intuition.
assert (exists x, n0 = N.size_nat k + x)%nat.
exists (minus n0 (N.size_nat k)).
omega.
destruct H0.
rewrite H0.
rewrite N2Bv_N2Bv_gen_above.
rewrite Bv2N_app_false.
apply Bv2N_N2Bv.
Qed.

Lemma bvToNat_natToBv_inverse : forall n k,
n >= lognat k ->
bvToNat (natToBv n k) = k.