Lemma CDRmultapCDRzero : ∏ x y : X, x * y ≠ 0 → x ≠ 0 ∧ y ≠ 0. 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.
Require Import UniMath.MoreFoundations.Tactics.