proposition: Lemma zring_zring_old : forall z : Z, zring z [=] zring_old z.
proof: Proof. simple induction z; simpl in |- *; intros. algebra. astepr (nring (R:=R) (nat_of_P p)). algebra. astepr ( [--] (nring (R:=R) (nat_of_P p))). algebra. 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)