induction n; intuition; simpl in *.
rewrite (vector_0 v).
unfold eqb_vector.
simpl.
trivial.
destruct (vector_S v).
destruct H.
subst.
unfold eqb_vector.
simpl.
rewrite eqb_refl.
eapply IHn.
Qed.

(* Specifications: *)
Theorem vector_fold_false :
forall (A : Set)(f : A -> A -> bool)(n : nat)(v1 v2 : Vector.t A n),
Vector.fold_left2 (fun b a1 a2 => b && (f a1 a2)) false v1 v2 = false.