proposition: Lemma cring_inv_mult_lft : forall x y : R, x[*] [--]y [=] [--] (x[*]y).
proof: Proof. intros x y. apply cg_inv_unique. astepl (x[*] (y[+] [--]y)). Step_final (x[*][0]). 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)