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