(** For basic operations, we can prove correspondence with their counterpart in [nat]. *)
Module NZOfNatOps (Import NZ:NZAxiomsSig').
Include NZOfNat NZ.
Local Open Scope ofnat.

(* Specifications: *)
Lemma ofnat_add_l : forall n m, [n]+m == (S^n) m.
Lemma ofnat_add : forall n m, [n+m] == [n]+[m].
Lemma ofnat_mul : forall n m, [n*m] == [n]*[m].
Lemma ofnat_sub_r : forall n m, n-[m] == (P^m) n.
Lemma ofnat_sub : forall n m, m<=n -> [n-m] == [n]-[m].
End NZOfNatOps.