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