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

Lemma Forall2_firstn : forall {A B} (P : A -> B -> Prop) l1 l2 n, Forall2 P l1 l2 -> Forall2 P (firstn n l1) (firstn n l2).