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_inj1 {A} l2 m2: forall (l1 m1:list A) (H:l1++l2=m1++m2), length l1=length m1 -> l1=m1 /\ l2=m2.