intros.
generalize dependent i.
generalize dependent v.
induction xs;
intros.
rewrite Coqlib.nth_error_nil in H.
discriminate.
destruct i; simpl in *;
now auto.
Qed.

Lemma forall2_and:
forall {A B : Type} (f g : A -> B -> Prop),
(forall x y, f x y /\ g x y) <->
(forall x y, f x y) /\ (forall x y, g x y).