proposition: Lemma CDRmultapCDRzero : ∏ x y : X, x * y ≠ 0 -> x ≠ 0 ∧ y ≠ 0.
proof: Proof. intros x y Hmult. split. - apply CDRmult_apcompat_l with y. rewrite islabsorb_CDRzero_CDRmult. exact Hmult. - apply CDRmult_apcompat_r with x. rewrite israbsorb_CDRzero_CDRmult. exact Hmult. Qed.
imports: UniMath.Algebra.DivisionRig UniMath.Algebra.Domains_and_Fields UniMath.Algebra.Apartness UniMath.MoreFoundations.Tactics