Lemma CDRmult_apcompat_r' : ∏ x y z : X, x ≠ 0 → y ≠ z → x * y ≠ x * z. Proof. intros x y z Hx Hap. refine (CDRmult_apcompat_r (CDRinv x Hx) _ _ _). rewrite <- !isassoc_CDRmult, islinv_CDRinv, !islunit_CDRone_CDRmult. exact Hap. Qed.
Require Import UniMath.MoreFoundations.Tactics.