Corollary Forall2_map1 : forall {A B C} (P : A -> B -> Prop) (f : C -> A) l1 l2, Forall2 P (map f l1) l2 <->
  Forall2 (fun a b => P (f a) b) l1 l2.Corollary Forall2_map2 : forall {A B C} (P : A -> B -> Prop) (f : C -> B) l1 l2, Forall2 P l1 (map f l2) <->
  Forall2 (fun a b => P a (f b)) l1 l2.

Lemma Forall2_upd_Znth_l : forall {A B}{d: Inhabitant B} (P : A -> B -> Prop) l1 l2 i x, Forall2 P l1 l2 -> P x (Znth i l2) -> 0 <= i < Zlength l1 -> Forall2 P (upd_Znth i l1 x) l2.