proposition: Lemma CDRmult_apcompat_l' : ∏ x y z : X, x ≠ 0 -> y ≠ z -> y * x ≠ z * x.
proof: 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.
imports: UniMath.Algebra.DivisionRig UniMath.Algebra.Domains_and_Fields UniMath.Algebra.Apartness UniMath.MoreFoundations.Tactics