Definition torsor_univalence {G:gr} {X Y:Torsor G} : (X = Y) ≃ (ActionIso X Y). Proof. intros. simple refine (weqcomp underlyingAction_injectivity _). apply Action_univalence. 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.