intuition.
apply vector_tl_eq in H.
simpl in *.
trivial.
Qed.

(* Specifications: *)
Lemma vector_cons_ne : forall (A : Set)(n : nat)(a1 a2 : Vector.t A n)(a : A),
a1 <> a2 ->
Vector.cons A a n a1 <> Vector.cons A a n a2.