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

Lemma Forall2_In_r (A B : Type) (R : A -> B -> Prop) y xs ys :
Forall2 R xs ys -> In y ys -> exists x, In x xs /\ R x y.