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