proposition: Lemma all_equiv2_impl2__all_equiv : forall l1 l2 x y x' y', all_equiv l1 -> all_equiv l2 -> In x l1 -> In y l2 -> (x -> y) -> In x' l2 -> In y' l1 -> (x' -> y') -> all_equiv (l1++l2).
proof: Proof. intros l1 l2 x y x' y'; intros. apply all_equiv2_stronger2__all_equiv; trivial. apply all_equiv2_impl__stronger with x y; assumption. apply all_equiv2_impl__stronger with x' y'; assumption. Qed.
imports: List