proposition: Lemma zring_old_plus_nat : forall n : nat, zring_old n [=] nring n.
proof: Proof. intro n. replace (n:Z) with (n - 0%nat)%Z. astepl (nring (R:=R) n[-]nring 0). simpl in |- *; algebra. simpl in |- *; auto with zarith. Qed.
imports: CoRN.tactics.CornTac CoRN.algebra.CSums CoRN.algebra.CAbMonoids Coq.Sorting.Permutation CoRN.util.SetoidPermutation Coq.Setoids.Setoid Coq.Classes.Morphisms Coq(Lia)