ; + Nat_Private_OrderTac_IsTotal_eq_equiv -> Nat_eq_equiv [] ; + Nat_Private_OrderTac_Tac_interp_ord -> _eq [] ; + Nat_Private_OrderTac_Tac_interp_ord -> _lt [] ; + Nat_Private_OrderTac_Tac_interp_ord -> OrdersTac_ord [] ; + RelationClasses_Equivalence_PER -> RelationClasses_Equivalence_Transitive [] ; + RelationClasses_Equivalence_PER -> RelationClasses_Equivalence_Symmetric [] ; + RelationClasses_Equivalence_PER -> RelationClasses_PER [] ; + RelationClasses_Equivalence_PER -> RelationClasses_Build_PER [] ; + OrdersTac_trans_ord -> OrdersTac_OLT [] ; + OrdersTac_trans_ord -> OrdersTac_ord [] ; + OrdersTac_trans_ord -> OrdersTac_OLE [] ; + RelationClasses_iff_Reflexive -> RelationClasses_Reflexive [] ; + RelationClasses_iff_Reflexive -> _iff_refl [] ; + Morphisms_reflexive_proper_proxy -> Morphisms_ProperProxy [] ; + Morphisms_reflexive_proper_proxy -> Morphisms_ReflexiveProxy [] ; + RelationClasses_Equivalence_Reflexive -> RelationClasses_Equivalence [] ; + RelationClasses_Reflexive -> Relation_Definitions_relation [] ; + RelationClasses_Equivalence -> RelationClasses_Transitive [] ; + RelationClasses_Equivalence -> RelationClasses_Reflexive [] ; + RelationClasses_Equivalence -> RelationClasses_Symmetric [] ; + Nat_lt_compat -> Nat_lt_wd [] ; + Nat_Private_OrderTac_Tac_lt_eq -> Nat_Private_OrderTac_Tac_trans [] ; + RelationClasses_Symmetric -> Relation_Definitions_relation [] ; + Morphisms_ReflexiveProxy -> Relation_Definitions_relation [] ; + _iff_refl -> _iff [] ; + _iff_refl -> _conj [] ; + RelationClasses_Equivalence_Symmetric -> RelationClasses_Equivalence [] ; + RelationClasses_PER -> RelationClasses_Transitive [] ; + RelationClasses_PER -> RelationClasses_Symmetric [] ; + RelationClasses_Build_PER -> RelationClasses_Transitive [] ; + RelationClasses_Build_PER -> RelationClasses_Symmetric [] ; + Morphisms_PER_morphism_obligation_1 -> _iff [] ; + Morphisms_PER_morphism_obligation_1 -> _conj [] ; + Morphisms_PER_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_PER_morphism_obligation_1 -> RelationClasses_transitivity [] ; + Morphisms_PER_morphism_obligation_1 -> RelationClasses_PER_Symmetric [] ; + Morphisms_PER_morphism_obligation_1 -> RelationClasses_symmetry [] ; + Morphisms_PER_morphism_obligation_1 -> RelationClasses_PER_Transitive [] ; + RelationClasses_PER_Symmetric -> RelationClasses_PER [] ; + RelationClasses_symmetry -> RelationClasses_Symmetric [] ; + RelationClasses_PER_Transitive -> RelationClasses_PER [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Basics_flip [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Basics_impl [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> RelationClasses_transitivity [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> RelationClasses_PER_Symmetric [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> RelationClasses_symmetry [] ; + Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> RelationClasses_PER_Transitive [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> _iff [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> _conj [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> RelationClasses_transitivity [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> RelationClasses_PER_Symmetric [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> RelationClasses_symmetry [] ; + Morphisms_per_partial_app_morphism_obligation_1 -> RelationClasses_PER_Transitive [] ; + RelationClasses_iff_Symmetric -> RelationClasses_Symmetric [] ; + RelationClasses_iff_Symmetric -> _iff_sym [] ; + RelationClasses_Build_Equivalence -> RelationClasses_Transitive [] ; + RelationClasses_Build_Equivalence -> RelationClasses_Reflexive [] ; + RelationClasses_Build_Equivalence -> RelationClasses_Symmetric [] ; + _iff_sym -> _iff [] ; + _iff_sym -> _conj [] ; + Nat_succ_wd -> Morphisms_Proper [] ; + Nat_succ_wd -> PeanoNat_Nat_succ_wd_obligation_1 [] ; + PeanoNat_Nat_succ_wd_obligation_1 -> _nat [] ; + PeanoNat_Nat_succ_wd_obligation_1 -> _S [] ; + PeanoNat_Nat_succ_wd_obligation_1 -> _eq_ind_r [] ; + PeanoNat_Nat_succ_wd_obligation_1 -> Morphisms_respectful [] ; + Nat_succ_inj -> Nat_eq_equiv [] ; + Nat_succ_inj -> Morphisms_reflexive_reflexive_proxy [] ; + Nat_succ_inj -> Morphisms_PER_morphism [] ; + Nat_succ_inj -> RelationClasses_Equivalence_PER [] ; + Nat_succ_inj -> Morphisms_reflexive_proper_proxy [] ; + Nat_succ_inj -> RelationClasses_Equivalence_Reflexive [] ; + Nat_succ_inj -> Morphisms_subrelation_proper [] ; + Nat_succ_inj -> Morphisms_subrelation_refl [] ; + Nat_succ_inj -> Morphisms_trans_co_impl_morphism [] ; + Nat_succ_inj -> Morphisms_iff_impl_subrelation [] ; + Nat_succ_inj -> Nat_pred_succ [] ; + Nat_succ_inj -> Nat_pred_wd [] ; + Nat_succ_inj -> Morphisms_subrelation_respectful [] ; + Nat_succ_inj -> _tt [] ; + Morphisms_subrelation_proper -> Morphisms_Proper [] ; + Morphisms_subrelation_proper -> RelationClasses_subrelation [] ; + Morphisms_subrelation_proper -> Init_Unconvertible [] ; + Morphisms_subrelation_refl -> RelationClasses_subrelation [] ; + Nat_pred -> _nat [] ; + Morphisms_trans_co_impl_morphism -> Morphisms_Proper [] ; + Morphisms_trans_co_impl_morphism -> Morphisms_trans_co_impl_morphism_obligation_1 [] ; + Morphisms_iff_impl_subrelation -> _iff [] ; + Morphisms_iff_impl_subrelation -> Basics_impl [] ; + Morphisms_iff_impl_subrelation -> RelationClasses_subrelation [] ; + Morphisms_iff_impl_subrelation -> _and_ind [] ; + Nat_pred_succ -> _eq [] ; + Nat_pred_succ -> _eq_refl [] ; + Nat_pred_succ -> _S [] ; + Nat_pred_succ -> Nat_pred [] ; + Nat_pred_wd -> Morphisms_Proper [] ; + Nat_pred_wd -> PeanoNat_Nat_pred_wd_obligation_1 [] ; + Morphisms_subrelation_respectful -> Morphisms_respectful [] ; + Morphisms_subrelation_respectful -> RelationClasses_subrelation [] ; + RelationClasses_subrelation -> Relation_Definitions_relation [] ; + PeanoNat_Nat_pred_wd_obligation_1 -> _eq_ind_r [] ; + PeanoNat_Nat_pred_wd_obligation_1 -> Morphisms_respectful [] ; + PeanoNat_Nat_pred_wd_obligation_1 -> Nat_pred [] ; + _and_ind -> _and [] ; + Morphisms_trans_co_impl_morphism_obligation_1 -> Basics_impl [] ; + Morphisms_trans_co_impl_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_trans_co_impl_morphism_obligation_1 -> RelationClasses_transitivity [] ; + Init_Unconvertible -> _unit [] ; + RelationClasses_eq_equivalence -> RelationClasses_Equivalence [] ; + RelationClasses_eq_equivalence -> RelationClasses_Build_Equivalence [] ; + RelationClasses_eq_equivalence -> RelationClasses_eq_Reflexive [] ; + RelationClasses_eq_equivalence -> RelationClasses_eq_Transitive [] ; + RelationClasses_eq_equivalence -> RelationClasses_eq_Symmetric [] ; + RelationClasses_eq_Reflexive -> _eq [] ; + RelationClasses_eq_Reflexive -> _eq_refl [] ; + RelationClasses_eq_Reflexive -> RelationClasses_Reflexive [] ; + RelationClasses_eq_Transitive -> RelationClasses_Transitive [] ; + RelationClasses_eq_Transitive -> _eq_trans [] ; + Nat_PrivateImplementsBitwiseSpec_land_spec -> Nat_land [] ; + Nat_PrivateImplementsBitwiseSpec_land_spec -> Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 [] ; + RelationClasses_eq_Symmetric -> _eq_sym [] ; + RelationClasses_eq_Symmetric -> RelationClasses_Symmetric [] ; + Nat_land -> _andb [] ; + Nat_land -> Nat_bitwise [] ; + _eq_trans -> _eq [] ; + _andb -> _bool [] ; + _andb -> _false [] ; + PeanoNat_Nat_add_wd_obligation_1 -> _eq_ind_r [] ; + PeanoNat_Nat_add_wd_obligation_1 -> Morphisms_respectful [] ; + PeanoNat_Nat_add_wd_obligation_1 -> Init_Nat_add [] ; + Nat_testbit -> Nat_odd [] ; + Nat_testbit -> Nat_div2 [] ; + Nat_PrivateImplementsBitwiseSpec_div2_succ_double -> Nat_div2 [] ; + Nat_PrivateImplementsBitwiseSpec_div2_succ_double -> Nat_mul [] ; + Nat_PrivateImplementsBitwiseSpec_div2_succ_double -> _f_equal [] ; + Nat_PrivateImplementsBitwiseSpec_div2_succ_double -> Nat_add_succ_r [] ; + Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l [] ; + Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr [] ; + Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 -> Nat_PrivateImplementsBitwiseSpec_div2_bitwise [] ; + Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 -> Nat_PrivateImplementsBitwiseSpec_odd_bitwise [] ; + Nat_PrivateImplementsBitwiseSpec_div2_double -> Nat_div2 [] ; + Nat_PrivateImplementsBitwiseSpec_div2_double -> Nat_mul [] ; + Nat_PrivateImplementsBitwiseSpec_div2_double -> _f_equal [] ; + Nat_PrivateImplementsBitwiseSpec_div2_double -> Nat_add_succ_r [] ; + Nat_le_0_l -> Nat_eq_le_incl [] ; + Nat_le_0_l -> Nat_le_le_succ_r [] ; + Nat_le_0_l -> Nat_le_succ_r [] ; + Nat_le_0_l -> Nat_neq_succ_0 [] ; + Nat_le_trans -> Nat_lt_trans [] ; + Nat_succ_le_mono -> Nat_succ_lt_mono [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_le_div2 -> Nat_div2 [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_le_div2 -> Nat_lt_succ_r [] ; + Nat_lt_succ_r -> _iff [] ; + Nat_lt_succ_r -> _conj [] ; + Nat_lt_succ_r -> _lt [] ; + Nat_lt_succ_r -> _le_S_n [] ; + _le_n -> _nat [] ; + _le_n -> _S [] ; + _lt -> _le [] ; + _le_S -> _nat [] ; + _le_S -> _S [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l -> Nat_testbit [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l -> _eq [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l -> _eq_refl [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l -> _nat_ind [] ; + _le_S_n -> _le_pred [] ; + Nat_odd -> Nat_even [] ; + Nat_odd -> _negb [] ; + _le_ind -> _le [] ; + _le_pred -> _le_n [] ; + _le_pred -> _O [] ; + _le_pred -> _le_S [] ; + _le_pred -> _le_ind [] ; + _le_pred -> Init_Nat_pred [] ; + Nat_div2 -> _nat [] ; + Nat_div2 -> _S [] ; + Nat_div2 -> _O [] ; + Init_Nat_pred -> _nat [] ; + _False_ind -> _False [] ; + Nat_lt_eq_cases -> Morphisms_reflexive_reflexive_proxy [] ; + Nat_lt_eq_cases -> Morphisms_Reflexive_partial_app_morphism [] ; + Nat_lt_eq_cases -> RelationClasses_iff_equivalence [] ; + Nat_lt_eq_cases -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_lt_eq_cases -> RelationClasses_Equivalence_PER [] ; + Nat_lt_eq_cases -> Morphisms_reflexive_proper_proxy [] ; + Nat_lt_eq_cases -> Morphisms_Prop_or_iff_morphism [] ; + Nat_lt_eq_cases -> Nat_compare_lt_iff [] ; + Nat_lt_eq_cases -> Nat_compare_eq_iff [] ; + Nat_lt_eq_cases -> Nat_compare_le_iff [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr -> Nat_le_0_l [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr -> Nat_le_trans [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr -> Nat_succ_le_mono [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_le_div2 [] ; + Nat_succ_lt_mono -> Nat_le_succ_l [] ; + Nat_PrivateImplementsBitwiseSpec_div2_bitwise -> Nat_bitwise [] ; + Nat_PrivateImplementsBitwiseSpec_div2_bitwise -> Nat_PrivateImplementsBitwiseSpec_div2_succ_double [] ; + Nat_PrivateImplementsBitwiseSpec_div2_bitwise -> Nat_PrivateImplementsBitwiseSpec_div2_double [] ; + Morphisms_Prop_or_iff_morphism -> Morphisms_Proper [] ; + Morphisms_Prop_or_iff_morphism -> Morphisms_Prop_or_iff_morphism_obligation_1 [] ; + _nat_ind -> _nat [] ; + _nat_ind -> _S [] ; + _nat_ind -> _O [] ; + _eq_ind -> _eq [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _iff [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _conj [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> Morphisms_respectful [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _and_ind [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _or_ind [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _or_introl [] ; + Morphisms_Prop_or_iff_morphism_obligation_1 -> _or_intror [] ; + _eq_sym -> _eq [] ; + _eq_sym -> _eq_refl [] ; + _or_ind -> _or [] ; + _eq_ind_r -> _eq_ind [] ; + _eq_ind_r -> _eq_sym [] ; + Nat_bitwise -> Nat_odd [] ; + Nat_bitwise -> Nat_div2 [] ; + Nat_bitwise -> Nat_mul [] ; + Nat_PrivateImplementsBitwiseSpec_odd_bitwise -> Nat_bitwise [] ; + Nat_PrivateImplementsBitwiseSpec_odd_bitwise -> Bool_negb_false_iff [] ; + Nat_PrivateImplementsBitwiseSpec_odd_bitwise -> Nat_add_comm [] ; + Nat_PrivateImplementsBitwiseSpec_odd_bitwise -> Nat_even_spec [] ; + Nat_PrivateImplementsBitwiseSpec_odd_bitwise -> Nat_odd_spec [] ; + Nat_le_succ_l -> Nat_succ_inj_wd [] ; + Nat_le_succ_l -> Morphisms_per_partial_app_morphism [] ; + Nat_le_succ_l -> Nat_nle_succ_diag_l [] ; + Nat_le_succ_l -> Nat_central_induction [] ; + Nat_le_succ_l -> Nat_le_wd [] ; + Nat_le_succ_l -> _or_cancel_r [] ; + Nat_lt_irrefl -> _eq_ind_r [] ; + Nat_lt_irrefl -> RelationClasses_symmetry [] ; + Nat_lt_irrefl -> RelationClasses_iff_Symmetric [] ; + Nat_lt_irrefl -> Morphisms_subrelation_proper [] ; + Nat_lt_irrefl -> Morphisms_subrelation_refl [] ; + Nat_lt_irrefl -> Morphisms_subrelation_respectful [] ; + Nat_lt_irrefl -> _tt [] ; + Nat_lt_irrefl -> Morphisms_iff_flip_impl_subrelation [] ; + Nat_lt_irrefl -> Nat_compare_refl [] ; + Nat_lt_irrefl -> Morphisms_Prop_not_iff_morphism [] ; + Nat_lt_irrefl -> Nat_compare_lt_iff [] ; + _le -> _nat [] ; + _le -> _S [] ; + Nat_nle_succ_diag_l -> Morphisms_iff_impl_subrelation [] ; + Nat_nle_succ_diag_l -> Nat_neq_succ_diag_l [] ; + Nat_nle_succ_diag_l -> Nat_nlt_succ_diag_l [] ; + Nat_central_induction -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_central_induction -> Morphisms_eq_proper_proxy [] ; + Nat_central_induction -> RelationClasses_iff_Transitive [] ; + Nat_central_induction -> Morphisms_reflexive_reflexive_proxy [] ; + Nat_central_induction -> Nat_bi_induction [] ; + Nat_central_induction -> RelationClasses_reflexivity [] ; + Nat_central_induction -> RelationClasses_iff_Reflexive [] ; + Nat_central_induction -> Morphisms_reflexive_proper_proxy [] ; + Nat_central_induction -> Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + Nat_le_wd -> Morphisms_trans_co_eq_inv_impl_morphism [] ; + Nat_le_wd -> Morphisms_eq_proper_proxy [] ; + Nat_le_wd -> Nat_eq_equiv [] ; + Nat_le_wd -> Morphisms_reflexive_reflexive_proxy [] ; + Nat_le_wd -> Morphisms_Reflexive_partial_app_morphism [] ; + Nat_le_wd -> RelationClasses_iff_equivalence [] ; + Nat_le_wd -> Morphisms_trans_sym_co_inv_impl_morphism [] ; + Nat_le_wd -> RelationClasses_reflexivity [] ; + Nat_le_wd -> RelationClasses_Equivalence_PER [] ; + Nat_le_wd -> Morphisms_reflexive_proper_proxy [] ; + Nat_le_wd -> RelationClasses_Equivalence_Reflexive [] ; + Nat_le_wd -> Nat_succ_wd [] ; + Nat_le_wd -> Nat_lt_succ_r [] ; + Nat_le_wd -> Nat_lt_wd [] ; + Bool_negb_false_iff -> _eq_sym [] ; + Bool_negb_false_iff -> _negb [] ; + Bool_negb_false_iff -> _iff [] ; + Bool_negb_false_iff -> _conj [] ; + Nat_lt_wd -> Morphisms_Proper [] ; + Nat_lt_wd -> PeanoNat_Nat_lt_wd_obligation_1 [] ; + _or_cancel_r -> _not [] ; + _or_cancel_r -> _or_iff_compat_r [] ; + Nat_add_comm -> Morphisms_Reflexive_partial_app_morphism [] ; + Nat_add_comm -> Nat_add_succ_r [] ; + Nat_add_comm -> Nat_add_0_r [] ; + _or_iff_compat_r -> _iff [] ; + _or_iff_compat_r -> _conj [] ; + _or_iff_compat_r -> _or [] ; + _or_iff_compat_r -> _or_introl [] ; + _or_iff_compat_r -> _or_intror [] ; + Nat_add -> _nat [] ; + Nat_add -> _S [] ; + Nat_mul -> _O [] ; + Nat_mul -> Nat_add [] ; + PeanoNat_Nat_lt_wd_obligation_1 -> _eq_ind_r [] ; + PeanoNat_Nat_lt_wd_obligation_1 -> _iff [] ; + PeanoNat_Nat_lt_wd_obligation_1 -> _conj [] ; + PeanoNat_Nat_lt_wd_obligation_1 -> Morphisms_respectful [] ; + PeanoNat_Nat_lt_wd_obligation_1 -> _lt [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism -> Morphisms_Proper [] ; + Morphisms_Prop_iff_iff_iff_impl_morphism -> Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 [] ; + Nat_even -> _nat [] ; + Nat_even -> _bool [] ; + Nat_even -> _false [] ; + Nat_even -> _true [] ; +subgraph cluster_Basics { label="Basics"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Basics_impl; Basics_flip; }; +subgraph cluster_RelationClasses { label="RelationClasses"; fillcolor="#FFFFC3"; labeljust=l; style=filled +RelationClasses_eq_Symmetric; RelationClasses_eq_Transitive; RelationClasses_eq_Reflexive; RelationClasses_eq_equivalence; RelationClasses_subrelation; RelationClasses_Build_Equivalence; RelationClasses_iff_Symmetric; RelationClasses_PER_Transitive; RelationClasses_symmetry; RelationClasses_PER_Symmetric; RelationClasses_Build_PER; RelationClasses_PER; RelationClasses_Equivalence_Symmetric; RelationClasses_Symmetric; RelationClasses_Equivalence; RelationClasses_Reflexive; RelationClasses_Equivalence_Reflexive; RelationClasses_iff_Reflexive; RelationClasses_Equivalence_PER; RelationClasses_reflexivity; RelationClasses_StrictOrder_Transitive; RelationClasses_Equivalence_Transitive; RelationClasses_Build_StrictOrder; RelationClasses_complement; RelationClasses_iff_equivalence; RelationClasses_Irreflexive; RelationClasses_StrictOrder; RelationClasses_StrictOrder_Irreflexive; RelationClasses_transitivity; RelationClasses_Transitive; RelationClasses_iff_Transitive; }; +subgraph cluster_Bool { label="Bool"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Bool_negb_false_iff; }; +subgraph cluster_Morphisms { label="Morphisms"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Morphisms_trans_co_impl_morphism_obligation_1; Morphisms_subrelation_respectful; Morphisms_iff_impl_subrelation; Morphisms_trans_co_impl_morphism; Morphisms_subrelation_refl; Morphisms_subrelation_proper; Morphisms_per_partial_app_morphism_obligation_1; Morphisms_trans_sym_co_inv_impl_morphism_obligation_1; Morphisms_PER_morphism_obligation_1; Morphisms_ReflexiveProxy; Morphisms_reflexive_proper_proxy; Morphisms_PER_morphism; Morphisms_trans_sym_co_inv_impl_morphism; Morphisms_per_partial_app_morphism; Morphisms_Reflexive_partial_app_morphism; Morphisms_reflexive_reflexive_proxy; Morphisms_trans_co_eq_inv_impl_morphism_obligation_1; Morphisms_Build_Params; Morphisms_respectful; Morphisms_Proper; Morphisms_Params; Morphisms_impl_pars; Morphisms_ProperProxy; Morphisms_eq_proper_proxy; Morphisms_trans_co_eq_inv_impl_morphism; Morphisms_iff_flip_impl_subrelation; }; +subgraph cluster_Nat { label="Nat"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Nat_PrivateImplementsBitwiseSpec { label="PrivateImplementsBitwiseSpec"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Nat_PrivateImplementsBitwiseSpec_odd_bitwise; Nat_PrivateImplementsBitwiseSpec_div2_bitwise; Nat_PrivateImplementsBitwiseSpec_div2_double; Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1; Nat_PrivateImplementsBitwiseSpec_div2_succ_double; Nat_PrivateImplementsBitwiseSpec_land_spec; }; +subgraph cluster_Nat_Private_OrderTac { label="Private_OrderTac"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Nat_Private_OrderTac_IsTotal { label="IsTotal"; fillcolor="#FFFF83"; labeljust=l; style=filled +Nat_Private_OrderTac_IsTotal_eq_equiv; Nat_Private_OrderTac_IsTotal_lt_compat; Nat_Private_OrderTac_IsTotal_lt_strorder; Nat_Private_OrderTac_IsTotal_lt_total; Nat_Private_OrderTac_IsTotal_le_lteq; }; +subgraph cluster_Nat_Private_OrderTac_Tac { label="Tac"; fillcolor="#FFFF83"; labeljust=l; style=filled +Nat_Private_OrderTac_Tac_lt_eq; Nat_Private_OrderTac_Tac_interp_ord; Nat_Private_OrderTac_Tac_trans; Nat_Private_OrderTac_Tac_not_gt_le; Nat_Private_OrderTac_Tac_lt_irrefl; Nat_Private_OrderTac_Tac_lt_trans; }; +}; +subgraph cluster_Nat_Private_Parity { label="Private_Parity"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Nat_Private_Parity_Even_2; Nat_Private_Parity_Even_1; Nat_Private_Parity_Even_0; Nat_Private_Parity_Odd_2; Nat_Private_Parity_Odd_1; Nat_Private_Parity_Odd_0; }; +Nat_even; Nat_mul; Nat_add; Nat_add_comm; Nat_lt_wd; Nat_le_wd; Nat_central_induction; Nat_nle_succ_diag_l; Nat_lt_irrefl; Nat_le_succ_l; Nat_bitwise; Nat_succ_lt_mono; Nat_lt_eq_cases; Nat_div2; Nat_odd; Nat_lt_succ_r; Nat_succ_le_mono; Nat_le_trans; Nat_le_0_l; Nat_testbit; Nat_land; Nat_pred_wd; Nat_pred_succ; Nat_pred; Nat_succ_inj; Nat_succ_wd; Nat_lt_compat; Nat_bi_induction; Nat_add_0_r; Nat_add_succ_r; Nat_add_succ_l; Nat_lt_strorder; Nat_succ_inj_wd; Nat_le_lteq; Nat_eq_equiv; Nat_le_gt_cases; Nat_add_wd; Nat_lt_trichotomy; Nat_lt_total; Nat_pred_0; Nat_neq_succ_0; Nat_le_succ_r; Nat_le_le_succ_r; Nat_eq_le_incl; Nat_lt_asymm; Nat_lt_trans; Nat_compare_le_iff; Nat_compare_eq_iff; Nat_compare_lt_iff; Nat_compare; Nat_compare_refl; Nat_le_refl; Nat_lt_succ_diag_r; Nat_odd_spec; Nat_Even; Nat_Odd; Nat_lt_le_incl; Nat_add_0_l; Nat_nlt_succ_diag_l; Nat_neq_succ_diag_l; Nat_even_spec; }; +subgraph cluster_Relation_Definitions { label="Relation_Definitions"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Relation_Definitions_relation; }; +subgraph cluster_Morphisms_Prop { label="Morphisms_Prop"; fillcolor="#FFFFC3"; labeljust=l; style=filled +Morphisms_Prop_iff_iff_iff_impl_morphism; Morphisms_Prop_or_iff_morphism_obligation_1; Morphisms_Prop_or_iff_morphism; Morphisms_Prop_not_iff_morphism_obligation_1; Morphisms_Prop_not_iff_morphism; Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1; }; +subgraph cluster_OrdersTac { label="OrdersTac"; fillcolor="#FFFFC3"; labeljust=l; style=filled +OrdersTac_OLE; OrdersTac_OEQ; OrdersTac_ord; OrdersTac_trans_ord; OrdersTac_OLT; }; +subgraph cluster_Stdlib { label="Stdlib"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Stdlib_Arith { label="Arith"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Stdlib_Arith_PeanoNat { label="PeanoNat"; fillcolor="#FFFF83"; labeljust=l; style=filled +subgraph cluster_Stdlib_Arith_PeanoNat_Nat { label="Nat"; fillcolor="#FFFF63"; labeljust=l; style=filled +subgraph cluster_Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec { label="PrivateImplementsBitwiseSpec"; fillcolor="#FFFF43"; labeljust=l; style=filled +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr; Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l; Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_le_div2; }; +}; +}; +}; +}; +subgraph cluster_PeanoNat { label="PeanoNat"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_PeanoNat_Nat { label="Nat"; fillcolor="#FFFFA3"; labeljust=l; style=filled +PeanoNat_Nat_lt_wd_obligation_1; PeanoNat_Nat_add_wd_obligation_1; PeanoNat_Nat_pred_wd_obligation_1; PeanoNat_Nat_succ_wd_obligation_1; }; +}; +subgraph cluster_Init { label="Init"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Init_Nat { label="Nat"; fillcolor="#FFFFA3"; labeljust=l; style=filled +Init_Nat_pred; Init_Nat_add; }; +Init_Unconvertible; }; +} /* END */ diff --git a/tests/PeanoNatBitwise.dpd.oracle b/tests/PeanoNatBitwise.dpd.oracle new file mode 100644 index 000000000..cb526b3b6 --- /dev/null +++ b/tests/PeanoNatBitwise.dpd.oracle @@ -0,0 +1,1869 @@ +N: 308 "Equivalence_PER" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 311 "Equivalence_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 317 "Equivalence_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 303 "Equivalence_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 260 "Even" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 290 "Even_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_Parity", ]; +N: 291 "Even_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_Parity", ]; +N: 292 "Even_2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_Parity", ]; +N: 237 "False_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 428 "Irreflexive" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 259 "Odd" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 266 "Odd_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_Parity", ]; +N: 267 "Odd_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_Parity", ]; +N: 268 "Odd_2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_Parity", ]; +N: 321 "PER_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 323 "PER_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 305 "PER_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 320 "PER_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 279 "Proper" [opaque=no, body=yes, kind=cnst, prop=no, path="Morphisms", ]; +N: 276 "ProperProxy" [opaque=no, body=yes, kind=cnst, prop=no, path="Morphisms", ]; +N: 312 "Reflexive" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 315 "ReflexiveProxy" [opaque=no, body=yes, kind=cnst, prop=no, path="Morphisms", ]; +N: 297 "Reflexive_partial_app_morphism" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 424 "StrictOrder_Irreflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 433 "StrictOrder_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 314 "Symmetric" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 273 "Transitive" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 345 "Unconvertible" [opaque=no, body=yes, kind=cnst, prop=no, path="Init", ]; +N: 287 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="Init.Nat", ]; +N: 253 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 258 "add_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 300 "add_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 252 "add_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 298 "add_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 299 "add_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 293 "add_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 352 "add_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="PeanoNat.Nat", ]; +N: 343 "and_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 224 "andb" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 306 "bi_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 244 "bitwise" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 377 "central_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 393 "compare" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 402 "compare_eq_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 404 "compare_le_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 394 "compare_lt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 391 "compare_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 429 "complement" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 236 "div2" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 239 "div2_bitwise" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.PrivateImplementsBitwiseSpec", ]; +N: 238 "div2_decr" [body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 354 "div2_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.PrivateImplementsBitwiseSpec", ]; +N: 353 "div2_succ_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.PrivateImplementsBitwiseSpec", ]; +N: 348 "eq_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 350 "eq_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 349 "eq_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 403 "eq_add_S" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 435 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.IsTotal", ]; +N: 294 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 347 "eq_equivalence" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 241 "eq_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 243 "eq_ind_r" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 410 "eq_le_incl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 270 "eq_proper_proxy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 242 "eq_sym" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 351 "eq_trans" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 255 "even" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 256 "even_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 285 "f_equal" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 288 "f_equal_nat" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 277 "flip" [opaque=no, body=yes, kind=cnst, prop=no, path="Basics", ]; +N: 265 "iff" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 309 "iff_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 326 "iff_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 271 "iff_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 301 "iff_equivalence" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 388 "iff_flip_impl_subrelation" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 383 "iff_iff_iff_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 384 "iff_iff_iff_impl_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 336 "iff_impl_subrelation" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 316 "iff_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 328 "iff_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 274 "iff_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 278 "impl" [opaque=no, body=yes, kind=cnst, prop=no, path="Basics", ]; +N: 405 "impl_pars" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 436 "interp_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat.Private_OrderTac.Tac", ]; +N: 223 "land" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 222 "land_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.PrivateImplementsBitwiseSpec", ]; +N: 355 "le_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 398 "le_0_n" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 362 "le_S_n" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 358 "le_div2" [body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 422 "le_gt_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 363 "le_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 411 "le_le_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 418 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.IsTotal", ]; +N: 423 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 399 "le_n_S" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 364 "le_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 390 "le_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 374 "le_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 412 "le_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 356 "le_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 378 "le_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 360 "lt" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 408 "lt_asymm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 434 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.IsTotal", ]; +N: 441 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 442 "lt_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 366 "lt_eq_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 375 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 416 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 387 "lt_le_incl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 425 "lt_strorder" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.IsTotal", ]; +N: 426 "lt_strorder" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 389 "lt_succ_diag_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 359 "lt_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 419 "lt_total" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.IsTotal", ]; +N: 420 "lt_total" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 406 "lt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 415 "lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 421 "lt_trichotomy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 379 "lt_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 382 "lt_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="PeanoNat.Nat", ]; +N: 254 "mul" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 240 "nat_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 257 "negb" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 251 "negb_false_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Bool", ]; +N: 413 "neq_succ_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 385 "neq_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 376 "nle_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 386 "nlt_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 289 "not" [opaque=no, body=yes, kind=cnst, prop=no, ]; +N: 417 "not_gt_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 392 "not_iff_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 401 "not_iff_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 235 "odd" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 245 "odd_bitwise" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.PrivateImplementsBitwiseSpec", ]; +N: 261 "odd_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 380 "or_cancel_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 381 "or_iff_compat_r" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 368 "or_iff_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 370 "or_iff_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms_Prop", ]; +N: 371 "or_ind" [opaque=no, body=yes, kind=cnst, prop=yes, ]; +N: 302 "per_partial_app_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 325 "per_partial_app_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 284 "plus_n_O" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 283 "plus_n_Sm" [opaque=yes, body=yes, kind=cnst, prop=yes, ]; +N: 365 "pred" [opaque=no, body=yes, kind=cnst, prop=no, path="Init.Nat", ]; +N: 334 "pred" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 414 "pred_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 337 "pred_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 338 "pred_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 342 "pred_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="PeanoNat.Nat", ]; +N: 310 "reflexive_proper_proxy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 295 "reflexive_reflexive_proxy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 307 "reflexivity" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 275 "relation" [opaque=no, body=yes, kind=cnst, prop=no, path="Relation_Definitions", ]; +N: 280 "respectful" [opaque=no, body=yes, kind=cnst, prop=no, path="Morphisms", ]; +N: 341 "subrelation" [opaque=no, body=yes, kind=cnst, prop=no, path="RelationClasses", ]; +N: 332 "subrelation_proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 333 "subrelation_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 