induction n; intuition.
rewrite (vector_0 v).
unfold Bvect_false.
simpl.
trivial.
destruct (vector_S v).
destruct H.
unfold Bvect_false.
subst.
simpl.
rewrite IHn.
rewrite xorb_false_r.
trivial.
Qed.

Lemma BVxor_id_l : forall n (v : Bvector n),
BVxor n (Bvect_false n) v = v.