induction n1; intuition.
rewrite (vector_0 v1).
simpl.
apply Bv2N_zero.
destruct (vector_S v1).
destruct H.
rewrite H.
simpl.
destruct x.
rewrite IHn1.
trivial.
rewrite IHn1.
trivial.
Qed.

Lemma Bv2N_N2Bv_gen : forall n0 k,
n0 >= N.size_nat k ->
Bv2N n0 (N2Bv_gen n0 k) = k.