proposition: Lemma zring_old_inv_one : forall x, zring_old (-1) [*]x [=] [--]x.
proof: Proof. intro x. simpl in |- *. astepl ( [--] ([0][+][1]) [*]x). astepl ( [--][1][*]x). Step_final ( [--] ([1][*]x)). 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)