Equations for symmetry

[mikeshulman]

• sym(sym(x)) = x
• sym(ap_ap(x)) = ap_ap(sym(x))
• sym(refl_refl) = refl_refl (special case of the previous)
• braid equation: sym(ap_sym(sym(x))) = ap_sym(sym(ap_sym(x)))
• naturality: sym_{B o f}^{d}(x) = sym_B^{AP (AP f) d}(x)