intuition.
unfold bvToNat, natToBv.
rewrite Bv2N_N2Bv_gen.
apply Nnat.Nat2N.id.
trivial.
Qed.

Lemma Nat_size_nat_monotonic : forall n1 n2,
(n1 < n2)%N ->
(N.size_nat n1 <= N.size_nat n2)%nat.