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(** Rewrite with the commutative property to ensure that all appearences of an identifier show up the same way *)
Ltac rewrite_with_comm id clem x y :=
first [ constr_eq x y; fail 1
| repeat match goal with
| [ H' : context[id y x] |- _ ]
=> rewrite clem in H'
| [ |- context[id y x] ]
=> rewrite clem
end ].
Ltac normalize_commutative_identifier id id_comm :=
repeat match goal with
| [ |- context[id ?x ?y] ] => progress rewrite_with_comm id (id_comm y x) x y
| [ H : context[id ?x ?y] |- _ ] => progress rewrite_with_comm id (id_comm y x) x y
end.
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