Context schema subsumption

[MartyO256]

Context variable checking against context schemas should support schema subsumption.

Let schema G1 = some [...S1] block (...B1) and schema G2 = some [...S2] block (...B2) be context schemas, with lists S1, B1, S2, B2 of terms.
If every element of S2 is in S1, and every element of B2 is in B1, then G1 should be subsumed by G2.

Load the following Harpoon signature:

LF con : type =;
LF kind : type =;

LF cn-of : con -> kind -> type =;
LF kd-wf : kind -> type =;

LF kd-equiv : kind -> kind -> type =;

LF eterm : type =;
LF etp : type =;

LF unmap : eterm -> con -> type =;
LF tunmap : etp -> kind -> type =;
LF eof : eterm -> etp -> type =;
LF tequiv : etp -> etp -> type =;

schema conbind-reg =
  some [K : kind, wf : kd-wf K]
  block (a : con, da : cn-of a K);

schema unmap-bind =
  some [K : kind, Dwf : kd-wf K, B : etp, Dmap : tunmap B K]
  block (a : con, da : cn-of a K, x : eterm, dx : eof x B, xt : unmap x a);

proof kd-equiv-reg/1 :
  (g : conbind-reg)
  [g |- kd-equiv K1 K2] ->
    [g |- kd-wf K1] =
/ total 1 /
?
;

proof kd-equiv-reg/1' :
  (g : unmap-bind)
  [g |- kd-equiv K1 K2] ->
    [g |- kd-wf K1] =
/ total /
?
;

Theorems kd-equiv-reg/1 and kd-equiv-reg/1' are the same except for the context schema.

Schema unmap-bind should be subsumed by conbind-reg.
That is because some [K : kind, Dwf : kd-wf K, B : etp, Dmap : tunmap B K] contains at least the required terms some [K : kind, wf : kd-wf K] for instantiating the block in conbind-reg, and block (a : con, da : cn-of a K, x : eterm, dx : eof x B, xt : unmap x a) contains at least the terms in block (a : con, da : cn-of a K).

So, every block instantiation of unmap-bind can be used to instantiate conbind-reg whenever it is used in kd-equiv-reg/1.
Ideally, this context schema subsumption should also work irrespective of the topological ordering of terms in both some and block of either schemas.

kd-equiv-reg/1' should be trivially provable using kd-equiv-reg/1.
However, running the following Harpoon commands:

select kd-equiv-reg/1'
solve kd-equiv-reg/1 x

yields

Context variable
  _
doesn't check against schema
  unmap-bind = some [K : kind, wf : kd-wf K] block (a : con, da : cn-of a K)