intuition.
unfold natToBv, bvToNat.
rewrite Nnat.N2Nat.id.
apply N2Bv_Bv2N.
Qed.

(* Specifications: *)
Lemma bvToNat_natToBv_eq : forall n (v : Bvector n) k,
bvToNat v = k ->
v = natToBv n k.