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

Lemma Forall2_In_l (A B : Type) (R : A -> B -> Prop) x xs ys :
Forall2 R xs ys -> In x xs -> exists y, In y ys /\ R x y.