proposition: Lemma list_eq_eq {A} (x y: list A): list_eq eq x y <-> x = y.
proof: Proof. Proof with auto. split; intro. apply (@list_eq_rect A eq)... intros. subst. reflexivity. subst. reflexivity. Qed.
imports: Coq.Lists.List Coq.Unicode.Utf8 Coq.Setoids.Setoid Coq.Sorting.Permutation Coq.Setoids.Setoid Coq.Classes.Morphisms CoRN.stdlib_omissions.Pair