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

(* Specifications: *)
Lemma BVxor_id_r : forall n (v : Bvector n),
BVxor n v (Bvect_false n) = v.