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

Lemma Forall2_trans (A: Type) (R: A -> A -> Prop) xs ys zs : (forall x y z, In x xs -> In y ys -> In z zs -> R x y -> R y z -> R x z) -> Forall2 R xs ys -> Forall2 R ys zs -> Forall2 R xs zs.