End prodl.
Definition clos_refl {A : Type} (R : A -> A -> Prop) (x y : A) : Prop :=
R x y \/ x = y.

Lemma Forall2_forall A (d: A) (R: A -> A -> Prop) (xs ys: list A) :
Forall2 R xs ys ->
forall i, i < length xs -> R (nth i xs d) (nth i ys d).