proposition: Lemma mult_cancel_ap_zero_lft : forall x y : F, x[*]y [#] [0] -> x [#] [0].
proof: Proof. intros x y H. cut (x[*]y [#] [0][*][0]). intro H0. elim (bin_op_strext_unfolded _ _ _ _ _ _ H0); intro H1. 3: astepr ([0]:F); auto. assumption. astepl (x[*]y[/] y[//]H1). apply div_resp_ap_zero_rev. assumption. Qed.
imports: CoRN.algebra.CRings