proposition: Lemma cring_mult_ap_zero_op : (forall x y : R, x[*]y [#] [0] -> y [#] [0]) :CProp.
proof: Proof. intros x y H. apply cring_mult_ap_zero with x. astepl (x[*]y). 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)