Definition invUnivalenceCompose {G:gr} {X Y Z : Torsor G} (f : ActionIso X Y) (g : ActionIso Y Z) : invmap torsor_univalence f @ invmap torsor_univalence g = invmap torsor_univalence (composeActionIso f g). Proof. torsor_induction' g Z. rewrite composeActionIsoId'. rewrite torsor_univalence_id. apply pathscomp0rid. 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.