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 app_inv_length1 {A}: forall (l1 m1 l2 m2:list A), l1++l2 = m1++m2 -> length l1 = length m1 -> l1=m1 /\ l2=m2.