Definition Vector_0_is_nil (T : Type) (v : Vector.t T 0) : v = Vector.nil T :=
  match v with Vector.nil => eq_refl end.

Lemma VectorToList_combine A n: forall (a:A) b v1 v2, combine (Vector.to_list (Vector.cons A a n v1)) (Vector.to_list (Vector.cons A b n v2)) = (a,b) :: combine (Vector.to_list v1) (Vector.to_list v2).