proposition: Lemma cring_mult_ap_zero :(forall x y : R, x[*]y [#] [0] -> x [#] [0]):CProp.
proof: Proof. intros x y H. elim (cs_bin_op_strext _ cr_mult x [0] y y). auto. intro contra; elim (ap_irreflexive _ _ contra). astepr ([0]:R). 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)