induction n; intuition; simpl in *.
rewrite (vector_0 v1).
rewrite (vector_0 v2).
simpl.
trivial.
destruct (vector_S v1).
destruct (vector_S v2).
destruct H.
destruct H0.
subst.
simpl.
eapply IHn.
Qed.

(* Specifications: *)
Theorem eqb_vector_leibniz:
forall (A : Set)(eqd : EqDec A)(n : nat)(v1 v2 : Vector.t A n),
eqb_vector _ v1 v2 = true -> v1 = v2.