intuition.
specialize (vector_S v1).
specialize (vector_S v2).
intuition.
destruct H0. destruct H0.
destruct H1. destruct H1.
subst.
simpl.
trivial.
Qed.

(* Specifications: *)
Lemma vector_cons_eq : forall (A : Set)(n : nat)(v1 v2 : Vector.t A n)(a1 a2 : A),
Vector.cons A a1 n v1 = Vector.cons A a2 n v2 ->
v1 = v2.