Corollary NoDup_app_swap : forall {A} (l1 l2 : list A), NoDup (l1 ++ l2) <-> NoDup (l2 ++ l1).

Lemma Forall2_impl' : forall {A B} (P Q : A -> B -> Prop) l1 l2, (forall a b, In a l1 -> In b l2 -> P a b -> Q a b) -> Forall2 P l1 l2 -> Forall2 Q l1 l2.