339 "subrelation_respectful" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 331 "succ_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 296 "succ_inj_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 357 "succ_le_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 367 "succ_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 329 "succ_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Nat", ]; +N: 330 "succ_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="PeanoNat.Nat", ]; +N: 322 "symmetry" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 225 "testbit" [opaque=no, body=yes, kind=cnst, prop=no, path="Nat", ]; +N: 234 "testbit_0_l" [body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 226 "testbit_bitwise_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.PrivateImplementsBitwiseSpec", ]; +N: 431 "trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Nat.Private_OrderTac.Tac", ]; +N: 269 "trans_co_eq_inv_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 281 "trans_co_eq_inv_impl_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 335 "trans_co_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 344 "trans_co_impl_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 437 "trans_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="OrdersTac", ]; +N: 304 "trans_sym_co_inv_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 324 "trans_sym_co_inv_impl_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Morphisms", ]; +N: 282 "transitivity" [opaque=no, body=yes, kind=cnst, prop=yes, path="RelationClasses", ]; +N: 313 "Equivalence" [kind=inductive, prop=no, path="RelationClasses", ]; +N: 247 "False" [kind=inductive, prop=no, ]; +N: 318 "PER" [kind=inductive, prop=no, path="RelationClasses", ]; +N: 407 "Params" [kind=inductive, prop=no, path="Morphisms", ]; +N: 427 "StrictOrder" [kind=inductive, prop=no, path="RelationClasses", ]; +N: 246 "True" [kind=inductive, prop=no, ]; +N: 262 "and" [kind=inductive, prop=no, ]; +N: 228 "bool" [kind=inductive, prop=no, ]; +N: 395 "comparison" [kind=inductive, prop=no, ]; +N: 229 "eq" [kind=inductive, prop=no, ]; +N: 286 "ex" [kind=inductive, prop=no, ]; +N: 248 "le" [kind=inductive, prop=no, ]; +N: 227 "nat" [kind=inductive, prop=no, ]; +N: 369 "or" [kind=inductive, prop=no, ]; +N: 438 "ord" [kind=inductive, prop=no, path="OrdersTac", ]; +N: 346 "unit" [kind=inductive, prop=no, ]; +N: 327 "Build_Equivalence" [kind=construct, prop=yes, path="RelationClasses", ]; +N: 319 "Build_PER" [kind=construct, prop=yes, path="RelationClasses", ]; +N: 409 "Build_Params" [kind=construct, prop=yes, path="Morphisms", ]; +N: 430 "Build_StrictOrder" [kind=construct, prop=yes, path="RelationClasses", ]; +N: 250 "I" [kind=construct, prop=yes, ]; +N: 272 "conj" [kind=construct, prop=yes, ]; +N: 263 "true" [kind=construct, prop=no, ]; +N: 396 "Eq" [kind=construct, prop=no, ]; +N: 231 "eq_refl" [kind=construct, prop=yes, ]; 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+E: 442 360 [weight=2, ]; +E: 442 431 [weight=1, ]; +E: 442 432 [weight=1, ]; +E: 442 439 [weight=1, ]; diff --git a/tests/PeanoNatBitwise.v b/tests/PeanoNatBitwise.v new file mode 100644 index 000000000..a397aaad7 --- /dev/null +++ b/tests/PeanoNatBitwise.v @@ -0,0 +1,5 @@ +From Stdlib Require Import Arith.PeanoNat. + +Require Import dpdgraph.dpdgraph. +Set DependGraph File "PeanoNatBitwise.dpd". +Print DependGraph Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec.land_spec. diff --git a/tests/Proofs.cmd b/tests/Proofs.cmd new file mode 100644 index 000000000..09a654833 --- /dev/null +++ b/tests/Proofs.cmd @@ -0,0 +1,5 @@ +Load "Proofs.v". +From dpdgraph Require Import dpdgraph. +Set Printing Fully Qualified. +Set DependGraph File "Proofs.dpd". +Print DependGraph Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec.land_spec. diff --git a/tests/Proofs.dot.oracle b/tests/Proofs.dot.oracle new file mode 100644 index 000000000..843195930 --- /dev/null +++ b/tests/Proofs.dot.oracle @@ -0,0 +1,883 @@ +digraph tests/Proofs { + graph [ratio=0.5] + node [style=filled] +Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 [label="iff_iff_iff_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_even_spec [label="even_spec", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_neq_succ_diag_l [label="neq_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_negb [label="negb", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_nlt_succ_diag_l [label="nlt_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_add_0_l [label="add_0_l", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_lt_le_incl [label="lt_le_incl", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Odd [label="Odd", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_Morphisms_iff_flip_impl_subrelation [label="iff_flip_impl_subrelation", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Even [label="Even", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_odd_spec [label="odd_spec", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_lt_succ_diag_r [label="lt_succ_diag_r", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_and [label="and", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_le_refl [label="le_refl", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_true [label="true", URL=, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_compare_refl [label="compare_refl", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_ex_intro [label="ex_intro", URL=, fillcolor="#7FAAFF"] ; +Corelib_Classes_Morphisms_Prop_not_iff_morphism [label="not_iff_morphism", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_iff [label="iff", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_compare [label="compare", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_compare_lt_iff [label="compare_lt_iff", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_0 [label="Odd_0", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_comparison [label="comparison", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_1 [label="Odd_1", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_Eq [label="Eq", URL=, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 [label="Odd_2", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_Lt [label="Lt", URL=, fillcolor="#7FAAFF"] ; +Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism [label="trans_co_eq_inv_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Peano_le_0_n [label="le_0_n", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_eq_proper_proxy [label="eq_proper_proxy", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Peano_le_n_S [label="le_n_S", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_iff_Transitive [label="iff_Transitive", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_Gt [label="Gt", URL=, fillcolor="#7FAAFF"] ; +Corelib_Init_Logic_conj [label="conj", URL=, fillcolor="#7FAAFF"] ; +Corelib_Classes_Morphisms_Prop_not_iff_morphism_obligation_1 [label="not_iff_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_Transitive [label="Transitive", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Logic_iff_trans [label="iff_trans", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_compare_eq_iff [label="compare_eq_iff", URL=, fillcolor="#7FFFD4"] ; +Corelib_Relations_Relation_Definitions_relation [label="relation", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Peano_eq_add_S [label="eq_add_S", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_compare_le_iff [label="compare_le_iff", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_ProperProxy [label="ProperProxy", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_Morphisms_impl_pars [label="impl_pars", URL=, fillcolor="#7FFFD4"] ; +Corelib_Program_Basics_flip [label="flip", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +Corelib_Program_Basics_impl [label="impl", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_Morphisms_Params [label="Params", URL=, fillcolor="#E2CDFA"] ; +Corelib_Classes_Morphisms_Proper [label="Proper", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_Morphisms_respectful [label="respectful", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_lt_asymm [label="lt_asymm", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_Build_Params [label="Build_Params", URL=, fillcolor="#7FAAFF"] ; +Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 [label="trans_co_eq_inv_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_transitivity [label="transitivity", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_eq_le_incl [label="eq_le_incl", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Peano_plus_n_Sm [label="plus_n_Sm", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_le_le_succ_r [label="le_le_succ_r", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Peano_plus_n_O [label="plus_n_O", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_le_succ_r [label="le_succ_r", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_neq_succ_0 [label="neq_succ_0", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_f_equal [label="f_equal", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_ex [label="ex", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_pred_0 [label="pred_0", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_trans [label="lt_trans", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Nat_add [label="add", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Peano_f_equal_nat [label="f_equal_nat", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_not_gt_le [label="not_gt_le", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_not [label="not", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_0 [label="Even_0", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_1 [label="Even_1", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_lt_total [label="lt_total", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 [label="Even_2", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_lt_trichotomy [label="lt_trichotomy", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_add_wd [label="add_wd", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_le_gt_cases [label="le_gt_cases", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_reflexive_reflexive_proxy [label="reflexive_reflexive_proxy", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_le_lteq [label="le_lteq", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_succ_inj_wd [label="succ_inj_wd", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_StrictOrder_Irreflexive [label="StrictOrder_Irreflexive", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_Reflexive_partial_app_morphism [label="Reflexive_partial_app_morphism", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_lt_strorder [label="lt_strorder", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_add_succ_l [label="add_succ_l", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_StrictOrder [label="StrictOrder", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_add_succ_r [label="add_succ_r", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_add_0_r [label="add_0_r", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_Irreflexive [label="Irreflexive", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_RelationClasses_iff_equivalence [label="iff_equivalence", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_complement [label="complement", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_RelationClasses_Build_StrictOrder [label="Build_StrictOrder", URL=, fillcolor="#7FAAFF"] ; +Corelib_Classes_Morphisms_per_partial_app_morphism [label="per_partial_app_morphism", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans [label="trans", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_Equivalence_Transitive [label="Equivalence_Transitive", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Structures_OrdersTac_OLT [label="OLT", URL=, fillcolor="#7FAAFF"] ; +Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism [label="trans_sym_co_inv_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_StrictOrder_Transitive [label="StrictOrder_Transitive", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_PER_morphism [label="PER_morphism", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_bi_induction [label="bi_induction", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_reflexivity [label="reflexivity", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_eq_equiv [label="eq_equiv", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_interp_ord [label="interp_ord", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_RelationClasses_Equivalence_PER [label="Equivalence_PER", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Structures_OrdersTac_trans_ord [label="trans_ord", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_RelationClasses_iff_Reflexive [label="iff_Reflexive", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Structures_OrdersTac_ord [label="ord", URL=, fillcolor="#E2CDFA"] ; +Corelib_Classes_Morphisms_reflexive_proper_proxy [label="reflexive_proper_proxy", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Structures_OrdersTac_OEQ [label="OEQ", URL=, fillcolor="#7FAAFF"] ; +Corelib_Classes_RelationClasses_Equivalence_Reflexive [label="Equivalence_Reflexive", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Structures_OrdersTac_OLE [label="OLE", URL=, fillcolor="#7FAAFF"] ; +Corelib_Classes_RelationClasses_Reflexive [label="Reflexive", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_RelationClasses_Equivalence [label="Equivalence", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_lt_compat [label="lt_compat", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_eq [label="lt_eq", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_Symmetric [label="Symmetric", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_Morphisms_ReflexiveProxy [label="ReflexiveProxy", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Logic_iff_refl [label="iff_refl", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_Equivalence_Symmetric [label="Equivalence_Symmetric", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_PER [label="PER", URL=, fillcolor="#E2CDFA"] ; +Corelib_Classes_RelationClasses_Build_PER [label="Build_PER", URL=, fillcolor="#7FAAFF"] ; +Corelib_Classes_Morphisms_PER_morphism_obligation_1 [label="PER_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_PER_Symmetric [label="PER_Symmetric", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_symmetry [label="symmetry", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_PER_Transitive [label="PER_Transitive", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 [label="trans_sym_co_inv_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_per_partial_app_morphism_obligation_1 [label="per_partial_app_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_iff_Symmetric [label="iff_Symmetric", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_Build_Equivalence [label="Build_Equivalence", URL=, fillcolor="#7FAAFF"] ; +Corelib_Init_Logic_iff_sym [label="iff_sym", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_succ_wd [label="succ_wd", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_succ_wd_obligation_1 [label="succ_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_succ_inj [label="succ_inj", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_subrelation_proper [label="subrelation_proper", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_subrelation_refl [label="subrelation_refl", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_pred [label="pred", URL=, fillcolor="#F070D1"] ; +Corelib_Classes_Morphisms_trans_co_impl_morphism [label="trans_co_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_iff_impl_subrelation [label="iff_impl_subrelation", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_pred_succ [label="pred_succ", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_pred_wd [label="pred_wd", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_subrelation_respectful [label="subrelation_respectful", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_tt [label="tt", URL=, fillcolor="#7FAAFF"] ; +Corelib_Classes_RelationClasses_subrelation [label="subrelation", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_pred_wd_obligation_1 [label="pred_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_and_ind [label="and_ind", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_trans_co_impl_morphism_obligation_1 [label="trans_co_impl_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Init_Unconvertible [label="Unconvertible", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Datatypes_unit [label="unit", URL=, fillcolor="#E2CDFA"] ; +Corelib_Classes_RelationClasses_eq_equivalence [label="eq_equivalence", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_eq_Reflexive [label="eq_Reflexive", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_eq_Transitive [label="eq_Transitive", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_land_spec [label="land_spec", URL=, peripheries=3, fillcolor="#7FFFD4"] ; +Corelib_Classes_RelationClasses_eq_Symmetric [label="eq_Symmetric", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_land [label="land", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Logic_eq_trans [label="eq_trans", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_andb [label="andb", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_add_wd_obligation_1 [label="add_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_testbit [label="testbit", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_succ_double [label="div2_succ_double", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 [label="testbit_bitwise_1", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_double [label="div2_double", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_nat [label="nat", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_le_0_l [label="le_0_l", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_bool [label="bool", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_le_trans [label="le_trans", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_eq [label="eq", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_succ_le_mono [label="succ_le_mono", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_false [label="false", URL=, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_le_div2 [label="le_div2", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Logic_eq_refl [label="eq_refl", URL=, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_lt_succ_r [label="lt_succ_r", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Peano_le_n [label="le_n", URL=, fillcolor="#7FAAFF"] ; +Corelib_Init_Peano_lt [label="lt", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Datatypes_S [label="S", URL=, fillcolor="#7FAAFF"] ; +Corelib_Init_Peano_le_S [label="le_S", URL=, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l [label="testbit_0_l", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Peano_le_S_n [label="le_S_n", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_odd [label="odd", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Peano_le_ind [label="le_ind", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Peano_le_pred [label="le_pred", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_div2 [label="div2", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Nat_pred [label="pred", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Logic_False_ind [label="False_ind", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_lt_eq_cases [label="lt_eq_cases", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr [label="div2_decr", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_succ_lt_mono [label="succ_lt_mono", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_bitwise [label="div2_bitwise", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_Prop_or_iff_morphism [label="or_iff_morphism", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_nat_ind [label="nat_ind", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_or [label="or", URL=, fillcolor="#E2CDFA"] ; +Corelib_Init_Logic_eq_ind [label="eq_ind", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_Prop_or_iff_morphism_obligation_1 [label="or_iff_morphism_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_eq_sym [label="eq_sym", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_or_ind [label="or_ind", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_eq_ind_r [label="eq_ind_r", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_or_introl [label="or_introl", URL=, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_bitwise [label="bitwise", URL=, fillcolor="#F070D1"] ; +Corelib_Init_Logic_or_intror [label="or_intror", URL=, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_odd_bitwise [label="odd_bitwise", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_True [label="True", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_le_succ_l [label="le_succ_l", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_False [label="False", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_lt_irrefl [label="lt_irrefl", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Peano_le [label="le", URL=, fillcolor="#E2CDFA"] ; +Stdlib_Arith_PeanoNat_Nat_nle_succ_diag_l [label="nle_succ_diag_l", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Datatypes_O [label="O", URL=, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_central_induction [label="central_induction", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_I [label="I", URL=, fillcolor="#7FAAFF"] ; +Stdlib_Arith_PeanoNat_Nat_le_wd [label="le_wd", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Bool_Bool_negb_false_iff [label="negb_false_iff", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_lt_wd [label="lt_wd", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_or_cancel_r [label="or_cancel_r", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_add_comm [label="add_comm", URL=, fillcolor="#7FFFD4"] ; +Corelib_Init_Logic_or_iff_compat_r [label="or_iff_compat_r", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_add [label="add", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_mul [label="mul", URL=, fillcolor="#F070D1"] ; +Stdlib_Arith_PeanoNat_Nat_lt_wd_obligation_1 [label="lt_wd_obligation_1", URL=, fillcolor="#7FFFD4"] ; +Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism [label="iff_iff_iff_impl_morphism", URL=, fillcolor="#7FFFD4"] ; +Stdlib_Arith_PeanoNat_Nat_even [label="even", URL=, fillcolor="#F070D1"] ; + Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> Corelib_Init_Logic_iff [] ; + Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> Corelib_Init_Logic_conj [] ; + Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> Corelib_Program_Basics_impl [] ; + Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 -> Corelib_Init_Logic_and_ind [] ; + Stdlib_Arith_PeanoNat_Nat_even_spec -> Stdlib_Arith_PeanoNat_Nat_even [] ; + Stdlib_Arith_PeanoNat_Nat_even_spec -> Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_even_spec -> Corelib_Classes_Morphisms_eq_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_even_spec -> Corelib_Classes_RelationClasses_iff_Transitive [] ; + Stdlib_Arith_PeanoNat_Nat_even_spec -> Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_0 [] ; + Stdlib_Arith_PeanoNat_Nat_even_spec -> Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_1 [] ; + Stdlib_Arith_PeanoNat_Nat_even_spec -> Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 [] ; + Stdlib_Arith_PeanoNat_Nat_neq_succ_diag_l -> Stdlib_Arith_PeanoNat_Nat_lt_irrefl [] ; + Stdlib_Arith_PeanoNat_Nat_neq_succ_diag_l -> Stdlib_Arith_PeanoNat_Nat_lt_wd [] ; + Stdlib_Arith_PeanoNat_Nat_neq_succ_diag_l -> Stdlib_Arith_PeanoNat_Nat_lt_succ_diag_r [] ; + Corelib_Init_Datatypes_negb -> Corelib_Init_Datatypes_bool [] ; + Corelib_Init_Datatypes_negb -> Corelib_Init_Datatypes_false [] ; + Corelib_Init_Datatypes_negb -> Corelib_Init_Datatypes_true [] ; + Stdlib_Arith_PeanoNat_Nat_nlt_succ_diag_l -> Stdlib_Arith_PeanoNat_Nat_lt_succ_r [] ; + Stdlib_Arith_PeanoNat_Nat_nlt_succ_diag_l -> Stdlib_Arith_PeanoNat_Nat_lt_irrefl [] ; + Stdlib_Arith_PeanoNat_Nat_nlt_succ_diag_l -> Stdlib_Arith_PeanoNat_Nat_lt_le_incl [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_l -> Corelib_Init_Logic_eq [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_l -> Corelib_Init_Logic_eq_refl [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_l -> Corelib_Init_Datatypes_O [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_l -> Stdlib_Arith_PeanoNat_Nat_add [] ; + Stdlib_Arith_PeanoNat_Nat_lt_le_incl -> Stdlib_Arith_PeanoNat_Nat_lt_eq_cases [] ; + Stdlib_Arith_PeanoNat_Nat_Odd -> Corelib_Init_Logic_eq [] ; + Stdlib_Arith_PeanoNat_Nat_Odd -> Stdlib_Arith_PeanoNat_Nat_mul [] ; + Stdlib_Arith_PeanoNat_Nat_Odd -> Corelib_Init_Logic_ex [] ; + Corelib_Classes_Morphisms_iff_flip_impl_subrelation -> Corelib_Init_Logic_iff [] ; + Corelib_Classes_Morphisms_iff_flip_impl_subrelation -> Corelib_Program_Basics_flip [] ; + Corelib_Classes_Morphisms_iff_flip_impl_subrelation -> Corelib_Program_Basics_impl [] ; + Corelib_Classes_Morphisms_iff_flip_impl_subrelation -> Corelib_Classes_RelationClasses_subrelation [] ; + Corelib_Classes_Morphisms_iff_flip_impl_subrelation -> Corelib_Init_Logic_and_ind [] ; + Stdlib_Arith_PeanoNat_Nat_Even -> Corelib_Init_Logic_eq [] ; + Stdlib_Arith_PeanoNat_Nat_Even -> Stdlib_Arith_PeanoNat_Nat_mul [] ; + Stdlib_Arith_PeanoNat_Nat_Even -> Corelib_Init_Logic_ex [] ; + Stdlib_Arith_PeanoNat_Nat_odd_spec -> Stdlib_Arith_PeanoNat_Nat_odd [] ; + Stdlib_Arith_PeanoNat_Nat_odd_spec -> Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_0 [] ; + Stdlib_Arith_PeanoNat_Nat_odd_spec -> Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_1 [] ; + Stdlib_Arith_PeanoNat_Nat_odd_spec -> Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 [] ; + Stdlib_Arith_PeanoNat_Nat_odd_spec -> Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_odd_spec -> Corelib_Classes_Morphisms_eq_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_odd_spec -> Corelib_Classes_RelationClasses_iff_Transitive [] ; + Stdlib_Arith_PeanoNat_Nat_lt_succ_diag_r -> Stdlib_Arith_PeanoNat_Nat_lt_succ_r [] ; + Stdlib_Arith_PeanoNat_Nat_lt_succ_diag_r -> Corelib_Classes_Morphisms_iff_flip_impl_subrelation [] ; + Stdlib_Arith_PeanoNat_Nat_lt_succ_diag_r -> Stdlib_Arith_PeanoNat_Nat_le_refl [] ; + Stdlib_Arith_PeanoNat_Nat_le_refl -> Stdlib_Arith_PeanoNat_Nat_eq_equiv [] ; + Stdlib_Arith_PeanoNat_Nat_le_refl -> Corelib_Classes_RelationClasses_reflexivity [] ; + Stdlib_Arith_PeanoNat_Nat_le_refl -> Corelib_Classes_RelationClasses_Equivalence_Reflexive [] ; + Stdlib_Arith_PeanoNat_Nat_le_refl -> Stdlib_Arith_PeanoNat_Nat_lt_eq_cases [] ; + Stdlib_Arith_PeanoNat_Nat_compare_refl -> Stdlib_Arith_PeanoNat_Nat_eq_equiv [] ; + Stdlib_Arith_PeanoNat_Nat_compare_refl -> Corelib_Classes_RelationClasses_reflexivity [] ; + Stdlib_Arith_PeanoNat_Nat_compare_refl -> Corelib_Classes_RelationClasses_Equivalence_Reflexive [] ; + Stdlib_Arith_PeanoNat_Nat_compare_refl -> Stdlib_Arith_PeanoNat_Nat_compare_eq_iff [] ; + Corelib_Classes_Morphisms_Prop_not_iff_morphism -> Corelib_Classes_Morphisms_Proper [] ; + Corelib_Classes_Morphisms_Prop_not_iff_morphism -> Corelib_Classes_Morphisms_Prop_not_iff_morphism_obligation_1 [] ; + Corelib_Init_Logic_iff -> Corelib_Init_Logic_and [] ; + Stdlib_Arith_PeanoNat_Nat_compare -> Corelib_Init_Datatypes_nat [] ; + Stdlib_Arith_PeanoNat_Nat_compare -> Corelib_Init_Datatypes_comparison [] ; + Stdlib_Arith_PeanoNat_Nat_compare -> Corelib_Init_Datatypes_Eq [] ; + Stdlib_Arith_PeanoNat_Nat_compare -> Corelib_Init_Datatypes_Lt [] ; + Stdlib_Arith_PeanoNat_Nat_compare -> Corelib_Init_Datatypes_Gt [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Init_Logic_False_ind [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Init_Logic_eq_ind [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Init_Logic_True [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Init_Logic_I [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Classes_Morphisms_eq_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Classes_RelationClasses_iff_Transitive [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Init_Peano_lt [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Init_Peano_le_S_n [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Stdlib_Arith_PeanoNat_Nat_compare [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Init_Peano_le_0_n [] ; + Stdlib_Arith_PeanoNat_Nat_compare_lt_iff -> Corelib_Init_Peano_le_n_S [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_0 -> Corelib_Init_Logic_eq_refl [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_0 -> Corelib_Init_Logic_False_ind [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_0 -> Corelib_Init_Logic_eq_ind [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_0 -> Corelib_Init_Logic_True [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_0 -> Corelib_Init_Logic_I [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_0 -> Stdlib_Arith_PeanoNat_Nat_Odd [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_0 -> Corelib_Init_Logic_not [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_1 -> Corelib_Init_Logic_eq_refl [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_1 -> Stdlib_Arith_PeanoNat_Nat_Odd [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_1 -> Corelib_Init_Logic_ex_intro [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 -> Corelib_Init_Logic_False_ind [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 -> Corelib_Init_Logic_eq_ind_r [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 -> Corelib_Init_Logic_True [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 -> Corelib_Init_Logic_I [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 -> Stdlib_Arith_PeanoNat_Nat_Odd [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 -> Corelib_Init_Logic_ex_intro [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 -> Corelib_Init_Logic_iff [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 -> Corelib_Init_Logic_conj [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 -> Corelib_Init_Peano_plus_n_Sm [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2 -> Corelib_Init_Peano_plus_n_O [] ; + Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism -> Corelib_Classes_Morphisms_Proper [] ; + Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism -> Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 [] ; + Corelib_Init_Peano_le_0_n -> Corelib_Init_Peano_le_n [] ; + Corelib_Init_Peano_le_0_n -> Corelib_Init_Datatypes_nat_ind [] ; + Corelib_Init_Peano_le_0_n -> Corelib_Init_Peano_le [] ; + Corelib_Init_Peano_le_0_n -> Corelib_Init_Peano_le_S [] ; + Corelib_Classes_Morphisms_eq_proper_proxy -> Corelib_Init_Logic_eq [] ; + Corelib_Classes_Morphisms_eq_proper_proxy -> Corelib_Init_Logic_eq_refl [] ; + Corelib_Classes_Morphisms_eq_proper_proxy -> Corelib_Classes_Morphisms_ProperProxy [] ; + Corelib_Init_Peano_le_n_S -> Corelib_Init_Peano_le_n [] ; + Corelib_Init_Peano_le_n_S -> Corelib_Init_Peano_le_S [] ; + Corelib_Init_Peano_le_n_S -> Corelib_Init_Peano_le_ind [] ; + Corelib_Classes_RelationClasses_iff_Transitive -> Corelib_Classes_RelationClasses_Transitive [] ; + Corelib_Classes_RelationClasses_iff_Transitive -> Corelib_Init_Logic_iff_trans [] ; + Corelib_Classes_Morphisms_Prop_not_iff_morphism_obligation_1 -> Corelib_Init_Logic_False_ind [] ; + Corelib_Classes_Morphisms_Prop_not_iff_morphism_obligation_1 -> Corelib_Init_Logic_iff [] ; + Corelib_Classes_Morphisms_Prop_not_iff_morphism_obligation_1 -> Corelib_Init_Logic_conj [] ; + Corelib_Classes_Morphisms_Prop_not_iff_morphism_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Corelib_Classes_Morphisms_Prop_not_iff_morphism_obligation_1 -> Corelib_Init_Logic_not [] ; + Corelib_Classes_Morphisms_Prop_not_iff_morphism_obligation_1 -> Corelib_Init_Logic_and_ind [] ; + Corelib_Classes_RelationClasses_Transitive -> Corelib_Relations_Relation_Definitions_relation [] ; + Corelib_Init_Logic_iff_trans -> Corelib_Init_Logic_iff [] ; + Corelib_Init_Logic_iff_trans -> Corelib_Init_Logic_conj [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Corelib_Init_Logic_False_ind [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Corelib_Init_Datatypes_nat_ind [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Corelib_Init_Logic_eq_ind [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Corelib_Init_Logic_True [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Corelib_Init_Logic_I [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Corelib_Classes_Morphisms_eq_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Corelib_Classes_RelationClasses_iff_Transitive [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Corelib_Init_Peano_f_equal_nat [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Stdlib_Arith_PeanoNat_Nat_compare [] ; + Stdlib_Arith_PeanoNat_Nat_compare_eq_iff -> Corelib_Init_Peano_eq_add_S [] ; + Corelib_Init_Peano_eq_add_S -> Corelib_Init_Datatypes_S [] ; + Corelib_Init_Peano_eq_add_S -> Corelib_Init_Logic_f_equal [] ; + Corelib_Init_Peano_eq_add_S -> Corelib_Init_Nat_pred [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Init_Logic_False_ind [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Init_Logic_eq_ind [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Init_Logic_True [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Init_Logic_I [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Classes_Morphisms_eq_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Classes_RelationClasses_iff_Transitive [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Init_Logic_not [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Init_Peano_le_S_n [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Stdlib_Arith_PeanoNat_Nat_compare [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Init_Peano_le_0_n [] ; + Stdlib_Arith_PeanoNat_Nat_compare_le_iff -> Corelib_Init_Peano_le_n_S [] ; + Corelib_Classes_Morphisms_ProperProxy -> Corelib_Relations_Relation_Definitions_relation [] ; + Corelib_Classes_Morphisms_impl_pars -> Corelib_Init_Datatypes_O [] ; + Corelib_Classes_Morphisms_impl_pars -> Corelib_Program_Basics_impl [] ; + Corelib_Classes_Morphisms_impl_pars -> Corelib_Classes_Morphisms_Params [] ; + Corelib_Classes_Morphisms_impl_pars -> Corelib_Classes_Morphisms_Build_Params [] ; + Stdlib_Arith_PeanoNat_Nat_lt_trans -> Corelib_Classes_Morphisms_impl_pars [] ; + Stdlib_Arith_PeanoNat_Nat_lt_trans -> Stdlib_Arith_PeanoNat_Nat_lt_asymm [] ; + Corelib_Classes_Morphisms_Params -> Corelib_Init_Datatypes_nat [] ; + Corelib_Classes_Morphisms_Proper -> Corelib_Relations_Relation_Definitions_relation [] ; + Corelib_Classes_Morphisms_respectful -> Corelib_Relations_Relation_Definitions_relation [] ; + Stdlib_Arith_PeanoNat_Nat_lt_asymm -> Stdlib_Arith_PeanoNat_Nat_le_succ_l [] ; + Corelib_Classes_Morphisms_Build_Params -> Corelib_Init_Datatypes_nat [] ; + Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Corelib_Init_Logic_eq [] ; + Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Corelib_Program_Basics_flip [] ; + Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Corelib_Program_Basics_impl [] ; + Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism_obligation_1 -> Corelib_Classes_RelationClasses_transitivity [] ; + Corelib_Classes_RelationClasses_transitivity -> Corelib_Classes_RelationClasses_Transitive [] ; + Stdlib_Arith_PeanoNat_Nat_eq_le_incl -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Stdlib_Arith_PeanoNat_Nat_eq_le_incl -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_not_gt_le [] ; + Stdlib_Arith_PeanoNat_Nat_eq_le_incl -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_eq [] ; + Corelib_Init_Peano_plus_n_Sm -> Corelib_Init_Datatypes_nat_ind [] ; + Corelib_Init_Peano_plus_n_Sm -> Corelib_Init_Nat_add [] ; + Corelib_Init_Peano_plus_n_Sm -> Corelib_Init_Peano_f_equal_nat [] ; + Stdlib_Arith_PeanoNat_Nat_le_le_succ_r -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_trans [] ; + Stdlib_Arith_PeanoNat_Nat_le_le_succ_r -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_irrefl [] ; + Stdlib_Arith_PeanoNat_Nat_le_le_succ_r -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_not_gt_le [] ; + Corelib_Init_Peano_plus_n_O -> Corelib_Init_Datatypes_nat_ind [] ; + Corelib_Init_Peano_plus_n_O -> Corelib_Init_Nat_add [] ; + Corelib_Init_Peano_plus_n_O -> Corelib_Init_Peano_f_equal_nat [] ; + Stdlib_Arith_PeanoNat_Nat_le_succ_r -> Corelib_Classes_RelationClasses_reflexivity [] ; + Stdlib_Arith_PeanoNat_Nat_le_succ_r -> Stdlib_Arith_PeanoNat_Nat_lt_succ_r [] ; + Stdlib_Arith_PeanoNat_Nat_le_succ_r -> Stdlib_Arith_PeanoNat_Nat_lt_eq_cases [] ; + Stdlib_Arith_PeanoNat_Nat_neq_succ_0 -> Corelib_Classes_Morphisms_PER_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_neq_succ_0 -> Stdlib_Arith_PeanoNat_Nat_succ_wd [] ; + Stdlib_Arith_PeanoNat_Nat_neq_succ_0 -> Corelib_Classes_Morphisms_iff_impl_subrelation [] ; + Stdlib_Arith_PeanoNat_Nat_neq_succ_0 -> Stdlib_Arith_PeanoNat_Nat_pred_succ [] ; + Stdlib_Arith_PeanoNat_Nat_neq_succ_0 -> Stdlib_Arith_PeanoNat_Nat_pred_wd [] ; + Stdlib_Arith_PeanoNat_Nat_neq_succ_0 -> Stdlib_Arith_PeanoNat_Nat_neq_succ_diag_l [] ; + Stdlib_Arith_PeanoNat_Nat_neq_succ_0 -> Stdlib_Arith_PeanoNat_Nat_pred_0 [] ; + Corelib_Init_Logic_f_equal -> Corelib_Init_Logic_eq [] ; + Corelib_Init_Logic_f_equal -> Corelib_Init_Logic_eq_refl [] ; + Stdlib_Arith_PeanoNat_Nat_pred_0 -> Corelib_Init_Logic_eq [] ; + Stdlib_Arith_PeanoNat_Nat_pred_0 -> Corelib_Init_Logic_eq_refl [] ; + Stdlib_Arith_PeanoNat_Nat_pred_0 -> Corelib_Init_Datatypes_O [] ; + Stdlib_Arith_PeanoNat_Nat_pred_0 -> Stdlib_Arith_PeanoNat_Nat_pred [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_trans -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans [] ; + Corelib_Init_Nat_add -> Corelib_Init_Datatypes_nat [] ; + Corelib_Init_Nat_add -> Corelib_Init_Datatypes_S [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_irrefl -> Corelib_Classes_RelationClasses_StrictOrder_Irreflexive [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_irrefl -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_strorder [] ; + Corelib_Init_Peano_f_equal_nat -> Corelib_Init_Datatypes_nat [] ; + Corelib_Init_Peano_f_equal_nat -> Corelib_Init_Logic_f_equal [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_not_gt_le -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_le_lteq [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_not_gt_le -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_total [] ; + Corelib_Init_Logic_not -> Corelib_Init_Logic_False [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_le_lteq -> Stdlib_Arith_PeanoNat_Nat_le_lteq [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_0 -> Corelib_Init_Logic_eq_refl [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_0 -> Stdlib_Arith_PeanoNat_Nat_Even [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_0 -> Corelib_Init_Logic_ex_intro [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_total -> Stdlib_Arith_PeanoNat_Nat_lt_total [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_1 -> Corelib_Init_Logic_False_ind [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_1 -> Corelib_Init_Logic_eq_ind_r [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_1 -> Corelib_Init_Logic_True [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_1 -> Corelib_Init_Logic_I [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_1 -> Stdlib_Arith_PeanoNat_Nat_Even [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_1 -> Corelib_Init_Peano_plus_n_Sm [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_1 -> Corelib_Init_Logic_not [] ; + Stdlib_Arith_PeanoNat_Nat_lt_total -> Stdlib_Arith_PeanoNat_Nat_lt_trichotomy [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 -> Corelib_Init_Logic_False_ind [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 -> Corelib_Init_Logic_eq_ind_r [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 -> Corelib_Init_Logic_True [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 -> Corelib_Init_Logic_I [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 -> Stdlib_Arith_PeanoNat_Nat_Even [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 -> Corelib_Init_Logic_ex_intro [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 -> Corelib_Init_Logic_iff [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 -> Corelib_Init_Logic_conj [] ; + Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2 -> Corelib_Init_Peano_plus_n_Sm [] ; + Stdlib_Arith_PeanoNat_Nat_lt_trichotomy -> Stdlib_Arith_PeanoNat_Nat_le_gt_cases [] ; + Stdlib_Arith_PeanoNat_Nat_add_wd -> Corelib_Classes_Morphisms_Proper [] ; + Stdlib_Arith_PeanoNat_Nat_add_wd -> Stdlib_Arith_PeanoNat_Nat_add_wd_obligation_1 [] ; + Stdlib_Arith_PeanoNat_Nat_le_gt_cases -> Stdlib_Arith_PeanoNat_Nat_le_succ_l [] ; + Stdlib_Arith_PeanoNat_Nat_eq_equiv -> Corelib_Init_Datatypes_nat [] ; + Stdlib_Arith_PeanoNat_Nat_eq_equiv -> Corelib_Classes_RelationClasses_eq_equivalence [] ; + Corelib_Classes_Morphisms_reflexive_reflexive_proxy -> Corelib_Classes_RelationClasses_Reflexive [] ; + Corelib_Classes_Morphisms_reflexive_reflexive_proxy -> Corelib_Classes_Morphisms_ReflexiveProxy [] ; + Stdlib_Arith_PeanoNat_Nat_le_lteq -> Stdlib_Arith_PeanoNat_Nat_lt_eq_cases [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj_wd -> Stdlib_Arith_PeanoNat_Nat_succ_wd [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj_wd -> Stdlib_Arith_PeanoNat_Nat_succ_inj [] ; + Corelib_Classes_RelationClasses_StrictOrder_Irreflexive -> Corelib_Classes_RelationClasses_StrictOrder [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_strorder -> Stdlib_Arith_PeanoNat_Nat_lt_strorder [] ; + Corelib_Classes_Morphisms_Reflexive_partial_app_morphism -> Corelib_Classes_Morphisms_ProperProxy [] ; + Corelib_Classes_Morphisms_Reflexive_partial_app_morphism -> Corelib_Classes_Morphisms_Proper [] ; + Corelib_Classes_Morphisms_Reflexive_partial_app_morphism -> Corelib_Classes_Morphisms_respectful [] ; + Stdlib_Arith_PeanoNat_Nat_lt_strorder -> Stdlib_Arith_PeanoNat_Nat_lt_trans [] ; + Stdlib_Arith_PeanoNat_Nat_lt_strorder -> Corelib_Classes_RelationClasses_StrictOrder [] ; + Stdlib_Arith_PeanoNat_Nat_lt_strorder -> Corelib_Classes_RelationClasses_Build_StrictOrder [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_l -> Corelib_Init_Logic_eq [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_l -> Corelib_Init_Logic_eq_refl [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_l -> Stdlib_Arith_PeanoNat_Nat_add [] ; + Corelib_Classes_RelationClasses_StrictOrder -> Corelib_Classes_RelationClasses_Transitive [] ; + Corelib_Classes_RelationClasses_StrictOrder -> Corelib_Classes_RelationClasses_Irreflexive [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Stdlib_Arith_PeanoNat_Nat_add_0_l [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Corelib_Classes_Morphisms_eq_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Stdlib_Arith_PeanoNat_Nat_add_wd [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Stdlib_Arith_PeanoNat_Nat_succ_inj_wd [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Stdlib_Arith_PeanoNat_Nat_add_succ_l [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Corelib_Classes_RelationClasses_iff_equivalence [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Corelib_Classes_Morphisms_per_partial_app_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Stdlib_Arith_PeanoNat_Nat_bi_induction [] ; + Stdlib_Arith_PeanoNat_Nat_add_succ_r -> Corelib_Classes_RelationClasses_reflexivity [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_r -> Stdlib_Arith_PeanoNat_Nat_add_0_l [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_r -> Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_r -> Corelib_Classes_Morphisms_eq_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_r -> Stdlib_Arith_PeanoNat_Nat_add_wd [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_r -> Stdlib_Arith_PeanoNat_Nat_succ_inj_wd [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_r -> Stdlib_Arith_PeanoNat_Nat_add_succ_l [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_r -> Corelib_Classes_RelationClasses_iff_equivalence [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_r -> Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_r -> Stdlib_Arith_PeanoNat_Nat_bi_induction [] ; + Stdlib_Arith_PeanoNat_Nat_add_0_r -> Corelib_Classes_RelationClasses_reflexivity [] ; + Corelib_Classes_RelationClasses_Irreflexive -> Corelib_Classes_RelationClasses_Reflexive [] ; + Corelib_Classes_RelationClasses_Irreflexive -> Corelib_Classes_RelationClasses_complement [] ; + Corelib_Classes_RelationClasses_iff_equivalence -> Corelib_Classes_RelationClasses_iff_Transitive [] ; + Corelib_Classes_RelationClasses_iff_equivalence -> Corelib_Classes_RelationClasses_iff_Reflexive [] ; + Corelib_Classes_RelationClasses_iff_equivalence -> Corelib_Classes_RelationClasses_Equivalence [] ; + Corelib_Classes_RelationClasses_iff_equivalence -> Corelib_Classes_RelationClasses_iff_Symmetric [] ; + Corelib_Classes_RelationClasses_iff_equivalence -> Corelib_Classes_RelationClasses_Build_Equivalence [] ; + Corelib_Classes_RelationClasses_complement -> Corelib_Init_Logic_False [] ; + Corelib_Classes_RelationClasses_complement -> Corelib_Relations_Relation_Definitions_relation [] ; + Corelib_Classes_RelationClasses_Build_StrictOrder -> Corelib_Classes_RelationClasses_Transitive [] ; + Corelib_Classes_RelationClasses_Build_StrictOrder -> Corelib_Classes_RelationClasses_Irreflexive [] ; + Corelib_Classes_Morphisms_per_partial_app_morphism -> Corelib_Classes_Morphisms_Proper [] ; + Corelib_Classes_Morphisms_per_partial_app_morphism -> Corelib_Classes_Morphisms_per_partial_app_morphism_obligation_1 [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_le_lteq [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_strorder [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans -> Corelib_Classes_RelationClasses_StrictOrder_Transitive [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_compat [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_eq_equiv [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_interp_ord [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans -> Stdlib_Structures_OrdersTac_trans_ord [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans -> Stdlib_Structures_OrdersTac_OEQ [] ; + Corelib_Classes_RelationClasses_Equivalence_Transitive -> Corelib_Classes_RelationClasses_Equivalence [] ; + Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism -> Corelib_Classes_Morphisms_Proper [] ; + Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism -> Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 [] ; + Corelib_Classes_RelationClasses_StrictOrder_Transitive -> Corelib_Classes_RelationClasses_StrictOrder [] ; + Corelib_Classes_Morphisms_PER_morphism -> Corelib_Classes_Morphisms_Proper [] ; + Corelib_Classes_Morphisms_PER_morphism -> Corelib_Classes_Morphisms_PER_morphism_obligation_1 [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_compat -> Stdlib_Arith_PeanoNat_Nat_lt_compat [] ; + Stdlib_Arith_PeanoNat_Nat_bi_induction -> Corelib_Init_Logic_eq [] ; + Stdlib_Arith_PeanoNat_Nat_bi_induction -> Corelib_Init_Datatypes_nat_ind [] ; + Stdlib_Arith_PeanoNat_Nat_bi_induction -> Corelib_Init_Logic_iff [] ; + Stdlib_Arith_PeanoNat_Nat_bi_induction -> Corelib_Classes_Morphisms_Proper [] ; + Stdlib_Arith_PeanoNat_Nat_bi_induction -> Corelib_Classes_Morphisms_respectful [] ; + Corelib_Classes_RelationClasses_reflexivity -> Corelib_Classes_RelationClasses_Reflexive [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_eq_equiv -> Stdlib_Arith_PeanoNat_Nat_eq_equiv [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_interp_ord -> Corelib_Init_Logic_eq [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_interp_ord -> Corelib_Init_Peano_lt [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_interp_ord -> Stdlib_Structures_OrdersTac_ord [] ; + Corelib_Classes_RelationClasses_Equivalence_PER -> Corelib_Classes_RelationClasses_Equivalence_Transitive [] ; + Corelib_Classes_RelationClasses_Equivalence_PER -> Corelib_Classes_RelationClasses_Equivalence_Symmetric [] ; + Corelib_Classes_RelationClasses_Equivalence_PER -> Corelib_Classes_RelationClasses_PER [] ; + Corelib_Classes_RelationClasses_Equivalence_PER -> Corelib_Classes_RelationClasses_Build_PER [] ; + Stdlib_Structures_OrdersTac_trans_ord -> Stdlib_Structures_OrdersTac_OLT [] ; + Stdlib_Structures_OrdersTac_trans_ord -> Stdlib_Structures_OrdersTac_ord [] ; + Stdlib_Structures_OrdersTac_trans_ord -> Stdlib_Structures_OrdersTac_OLE [] ; + Corelib_Classes_RelationClasses_iff_Reflexive -> Corelib_Classes_RelationClasses_Reflexive [] ; + Corelib_Classes_RelationClasses_iff_Reflexive -> Corelib_Init_Logic_iff_refl [] ; + Corelib_Classes_Morphisms_reflexive_proper_proxy -> Corelib_Classes_Morphisms_ProperProxy [] ; + Corelib_Classes_Morphisms_reflexive_proper_proxy -> Corelib_Classes_Morphisms_ReflexiveProxy [] ; + Corelib_Classes_RelationClasses_Equivalence_Reflexive -> Corelib_Classes_RelationClasses_Equivalence [] ; + Corelib_Classes_RelationClasses_Reflexive -> Corelib_Relations_Relation_Definitions_relation [] ; + Corelib_Classes_RelationClasses_Equivalence -> Corelib_Classes_RelationClasses_Transitive [] ; + Corelib_Classes_RelationClasses_Equivalence -> Corelib_Classes_RelationClasses_Reflexive [] ; + Corelib_Classes_RelationClasses_Equivalence -> Corelib_Classes_RelationClasses_Symmetric [] ; + Stdlib_Arith_PeanoNat_Nat_lt_compat -> Stdlib_Arith_PeanoNat_Nat_lt_wd [] ; + Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_eq -> Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans [] ; + Corelib_Classes_RelationClasses_Symmetric -> Corelib_Relations_Relation_Definitions_relation [] ; + Corelib_Classes_Morphisms_ReflexiveProxy -> Corelib_Relations_Relation_Definitions_relation [] ; + Corelib_Init_Logic_iff_refl -> Corelib_Init_Logic_iff [] ; + Corelib_Init_Logic_iff_refl -> Corelib_Init_Logic_conj [] ; + Corelib_Classes_RelationClasses_Equivalence_Symmetric -> Corelib_Classes_RelationClasses_Equivalence [] ; + Corelib_Classes_RelationClasses_PER -> Corelib_Classes_RelationClasses_Transitive [] ; + Corelib_Classes_RelationClasses_PER -> Corelib_Classes_RelationClasses_Symmetric [] ; + Corelib_Classes_RelationClasses_Build_PER -> Corelib_Classes_RelationClasses_Transitive [] ; + Corelib_Classes_RelationClasses_Build_PER -> Corelib_Classes_RelationClasses_Symmetric [] ; + Corelib_Classes_Morphisms_PER_morphism_obligation_1 -> Corelib_Init_Logic_iff [] ; + Corelib_Classes_Morphisms_PER_morphism_obligation_1 -> Corelib_Init_Logic_conj [] ; + Corelib_Classes_Morphisms_PER_morphism_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Corelib_Classes_Morphisms_PER_morphism_obligation_1 -> Corelib_Classes_RelationClasses_transitivity [] ; + Corelib_Classes_Morphisms_PER_morphism_obligation_1 -> Corelib_Classes_RelationClasses_PER_Symmetric [] ; + Corelib_Classes_Morphisms_PER_morphism_obligation_1 -> Corelib_Classes_RelationClasses_symmetry [] ; + Corelib_Classes_Morphisms_PER_morphism_obligation_1 -> Corelib_Classes_RelationClasses_PER_Transitive [] ; + Corelib_Classes_RelationClasses_PER_Symmetric -> Corelib_Classes_RelationClasses_PER [] ; + Corelib_Classes_RelationClasses_symmetry -> Corelib_Classes_RelationClasses_Symmetric [] ; + Corelib_Classes_RelationClasses_PER_Transitive -> Corelib_Classes_RelationClasses_PER [] ; + Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Corelib_Program_Basics_flip [] ; + Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Corelib_Program_Basics_impl [] ; + Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Corelib_Classes_RelationClasses_transitivity [] ; + Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Corelib_Classes_RelationClasses_PER_Symmetric [] ; + Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Corelib_Classes_RelationClasses_symmetry [] ; + Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism_obligation_1 -> Corelib_Classes_RelationClasses_PER_Transitive [] ; + Corelib_Classes_Morphisms_per_partial_app_morphism_obligation_1 -> Corelib_Init_Logic_iff [] ; + Corelib_Classes_Morphisms_per_partial_app_morphism_obligation_1 -> Corelib_Init_Logic_conj [] ; + Corelib_Classes_Morphisms_per_partial_app_morphism_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Corelib_Classes_Morphisms_per_partial_app_morphism_obligation_1 -> Corelib_Classes_RelationClasses_transitivity [] ; + Corelib_Classes_Morphisms_per_partial_app_morphism_obligation_1 -> Corelib_Classes_RelationClasses_PER_Symmetric [] ; + Corelib_Classes_Morphisms_per_partial_app_morphism_obligation_1 -> Corelib_Classes_RelationClasses_symmetry [] ; + Corelib_Classes_Morphisms_per_partial_app_morphism_obligation_1 -> Corelib_Classes_RelationClasses_PER_Transitive [] ; + Corelib_Classes_RelationClasses_iff_Symmetric -> Corelib_Classes_RelationClasses_Symmetric [] ; + Corelib_Classes_RelationClasses_iff_Symmetric -> Corelib_Init_Logic_iff_sym [] ; + Corelib_Classes_RelationClasses_Build_Equivalence -> Corelib_Classes_RelationClasses_Transitive [] ; + Corelib_Classes_RelationClasses_Build_Equivalence -> Corelib_Classes_RelationClasses_Reflexive [] ; + Corelib_Classes_RelationClasses_Build_Equivalence -> Corelib_Classes_RelationClasses_Symmetric [] ; + Corelib_Init_Logic_iff_sym -> Corelib_Init_Logic_iff [] ; + Corelib_Init_Logic_iff_sym -> Corelib_Init_Logic_conj [] ; + Stdlib_Arith_PeanoNat_Nat_succ_wd -> Corelib_Classes_Morphisms_Proper [] ; + Stdlib_Arith_PeanoNat_Nat_succ_wd -> Stdlib_Arith_PeanoNat_Nat_succ_wd_obligation_1 [] ; + Stdlib_Arith_PeanoNat_Nat_succ_wd_obligation_1 -> Corelib_Init_Datatypes_nat [] ; + Stdlib_Arith_PeanoNat_Nat_succ_wd_obligation_1 -> Corelib_Init_Datatypes_S [] ; + Stdlib_Arith_PeanoNat_Nat_succ_wd_obligation_1 -> Corelib_Init_Logic_eq_ind_r [] ; + Stdlib_Arith_PeanoNat_Nat_succ_wd_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Stdlib_Arith_PeanoNat_Nat_eq_equiv [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Classes_Morphisms_reflexive_reflexive_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Classes_Morphisms_PER_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Classes_RelationClasses_Equivalence_PER [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Classes_Morphisms_reflexive_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Classes_RelationClasses_Equivalence_Reflexive [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Classes_Morphisms_subrelation_proper [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Classes_Morphisms_subrelation_refl [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Classes_Morphisms_trans_co_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Classes_Morphisms_iff_impl_subrelation [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Stdlib_Arith_PeanoNat_Nat_pred_succ [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Stdlib_Arith_PeanoNat_Nat_pred_wd [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Classes_Morphisms_subrelation_respectful [] ; + Stdlib_Arith_PeanoNat_Nat_succ_inj -> Corelib_Init_Datatypes_tt [] ; + Corelib_Classes_Morphisms_subrelation_proper -> Corelib_Classes_Morphisms_Proper [] ; + Corelib_Classes_Morphisms_subrelation_proper -> Corelib_Classes_RelationClasses_subrelation [] ; + Corelib_Classes_Morphisms_subrelation_proper -> Corelib_Classes_Init_Unconvertible [] ; + Corelib_Classes_Morphisms_subrelation_refl -> Corelib_Classes_RelationClasses_subrelation [] ; + Stdlib_Arith_PeanoNat_Nat_pred -> Corelib_Init_Datatypes_nat [] ; + Corelib_Classes_Morphisms_trans_co_impl_morphism -> Corelib_Classes_Morphisms_Proper [] ; + Corelib_Classes_Morphisms_trans_co_impl_morphism -> Corelib_Classes_Morphisms_trans_co_impl_morphism_obligation_1 [] ; + Corelib_Classes_Morphisms_iff_impl_subrelation -> Corelib_Init_Logic_iff [] ; + Corelib_Classes_Morphisms_iff_impl_subrelation -> Corelib_Program_Basics_impl [] ; + Corelib_Classes_Morphisms_iff_impl_subrelation -> Corelib_Classes_RelationClasses_subrelation [] ; + Corelib_Classes_Morphisms_iff_impl_subrelation -> Corelib_Init_Logic_and_ind [] ; + Stdlib_Arith_PeanoNat_Nat_pred_succ -> Corelib_Init_Logic_eq [] ; + Stdlib_Arith_PeanoNat_Nat_pred_succ -> Corelib_Init_Logic_eq_refl [] ; + Stdlib_Arith_PeanoNat_Nat_pred_succ -> Corelib_Init_Datatypes_S [] ; + Stdlib_Arith_PeanoNat_Nat_pred_succ -> Stdlib_Arith_PeanoNat_Nat_pred [] ; + Stdlib_Arith_PeanoNat_Nat_pred_wd -> Corelib_Classes_Morphisms_Proper [] ; + Stdlib_Arith_PeanoNat_Nat_pred_wd -> Stdlib_Arith_PeanoNat_Nat_pred_wd_obligation_1 [] ; + Corelib_Classes_Morphisms_subrelation_respectful -> Corelib_Classes_Morphisms_respectful [] ; + Corelib_Classes_Morphisms_subrelation_respectful -> Corelib_Classes_RelationClasses_subrelation [] ; + Corelib_Classes_RelationClasses_subrelation -> Corelib_Relations_Relation_Definitions_relation [] ; + Stdlib_Arith_PeanoNat_Nat_pred_wd_obligation_1 -> Corelib_Init_Logic_eq_ind_r [] ; + Stdlib_Arith_PeanoNat_Nat_pred_wd_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Stdlib_Arith_PeanoNat_Nat_pred_wd_obligation_1 -> Stdlib_Arith_PeanoNat_Nat_pred [] ; + Corelib_Init_Logic_and_ind -> Corelib_Init_Logic_and [] ; + Corelib_Classes_Morphisms_trans_co_impl_morphism_obligation_1 -> Corelib_Program_Basics_impl [] ; + Corelib_Classes_Morphisms_trans_co_impl_morphism_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Corelib_Classes_Morphisms_trans_co_impl_morphism_obligation_1 -> Corelib_Classes_RelationClasses_transitivity [] ; + Corelib_Classes_Init_Unconvertible -> Corelib_Init_Datatypes_unit [] ; + Corelib_Classes_RelationClasses_eq_equivalence -> Corelib_Classes_RelationClasses_Equivalence [] ; + Corelib_Classes_RelationClasses_eq_equivalence -> Corelib_Classes_RelationClasses_Build_Equivalence [] ; + Corelib_Classes_RelationClasses_eq_equivalence -> Corelib_Classes_RelationClasses_eq_Reflexive [] ; + Corelib_Classes_RelationClasses_eq_equivalence -> Corelib_Classes_RelationClasses_eq_Transitive [] ; + Corelib_Classes_RelationClasses_eq_equivalence -> Corelib_Classes_RelationClasses_eq_Symmetric [] ; + Corelib_Classes_RelationClasses_eq_Reflexive -> Corelib_Init_Logic_eq [] ; + Corelib_Classes_RelationClasses_eq_Reflexive -> Corelib_Init_Logic_eq_refl [] ; + Corelib_Classes_RelationClasses_eq_Reflexive -> Corelib_Classes_RelationClasses_Reflexive [] ; + Corelib_Classes_RelationClasses_eq_Transitive -> Corelib_Classes_RelationClasses_Transitive [] ; + Corelib_Classes_RelationClasses_eq_Transitive -> Corelib_Init_Logic_eq_trans [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_land_spec -> Stdlib_Arith_PeanoNat_Nat_land [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_land_spec -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 [] ; + Corelib_Classes_RelationClasses_eq_Symmetric -> Corelib_Init_Logic_eq_sym [] ; + Corelib_Classes_RelationClasses_eq_Symmetric -> Corelib_Classes_RelationClasses_Symmetric [] ; + Stdlib_Arith_PeanoNat_Nat_land -> Corelib_Init_Datatypes_andb [] ; + Stdlib_Arith_PeanoNat_Nat_land -> Stdlib_Arith_PeanoNat_Nat_bitwise [] ; + Corelib_Init_Logic_eq_trans -> Corelib_Init_Logic_eq [] ; + Corelib_Init_Datatypes_andb -> Corelib_Init_Datatypes_bool [] ; + Corelib_Init_Datatypes_andb -> Corelib_Init_Datatypes_false [] ; + Stdlib_Arith_PeanoNat_Nat_add_wd_obligation_1 -> Corelib_Init_Logic_eq_ind_r [] ; + Stdlib_Arith_PeanoNat_Nat_add_wd_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Stdlib_Arith_PeanoNat_Nat_add_wd_obligation_1 -> Corelib_Init_Nat_add [] ; + Stdlib_Arith_PeanoNat_Nat_testbit -> Stdlib_Arith_PeanoNat_Nat_odd [] ; + Stdlib_Arith_PeanoNat_Nat_testbit -> Stdlib_Arith_PeanoNat_Nat_div2 [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_succ_double -> Stdlib_Arith_PeanoNat_Nat_div2 [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_succ_double -> Stdlib_Arith_PeanoNat_Nat_mul [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_succ_double -> Corelib_Init_Logic_f_equal [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_succ_double -> Stdlib_Arith_PeanoNat_Nat_add_succ_r [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_bitwise [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1 -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_odd_bitwise [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_double -> Stdlib_Arith_PeanoNat_Nat_div2 [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_double -> Stdlib_Arith_PeanoNat_Nat_mul [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_double -> Corelib_Init_Logic_f_equal [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_double -> Stdlib_Arith_PeanoNat_Nat_add_succ_r [] ; + Stdlib_Arith_PeanoNat_Nat_le_0_l -> Stdlib_Arith_PeanoNat_Nat_eq_le_incl [] ; + Stdlib_Arith_PeanoNat_Nat_le_0_l -> Stdlib_Arith_PeanoNat_Nat_le_le_succ_r [] ; + Stdlib_Arith_PeanoNat_Nat_le_0_l -> Stdlib_Arith_PeanoNat_Nat_le_succ_r [] ; + Stdlib_Arith_PeanoNat_Nat_le_0_l -> Stdlib_Arith_PeanoNat_Nat_neq_succ_0 [] ; + Stdlib_Arith_PeanoNat_Nat_le_trans -> Stdlib_Arith_PeanoNat_Nat_lt_trans [] ; + Stdlib_Arith_PeanoNat_Nat_succ_le_mono -> Stdlib_Arith_PeanoNat_Nat_succ_lt_mono [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_le_div2 -> Stdlib_Arith_PeanoNat_Nat_div2 [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_le_div2 -> Stdlib_Arith_PeanoNat_Nat_lt_succ_r [] ; + Stdlib_Arith_PeanoNat_Nat_lt_succ_r -> Corelib_Init_Logic_iff [] ; + Stdlib_Arith_PeanoNat_Nat_lt_succ_r -> Corelib_Init_Logic_conj [] ; + Stdlib_Arith_PeanoNat_Nat_lt_succ_r -> Corelib_Init_Peano_lt [] ; + Stdlib_Arith_PeanoNat_Nat_lt_succ_r -> Corelib_Init_Peano_le_S_n [] ; + Corelib_Init_Peano_le_n -> Corelib_Init_Datatypes_nat [] ; + Corelib_Init_Peano_le_n -> Corelib_Init_Datatypes_S [] ; + Corelib_Init_Peano_lt -> Corelib_Init_Peano_le [] ; + Corelib_Init_Peano_le_S -> Corelib_Init_Datatypes_nat [] ; + Corelib_Init_Peano_le_S -> Corelib_Init_Datatypes_S [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l -> Stdlib_Arith_PeanoNat_Nat_testbit [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l -> Corelib_Init_Logic_eq [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l -> Corelib_Init_Logic_eq_refl [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l -> Corelib_Init_Datatypes_nat_ind [] ; + Corelib_Init_Peano_le_S_n -> Corelib_Init_Peano_le_pred [] ; + Stdlib_Arith_PeanoNat_Nat_odd -> Stdlib_Arith_PeanoNat_Nat_even [] ; + Stdlib_Arith_PeanoNat_Nat_odd -> Corelib_Init_Datatypes_negb [] ; + Corelib_Init_Peano_le_ind -> Corelib_Init_Peano_le [] ; + Corelib_Init_Peano_le_pred -> Corelib_Init_Peano_le_n [] ; + Corelib_Init_Peano_le_pred -> Corelib_Init_Datatypes_O [] ; + Corelib_Init_Peano_le_pred -> Corelib_Init_Peano_le_S [] ; + Corelib_Init_Peano_le_pred -> Corelib_Init_Peano_le_ind [] ; + Corelib_Init_Peano_le_pred -> Corelib_Init_Nat_pred [] ; + Stdlib_Arith_PeanoNat_Nat_div2 -> Corelib_Init_Datatypes_nat [] ; + Stdlib_Arith_PeanoNat_Nat_div2 -> Corelib_Init_Datatypes_S [] ; + Stdlib_Arith_PeanoNat_Nat_div2 -> Corelib_Init_Datatypes_O [] ; + Corelib_Init_Nat_pred -> Corelib_Init_Datatypes_nat [] ; + Corelib_Init_Logic_False_ind -> Corelib_Init_Logic_False [] ; + Stdlib_Arith_PeanoNat_Nat_lt_eq_cases -> Corelib_Classes_Morphisms_reflexive_reflexive_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_lt_eq_cases -> Corelib_Classes_Morphisms_Reflexive_partial_app_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_lt_eq_cases -> Corelib_Classes_RelationClasses_iff_equivalence [] ; + Stdlib_Arith_PeanoNat_Nat_lt_eq_cases -> Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_lt_eq_cases -> Corelib_Classes_RelationClasses_Equivalence_PER [] ; + Stdlib_Arith_PeanoNat_Nat_lt_eq_cases -> Corelib_Classes_Morphisms_reflexive_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_lt_eq_cases -> Corelib_Classes_Morphisms_Prop_or_iff_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_lt_eq_cases -> Stdlib_Arith_PeanoNat_Nat_compare_lt_iff [] ; + Stdlib_Arith_PeanoNat_Nat_lt_eq_cases -> Stdlib_Arith_PeanoNat_Nat_compare_eq_iff [] ; + Stdlib_Arith_PeanoNat_Nat_lt_eq_cases -> Stdlib_Arith_PeanoNat_Nat_compare_le_iff [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr -> Stdlib_Arith_PeanoNat_Nat_le_0_l [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr -> Stdlib_Arith_PeanoNat_Nat_le_trans [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr -> Stdlib_Arith_PeanoNat_Nat_succ_le_mono [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_le_div2 [] ; + Stdlib_Arith_PeanoNat_Nat_succ_lt_mono -> Stdlib_Arith_PeanoNat_Nat_le_succ_l [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_bitwise -> Stdlib_Arith_PeanoNat_Nat_bitwise [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_bitwise -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_succ_double [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_bitwise -> Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_double [] ; + Corelib_Classes_Morphisms_Prop_or_iff_morphism -> Corelib_Classes_Morphisms_Proper [] ; + Corelib_Classes_Morphisms_Prop_or_iff_morphism -> Corelib_Classes_Morphisms_Prop_or_iff_morphism_obligation_1 [] ; + Corelib_Init_Datatypes_nat_ind -> Corelib_Init_Datatypes_nat [] ; + Corelib_Init_Datatypes_nat_ind -> Corelib_Init_Datatypes_S [] ; + Corelib_Init_Datatypes_nat_ind -> Corelib_Init_Datatypes_O [] ; + Corelib_Init_Logic_eq_ind -> Corelib_Init_Logic_eq [] ; + Corelib_Classes_Morphisms_Prop_or_iff_morphism_obligation_1 -> Corelib_Init_Logic_iff [] ; + Corelib_Classes_Morphisms_Prop_or_iff_morphism_obligation_1 -> Corelib_Init_Logic_conj [] ; + Corelib_Classes_Morphisms_Prop_or_iff_morphism_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Corelib_Classes_Morphisms_Prop_or_iff_morphism_obligation_1 -> Corelib_Init_Logic_and_ind [] ; + Corelib_Classes_Morphisms_Prop_or_iff_morphism_obligation_1 -> Corelib_Init_Logic_or_ind [] ; + Corelib_Classes_Morphisms_Prop_or_iff_morphism_obligation_1 -> Corelib_Init_Logic_or_introl [] ; + Corelib_Classes_Morphisms_Prop_or_iff_morphism_obligation_1 -> Corelib_Init_Logic_or_intror [] ; + Corelib_Init_Logic_eq_sym -> Corelib_Init_Logic_eq [] ; + Corelib_Init_Logic_eq_sym -> Corelib_Init_Logic_eq_refl [] ; + Corelib_Init_Logic_or_ind -> Corelib_Init_Logic_or [] ; + Corelib_Init_Logic_eq_ind_r -> Corelib_Init_Logic_eq_ind [] ; + Corelib_Init_Logic_eq_ind_r -> Corelib_Init_Logic_eq_sym [] ; + Stdlib_Arith_PeanoNat_Nat_bitwise -> Stdlib_Arith_PeanoNat_Nat_odd [] ; + Stdlib_Arith_PeanoNat_Nat_bitwise -> Stdlib_Arith_PeanoNat_Nat_div2 [] ; + Stdlib_Arith_PeanoNat_Nat_bitwise -> Stdlib_Arith_PeanoNat_Nat_mul [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_odd_bitwise -> Stdlib_Arith_PeanoNat_Nat_bitwise [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_odd_bitwise -> Stdlib_Bool_Bool_negb_false_iff [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_odd_bitwise -> Stdlib_Arith_PeanoNat_Nat_add_comm [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_odd_bitwise -> Stdlib_Arith_PeanoNat_Nat_even_spec [] ; + Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_odd_bitwise -> Stdlib_Arith_PeanoNat_Nat_odd_spec [] ; + Stdlib_Arith_PeanoNat_Nat_le_succ_l -> Stdlib_Arith_PeanoNat_Nat_succ_inj_wd [] ; + Stdlib_Arith_PeanoNat_Nat_le_succ_l -> Corelib_Classes_Morphisms_per_partial_app_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_le_succ_l -> Stdlib_Arith_PeanoNat_Nat_nle_succ_diag_l [] ; + Stdlib_Arith_PeanoNat_Nat_le_succ_l -> Stdlib_Arith_PeanoNat_Nat_central_induction [] ; + Stdlib_Arith_PeanoNat_Nat_le_succ_l -> Stdlib_Arith_PeanoNat_Nat_le_wd [] ; + Stdlib_Arith_PeanoNat_Nat_le_succ_l -> Corelib_Init_Logic_or_cancel_r [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Corelib_Init_Logic_eq_ind_r [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Corelib_Classes_RelationClasses_symmetry [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Corelib_Classes_RelationClasses_iff_Symmetric [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Corelib_Classes_Morphisms_subrelation_proper [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Corelib_Classes_Morphisms_subrelation_refl [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Corelib_Classes_Morphisms_subrelation_respectful [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Corelib_Init_Datatypes_tt [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Corelib_Classes_Morphisms_iff_flip_impl_subrelation [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Stdlib_Arith_PeanoNat_Nat_compare_refl [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Corelib_Classes_Morphisms_Prop_not_iff_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_lt_irrefl -> Stdlib_Arith_PeanoNat_Nat_compare_lt_iff [] ; + Corelib_Init_Peano_le -> Corelib_Init_Datatypes_nat [] ; + Corelib_Init_Peano_le -> Corelib_Init_Datatypes_S [] ; + Stdlib_Arith_PeanoNat_Nat_nle_succ_diag_l -> Corelib_Classes_Morphisms_iff_impl_subrelation [] ; + Stdlib_Arith_PeanoNat_Nat_nle_succ_diag_l -> Stdlib_Arith_PeanoNat_Nat_neq_succ_diag_l [] ; + Stdlib_Arith_PeanoNat_Nat_nle_succ_diag_l -> Stdlib_Arith_PeanoNat_Nat_nlt_succ_diag_l [] ; + Stdlib_Arith_PeanoNat_Nat_central_induction -> Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_central_induction -> Corelib_Classes_Morphisms_eq_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_central_induction -> Corelib_Classes_RelationClasses_iff_Transitive [] ; + Stdlib_Arith_PeanoNat_Nat_central_induction -> Corelib_Classes_Morphisms_reflexive_reflexive_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_central_induction -> Stdlib_Arith_PeanoNat_Nat_bi_induction [] ; + Stdlib_Arith_PeanoNat_Nat_central_induction -> Corelib_Classes_RelationClasses_reflexivity [] ; + Stdlib_Arith_PeanoNat_Nat_central_induction -> Corelib_Classes_RelationClasses_iff_Reflexive [] ; + Stdlib_Arith_PeanoNat_Nat_central_induction -> Corelib_Classes_Morphisms_reflexive_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_central_induction -> Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Corelib_Classes_Morphisms_eq_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Stdlib_Arith_PeanoNat_Nat_eq_equiv [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Corelib_Classes_Morphisms_reflexive_reflexive_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Corelib_Classes_Morphisms_Reflexive_partial_app_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Corelib_Classes_RelationClasses_iff_equivalence [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Corelib_Classes_RelationClasses_reflexivity [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Corelib_Classes_RelationClasses_Equivalence_PER [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Corelib_Classes_Morphisms_reflexive_proper_proxy [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Corelib_Classes_RelationClasses_Equivalence_Reflexive [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Stdlib_Arith_PeanoNat_Nat_succ_wd [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Stdlib_Arith_PeanoNat_Nat_lt_succ_r [] ; + Stdlib_Arith_PeanoNat_Nat_le_wd -> Stdlib_Arith_PeanoNat_Nat_lt_wd [] ; + Stdlib_Bool_Bool_negb_false_iff -> Corelib_Init_Logic_eq_sym [] ; + Stdlib_Bool_Bool_negb_false_iff -> Corelib_Init_Datatypes_negb [] ; + Stdlib_Bool_Bool_negb_false_iff -> Corelib_Init_Logic_iff [] ; + Stdlib_Bool_Bool_negb_false_iff -> Corelib_Init_Logic_conj [] ; + Stdlib_Arith_PeanoNat_Nat_lt_wd -> Corelib_Classes_Morphisms_Proper [] ; + Stdlib_Arith_PeanoNat_Nat_lt_wd -> Stdlib_Arith_PeanoNat_Nat_lt_wd_obligation_1 [] ; + Corelib_Init_Logic_or_cancel_r -> Corelib_Init_Logic_not [] ; + Corelib_Init_Logic_or_cancel_r -> Corelib_Init_Logic_or_iff_compat_r [] ; + Stdlib_Arith_PeanoNat_Nat_add_comm -> Corelib_Classes_Morphisms_Reflexive_partial_app_morphism [] ; + Stdlib_Arith_PeanoNat_Nat_add_comm -> Stdlib_Arith_PeanoNat_Nat_add_succ_r [] ; + Stdlib_Arith_PeanoNat_Nat_add_comm -> Stdlib_Arith_PeanoNat_Nat_add_0_r [] ; + Corelib_Init_Logic_or_iff_compat_r -> Corelib_Init_Logic_iff [] ; + Corelib_Init_Logic_or_iff_compat_r -> Corelib_Init_Logic_conj [] ; + Corelib_Init_Logic_or_iff_compat_r -> Corelib_Init_Logic_or [] ; + Corelib_Init_Logic_or_iff_compat_r -> Corelib_Init_Logic_or_introl [] ; + Corelib_Init_Logic_or_iff_compat_r -> Corelib_Init_Logic_or_intror [] ; + Stdlib_Arith_PeanoNat_Nat_add -> Corelib_Init_Datatypes_nat [] ; + Stdlib_Arith_PeanoNat_Nat_add -> Corelib_Init_Datatypes_S [] ; + Stdlib_Arith_PeanoNat_Nat_mul -> Corelib_Init_Datatypes_O [] ; + Stdlib_Arith_PeanoNat_Nat_mul -> Stdlib_Arith_PeanoNat_Nat_add [] ; + Stdlib_Arith_PeanoNat_Nat_lt_wd_obligation_1 -> Corelib_Init_Logic_eq_ind_r [] ; + Stdlib_Arith_PeanoNat_Nat_lt_wd_obligation_1 -> Corelib_Init_Logic_iff [] ; + Stdlib_Arith_PeanoNat_Nat_lt_wd_obligation_1 -> Corelib_Init_Logic_conj [] ; + Stdlib_Arith_PeanoNat_Nat_lt_wd_obligation_1 -> Corelib_Classes_Morphisms_respectful [] ; + Stdlib_Arith_PeanoNat_Nat_lt_wd_obligation_1 -> Corelib_Init_Peano_lt [] ; + Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism -> Corelib_Classes_Morphisms_Proper [] ; + Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism -> Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1 [] ; + Stdlib_Arith_PeanoNat_Nat_even -> Corelib_Init_Datatypes_nat [] ; + Stdlib_Arith_PeanoNat_Nat_even -> Corelib_Init_Datatypes_bool [] ; + Stdlib_Arith_PeanoNat_Nat_even -> Corelib_Init_Datatypes_false [] ; + Stdlib_Arith_PeanoNat_Nat_even -> Corelib_Init_Datatypes_true [] ; +subgraph cluster_Corelib { label="Corelib"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Corelib_Program { label="Program"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Corelib_Program_Basics { label="Basics"; fillcolor="#FFFF83"; labeljust=l; style=filled +Corelib_Program_Basics_impl; Corelib_Program_Basics_flip; }; +}; +subgraph cluster_Corelib_Relations { label="Relations"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Corelib_Relations_Relation_Definitions { label="Relation_Definitions"; fillcolor="#FFFF83"; labeljust=l; style=filled +Corelib_Relations_Relation_Definitions_relation; }; +}; +subgraph cluster_Corelib_Init { label="Init"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Corelib_Init_Nat { label="Nat"; fillcolor="#FFFF83"; labeljust=l; style=filled +Corelib_Init_Nat_pred; Corelib_Init_Nat_add; }; +subgraph cluster_Corelib_Init_Peano { label="Peano"; fillcolor="#FFFF83"; labeljust=l; style=filled +Corelib_Init_Peano_le; Corelib_Init_Peano_le_pred; Corelib_Init_Peano_le_ind; Corelib_Init_Peano_le_S_n; Corelib_Init_Peano_le_S; Corelib_Init_Peano_lt; Corelib_Init_Peano_le_n; Corelib_Init_Peano_f_equal_nat; Corelib_Init_Peano_plus_n_O; Corelib_Init_Peano_plus_n_Sm; Corelib_Init_Peano_eq_add_S; Corelib_Init_Peano_le_n_S; Corelib_Init_Peano_le_0_n; }; +subgraph cluster_Corelib_Init_Logic { label="Logic"; fillcolor="#FFFF83"; labeljust=l; style=filled +Corelib_Init_Logic_or_iff_compat_r; Corelib_Init_Logic_or_cancel_r; Corelib_Init_Logic_I; Corelib_Init_Logic_False; Corelib_Init_Logic_True; Corelib_Init_Logic_or_intror; Corelib_Init_Logic_or_introl; Corelib_Init_Logic_eq_ind_r; Corelib_Init_Logic_or_ind; Corelib_Init_Logic_eq_sym; Corelib_Init_Logic_eq_ind; Corelib_Init_Logic_or; Corelib_Init_Logic_False_ind; Corelib_Init_Logic_eq_refl; Corelib_Init_Logic_eq; Corelib_Init_Logic_eq_trans; Corelib_Init_Logic_and_ind; Corelib_Init_Logic_iff_sym; Corelib_Init_Logic_iff_refl; Corelib_Init_Logic_not; Corelib_Init_Logic_ex; Corelib_Init_Logic_f_equal; Corelib_Init_Logic_iff_trans; Corelib_Init_Logic_conj; Corelib_Init_Logic_iff; Corelib_Init_Logic_ex_intro; Corelib_Init_Logic_and; }; +subgraph cluster_Corelib_Init_Datatypes { label="Datatypes"; fillcolor="#FFFF83"; labeljust=l; style=filled +Corelib_Init_Datatypes_O; Corelib_Init_Datatypes_nat_ind; Corelib_Init_Datatypes_S; Corelib_Init_Datatypes_false; Corelib_Init_Datatypes_bool; Corelib_Init_Datatypes_nat; Corelib_Init_Datatypes_andb; Corelib_Init_Datatypes_unit; Corelib_Init_Datatypes_tt; Corelib_Init_Datatypes_Gt; Corelib_Init_Datatypes_Lt; Corelib_Init_Datatypes_Eq; Corelib_Init_Datatypes_comparison; Corelib_Init_Datatypes_true; Corelib_Init_Datatypes_negb; }; +}; +subgraph cluster_Corelib_Classes { label="Classes"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Corelib_Classes_Init { label="Init"; fillcolor="#FFFF83"; labeljust=l; style=filled +Corelib_Classes_Init_Unconvertible; }; +subgraph cluster_Corelib_Classes_RelationClasses { label="RelationClasses"; fillcolor="#FFFF83"; labeljust=l; style=filled +Corelib_Classes_RelationClasses_eq_Symmetric; Corelib_Classes_RelationClasses_eq_Transitive; Corelib_Classes_RelationClasses_eq_Reflexive; Corelib_Classes_RelationClasses_eq_equivalence; Corelib_Classes_RelationClasses_subrelation; Corelib_Classes_RelationClasses_Build_Equivalence; Corelib_Classes_RelationClasses_iff_Symmetric; Corelib_Classes_RelationClasses_PER_Transitive; Corelib_Classes_RelationClasses_symmetry; Corelib_Classes_RelationClasses_PER_Symmetric; Corelib_Classes_RelationClasses_Build_PER; Corelib_Classes_RelationClasses_PER; Corelib_Classes_RelationClasses_Equivalence_Symmetric; Corelib_Classes_RelationClasses_Symmetric; Corelib_Classes_RelationClasses_Equivalence; Corelib_Classes_RelationClasses_Reflexive; Corelib_Classes_RelationClasses_Equivalence_Reflexive; Corelib_Classes_RelationClasses_iff_Reflexive; Corelib_Classes_RelationClasses_Equivalence_PER; Corelib_Classes_RelationClasses_reflexivity; Corelib_Classes_RelationClasses_StrictOrder_Transitive; Corelib_Classes_RelationClasses_Equivalence_Transitive; Corelib_Classes_RelationClasses_Build_StrictOrder; Corelib_Classes_RelationClasses_complement; Corelib_Classes_RelationClasses_iff_equivalence; Corelib_Classes_RelationClasses_Irreflexive; Corelib_Classes_RelationClasses_StrictOrder; Corelib_Classes_RelationClasses_StrictOrder_Irreflexive; Corelib_Classes_RelationClasses_transitivity; Corelib_Classes_RelationClasses_Transitive; Corelib_Classes_RelationClasses_iff_Transitive; }; +subgraph cluster_Corelib_Classes_Morphisms { label="Morphisms"; fillcolor="#FFFF83"; labeljust=l; style=filled +Corelib_Classes_Morphisms_trans_co_impl_morphism_obligation_1; Corelib_Classes_Morphisms_subrelation_respectful; Corelib_Classes_Morphisms_iff_impl_subrelation; Corelib_Classes_Morphisms_trans_co_impl_morphism; Corelib_Classes_Morphisms_subrelation_refl; Corelib_Classes_Morphisms_subrelation_proper; Corelib_Classes_Morphisms_per_partial_app_morphism_obligation_1; Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism_obligation_1; Corelib_Classes_Morphisms_PER_morphism_obligation_1; Corelib_Classes_Morphisms_ReflexiveProxy; Corelib_Classes_Morphisms_reflexive_proper_proxy; Corelib_Classes_Morphisms_PER_morphism; Corelib_Classes_Morphisms_trans_sym_co_inv_impl_morphism; Corelib_Classes_Morphisms_per_partial_app_morphism; Corelib_Classes_Morphisms_Reflexive_partial_app_morphism; Corelib_Classes_Morphisms_reflexive_reflexive_proxy; Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism_obligation_1; Corelib_Classes_Morphisms_Build_Params; Corelib_Classes_Morphisms_respectful; Corelib_Classes_Morphisms_Proper; Corelib_Classes_Morphisms_Params; Corelib_Classes_Morphisms_impl_pars; Corelib_Classes_Morphisms_ProperProxy; Corelib_Classes_Morphisms_eq_proper_proxy; Corelib_Classes_Morphisms_trans_co_eq_inv_impl_morphism; Corelib_Classes_Morphisms_iff_flip_impl_subrelation; }; +subgraph cluster_Corelib_Classes_Morphisms_Prop { label="Morphisms_Prop"; fillcolor="#FFFF83"; labeljust=l; style=filled +Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism; Corelib_Classes_Morphisms_Prop_or_iff_morphism_obligation_1; Corelib_Classes_Morphisms_Prop_or_iff_morphism; Corelib_Classes_Morphisms_Prop_not_iff_morphism_obligation_1; Corelib_Classes_Morphisms_Prop_not_iff_morphism; Corelib_Classes_Morphisms_Prop_iff_iff_iff_impl_morphism_obligation_1; }; +}; +}; +subgraph cluster_Stdlib { label="Stdlib"; fillcolor="#FFFFC3"; labeljust=l; style=filled +subgraph cluster_Stdlib_Bool { label="Bool"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Stdlib_Bool_Bool { label="Bool"; fillcolor="#FFFF83"; labeljust=l; style=filled +Stdlib_Bool_Bool_negb_false_iff; }; +}; +subgraph cluster_Stdlib_Structures { label="Structures"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Stdlib_Structures_OrdersTac { label="OrdersTac"; fillcolor="#FFFF83"; labeljust=l; style=filled +Stdlib_Structures_OrdersTac_OLE; Stdlib_Structures_OrdersTac_OEQ; Stdlib_Structures_OrdersTac_ord; Stdlib_Structures_OrdersTac_trans_ord; Stdlib_Structures_OrdersTac_OLT; }; +}; +subgraph cluster_Stdlib_Arith { label="Arith"; fillcolor="#FFFFA3"; labeljust=l; style=filled +subgraph cluster_Stdlib_Arith_PeanoNat { label="PeanoNat"; fillcolor="#FFFF83"; labeljust=l; style=filled +subgraph cluster_Stdlib_Arith_PeanoNat_Nat { label="Nat"; fillcolor="#FFFF63"; labeljust=l; style=filled +subgraph cluster_Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec { label="PrivateImplementsBitwiseSpec"; fillcolor="#FFFF43"; labeljust=l; style=filled +Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_odd_bitwise; Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_bitwise; Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_decr; Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_0_l; Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_le_div2; Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_double; Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_testbit_bitwise_1; Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_div2_succ_double; Stdlib_Arith_PeanoNat_Nat_PrivateImplementsBitwiseSpec_land_spec; }; +subgraph cluster_Stdlib_Arith_PeanoNat_Nat_Private_OrderTac { label="Private_OrderTac"; fillcolor="#FFFF43"; labeljust=l; style=filled +subgraph cluster_Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal { label="IsTotal"; fillcolor="#FFFF23"; labeljust=l; style=filled +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_eq_equiv; Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_compat; Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_strorder; Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_lt_total; Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_IsTotal_le_lteq; }; +subgraph cluster_Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac { label="Tac"; fillcolor="#FFFF23"; labeljust=l; style=filled +Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_eq; Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_interp_ord; Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_trans; Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_not_gt_le; Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_irrefl; Stdlib_Arith_PeanoNat_Nat_Private_OrderTac_Tac_lt_trans; }; +}; +subgraph cluster_Stdlib_Arith_PeanoNat_Nat_Private_Parity { label="Private_Parity"; fillcolor="#FFFF43"; labeljust=l; style=filled +Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_2; Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_1; Stdlib_Arith_PeanoNat_Nat_Private_Parity_Even_0; Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_2; Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_1; Stdlib_Arith_PeanoNat_Nat_Private_Parity_Odd_0; }; +Stdlib_Arith_PeanoNat_Nat_even; Stdlib_Arith_PeanoNat_Nat_lt_wd_obligation_1; Stdlib_Arith_PeanoNat_Nat_mul; Stdlib_Arith_PeanoNat_Nat_add; Stdlib_Arith_PeanoNat_Nat_add_comm; Stdlib_Arith_PeanoNat_Nat_lt_wd; Stdlib_Arith_PeanoNat_Nat_le_wd; Stdlib_Arith_PeanoNat_Nat_central_induction; Stdlib_Arith_PeanoNat_Nat_nle_succ_diag_l; Stdlib_Arith_PeanoNat_Nat_lt_irrefl; Stdlib_Arith_PeanoNat_Nat_le_succ_l; Stdlib_Arith_PeanoNat_Nat_bitwise; Stdlib_Arith_PeanoNat_Nat_succ_lt_mono; Stdlib_Arith_PeanoNat_Nat_lt_eq_cases; Stdlib_Arith_PeanoNat_Nat_div2; Stdlib_Arith_PeanoNat_Nat_odd; Stdlib_Arith_PeanoNat_Nat_lt_succ_r; Stdlib_Arith_PeanoNat_Nat_succ_le_mono; Stdlib_Arith_PeanoNat_Nat_le_trans; Stdlib_Arith_PeanoNat_Nat_le_0_l; Stdlib_Arith_PeanoNat_Nat_testbit; Stdlib_Arith_PeanoNat_Nat_add_wd_obligation_1; Stdlib_Arith_PeanoNat_Nat_land; Stdlib_Arith_PeanoNat_Nat_pred_wd_obligation_1; Stdlib_Arith_PeanoNat_Nat_pred_wd; Stdlib_Arith_PeanoNat_Nat_pred_succ; Stdlib_Arith_PeanoNat_Nat_pred; Stdlib_Arith_PeanoNat_Nat_succ_inj; Stdlib_Arith_PeanoNat_Nat_succ_wd_obligation_1; Stdlib_Arith_PeanoNat_Nat_succ_wd; Stdlib_Arith_PeanoNat_Nat_lt_compat; Stdlib_Arith_PeanoNat_Nat_bi_induction; Stdlib_Arith_PeanoNat_Nat_add_0_r; Stdlib_Arith_PeanoNat_Nat_add_succ_r; Stdlib_Arith_PeanoNat_Nat_add_succ_l; Stdlib_Arith_PeanoNat_Nat_lt_strorder; Stdlib_Arith_PeanoNat_Nat_succ_inj_wd; Stdlib_Arith_PeanoNat_Nat_le_lteq; Stdlib_Arith_PeanoNat_Nat_eq_equiv; Stdlib_Arith_PeanoNat_Nat_le_gt_cases; Stdlib_Arith_PeanoNat_Nat_add_wd; Stdlib_Arith_PeanoNat_Nat_lt_trichotomy; Stdlib_Arith_PeanoNat_Nat_lt_total; Stdlib_Arith_PeanoNat_Nat_pred_0; Stdlib_Arith_PeanoNat_Nat_neq_succ_0; Stdlib_Arith_PeanoNat_Nat_le_succ_r; Stdlib_Arith_PeanoNat_Nat_le_le_succ_r; Stdlib_Arith_PeanoNat_Nat_eq_le_incl; Stdlib_Arith_PeanoNat_Nat_lt_asymm; Stdlib_Arith_PeanoNat_Nat_lt_trans; Stdlib_Arith_PeanoNat_Nat_compare_le_iff; Stdlib_Arith_PeanoNat_Nat_compare_eq_iff; Stdlib_Arith_PeanoNat_Nat_compare_lt_iff; Stdlib_Arith_PeanoNat_Nat_compare; Stdlib_Arith_PeanoNat_Nat_compare_refl; Stdlib_Arith_PeanoNat_Nat_le_refl; Stdlib_Arith_PeanoNat_Nat_lt_succ_diag_r; Stdlib_Arith_PeanoNat_Nat_odd_spec; Stdlib_Arith_PeanoNat_Nat_Even; Stdlib_Arith_PeanoNat_Nat_Odd; Stdlib_Arith_PeanoNat_Nat_lt_le_incl; Stdlib_Arith_PeanoNat_Nat_add_0_l; Stdlib_Arith_PeanoNat_Nat_nlt_succ_diag_l; Stdlib_Arith_PeanoNat_Nat_neq_succ_diag_l; Stdlib_Arith_PeanoNat_Nat_even_spec; }; +}; +}; +}; +} /* END */ diff --git a/tests/Proofs.dpd.oracle b/tests/Proofs.dpd.oracle new file mode 100644 index 000000000..e16c5ab46 --- /dev/null +++ b/tests/Proofs.dpd.oracle @@ -0,0 +1,1869 @@ +N: 308 "Equivalence_PER" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 311 "Equivalence_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 317 "Equivalence_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 303 "Equivalence_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 260 "Even" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 290 "Even_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_Parity", ]; +N: 291 "Even_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_Parity", ]; +N: 292 "Even_2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_Parity", ]; +N: 237 "False_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 428 "Irreflexive" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.RelationClasses", ]; +N: 259 "Odd" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 266 "Odd_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_Parity", ]; +N: 267 "Odd_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_Parity", ]; +N: 268 "Odd_2" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_Parity", ]; +N: 321 "PER_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 323 "PER_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 305 "PER_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 320 "PER_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 279 "Proper" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.Morphisms", ]; +N: 276 "ProperProxy" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.Morphisms", ]; +N: 312 "Reflexive" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.RelationClasses", ]; +N: 315 "ReflexiveProxy" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.Morphisms", ]; +N: 297 "Reflexive_partial_app_morphism" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 424 "StrictOrder_Irreflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 433 "StrictOrder_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 314 "Symmetric" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.RelationClasses", ]; +N: 273 "Transitive" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.RelationClasses", ]; +N: 345 "Unconvertible" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.Init", ]; +N: 287 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Init.Nat", ]; +N: 253 "add" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 258 "add_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 300 "add_0_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 252 "add_comm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 298 "add_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 299 "add_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 293 "add_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 352 "add_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 343 "and_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 224 "andb" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Init.Datatypes", ]; +N: 306 "bi_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 244 "bitwise" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 377 "central_induction" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 393 "compare" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 402 "compare_eq_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 404 "compare_le_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 394 "compare_lt_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 391 "compare_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 429 "complement" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.RelationClasses", ]; +N: 236 "div2" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 239 "div2_bitwise" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 238 "div2_decr" [body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 354 "div2_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 353 "div2_succ_double" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 348 "eq_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 350 "eq_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 349 "eq_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 403 "eq_add_S" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Peano", ]; +N: 435 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.IsTotal", ]; +N: 294 "eq_equiv" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 347 "eq_equivalence" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 241 "eq_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 243 "eq_ind_r" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 410 "eq_le_incl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 270 "eq_proper_proxy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 242 "eq_sym" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 351 "eq_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 255 "even" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 256 "even_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 285 "f_equal" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 288 "f_equal_nat" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Peano", ]; +N: 277 "flip" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Program.Basics", ]; +N: 265 "iff" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Init.Logic", ]; +N: 309 "iff_Reflexive" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 326 "iff_Symmetric" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 271 "iff_Transitive" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 301 "iff_equivalence" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 388 "iff_flip_impl_subrelation" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 383 "iff_iff_iff_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms_Prop", ]; +N: 384 "iff_iff_iff_impl_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms_Prop", ]; +N: 336 "iff_impl_subrelation" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 316 "iff_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 328 "iff_sym" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 274 "iff_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 278 "impl" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Program.Basics", ]; +N: 405 "impl_pars" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 436 "interp_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.Tac", ]; +N: 223 "land" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 222 "land_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 355 "le_0_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 398 "le_0_n" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Peano", ]; +N: 362 "le_S_n" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Peano", ]; +N: 358 "le_div2" [body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 422 "le_gt_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 363 "le_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Peano", ]; +N: 411 "le_le_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 418 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.IsTotal", ]; +N: 423 "le_lteq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 399 "le_n_S" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Peano", ]; +N: 364 "le_pred" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Peano", ]; +N: 390 "le_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 374 "le_succ_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 412 "le_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 356 "le_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 378 "le_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 360 "lt" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Init.Peano", ]; +N: 408 "lt_asymm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 434 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.IsTotal", ]; +N: 441 "lt_compat" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 442 "lt_eq" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.Tac", ]; +N: 366 "lt_eq_cases" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 375 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 416 "lt_irrefl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.Tac", ]; +N: 387 "lt_le_incl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 425 "lt_strorder" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.IsTotal", ]; +N: 426 "lt_strorder" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 389 "lt_succ_diag_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 359 "lt_succ_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 419 "lt_total" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.IsTotal", ]; +N: 420 "lt_total" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 406 "lt_trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 415 "lt_trans" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.Tac", ]; +N: 421 "lt_trichotomy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 379 "lt_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 382 "lt_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 254 "mul" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 240 "nat_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Datatypes", ]; +N: 257 "negb" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Init.Datatypes", ]; +N: 251 "negb_false_iff" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Bool.Bool", ]; +N: 413 "neq_succ_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 385 "neq_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 376 "nle_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 386 "nlt_succ_diag_l" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 289 "not" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Init.Logic", ]; +N: 417 "not_gt_le" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.Tac", ]; +N: 392 "not_iff_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms_Prop", ]; +N: 401 "not_iff_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms_Prop", ]; +N: 235 "odd" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 245 "odd_bitwise" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 261 "odd_spec" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 380 "or_cancel_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 381 "or_iff_compat_r" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 368 "or_iff_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms_Prop", ]; +N: 370 "or_iff_morphism_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms_Prop", ]; +N: 371 "or_ind" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Logic", ]; +N: 302 "per_partial_app_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 325 "per_partial_app_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 284 "plus_n_O" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Peano", ]; +N: 283 "plus_n_Sm" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Init.Peano", ]; +N: 365 "pred" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Init.Nat", ]; +N: 334 "pred" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 414 "pred_0" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 337 "pred_succ" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 338 "pred_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 342 "pred_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 310 "reflexive_proper_proxy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 295 "reflexive_reflexive_proxy" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 307 "reflexivity" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 275 "relation" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Relations.Relation_Definitions", ]; +N: 280 "respectful" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.Morphisms", ]; +N: 341 "subrelation" [opaque=no, body=yes, kind=cnst, prop=no, path="Corelib.Classes.RelationClasses", ]; +N: 332 "subrelation_proper" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 333 "subrelation_refl" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 339 "subrelation_respectful" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 331 "succ_inj" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 296 "succ_inj_wd" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 357 "succ_le_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 367 "succ_lt_mono" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 329 "succ_wd" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 330 "succ_wd_obligation_1" [opaque=no, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 322 "symmetry" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 225 "testbit" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat", ]; +N: 234 "testbit_0_l" [body=yes, kind=cnst, prop=no, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 226 "testbit_bitwise_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec", ]; +N: 431 "trans" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Stdlib.Arith.PeanoNat.Nat.Private_OrderTac.Tac", ]; +N: 269 "trans_co_eq_inv_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 281 "trans_co_eq_inv_impl_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 335 "trans_co_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 344 "trans_co_impl_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 437 "trans_ord" [opaque=no, body=yes, kind=cnst, prop=no, path="Stdlib.Structures.OrdersTac", ]; +N: 304 "trans_sym_co_inv_impl_morphism" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 324 "trans_sym_co_inv_impl_morphism_obligation_1" [opaque=yes, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.Morphisms", ]; +N: 282 "transitivity" [opaque=no, body=yes, kind=cnst, prop=yes, path="Corelib.Classes.RelationClasses", ]; +N: 313 "Equivalence" [kind=inductive, prop=no, path="Corelib.Classes.RelationClasses", ]; +N: 247 "False" [kind=inductive, prop=no, path="Corelib.Init.Logic", ]; +N: 318 "PER" [kind=inductive, prop=no, path="Corelib.Classes.RelationClasses", ]; +N: 407 "Params" [kind=inductive, prop=no, path="Corelib.Classes.Morphisms", ]; +N: 427 "StrictOrder" [kind=inductive, prop=no, path="Corelib.Classes.RelationClasses", ]; +N: 246 "True" [kind=inductive, prop=no, path="Corelib.Init.Logic", ]; +N: 262 "and" [kind=inductive, prop=no, path="Corelib.Init.Logic", ]; +N: 228 "bool" [kind=inductive, prop=no, path="Corelib.Init.Datatypes", ]; +N: 395 "comparison" [kind=inductive, prop=no, path="Corelib.Init.Datatypes", ]; +N: 229 "eq" [kind=inductive, prop=no, path="Corelib.Init.Logic", ]; +N: 286 "ex" [kind=inductive, prop=no, path="Corelib.Init.Logic", ]; +N: 248 "le" [kind=inductive, prop=no, path="Corelib.Init.Peano", ]; 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+E: 436 248 [weight=1, ]; +E: 436 360 [weight=1, ]; +E: 436 438 [weight=3, ]; +E: 437 432 [weight=3, ]; +E: 437 438 [weight=11, ]; +E: 437 440 [weight=1, ]; +E: 441 227 [weight=7, ]; +E: 441 229 [weight=2, ]; +E: 441 265 [weight=1, ]; +E: 441 279 [weight=1, ]; +E: 441 280 [weight=2, ]; +E: 441 360 [weight=1, ]; +E: 441 379 [weight=1, ]; +E: 442 227 [weight=7, ]; +E: 442 229 [weight=1, ]; +E: 442 360 [weight=2, ]; +E: 442 431 [weight=1, ]; +E: 442 432 [weight=1, ]; +E: 442 439 [weight=1, ]; diff --git a/tests/Proofs.v b/tests/Proofs.v new file mode 100644 index 000000000..eced12dbc --- /dev/null +++ b/tests/Proofs.v @@ -0,0 +1,6 @@ +#[local] Unset Universe Checking. +Require Arith.PeanoNat. +From dpdgraph Require Import dpdgraph. +Set Printing Fully Qualified. +Set DependGraph File "Proofs.dpd". +Print DependGraph Stdlib.Arith.PeanoNat.Nat.PrivateImplementsBitwiseSpec.land_spec.