intuition.
rewrite <- BVxor_id_l at 1.
rewrite <- (BVxor_same_id v1).
rewrite BVxor_assoc.
f_equal; intuition.
Qed.

Lemma BVxor_id_inv : forall n (v1 v2 : Bvector n),
BVxor n v1 v2 = Bvect_false n ->
v1 = v2.