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

Lemma Forall2_conj (A B : Type) (R1 R2 : A -> B -> Prop) xs ys : Forall2 R1 xs ys -> Forall2 R2 xs ys -> Forall2 (fun x y => R1 x y /\ R2 x y) xs ys.