proposition: Lemma zring_old_inv_nat : forall n : nat, zring_old (- n) [=] [--] (nring n).
proof: Proof. intro n. replace (- n)%Z with (0%nat - n)%Z. astepl (nring 0[-]nring (R:=R) n). simpl in |- *; algebra. simpl in |- *; auto. 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)