Lemma quotient_product {G} (X:Torsor G) (z y x:X) : op (z/y) (y/x) = z/x. Proof. intros. apply quotient_uniqueness. exact (ac_assoc _ _ _ _ @ maponpaths (left_mult (z/y)) (quotient_times y x) @ quotient_times z y). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.OrderTheory.OrderedSets.OrderedSets. Import UniMath.MoreFoundations.PartA.