Definition Pointedtorsor_univalence {G:gr} {X Y:PointedTorsor G} : (X = Y) ≃ (PointedActionIso X Y). Proof. intros. simple refine (weqcomp (total2_paths_equiv _ X Y) _). simple refine (weqbandf _ _ _ _). { intros. exact (weqcomp (weqonpathsincl underlyingAction underlyingAction_incl X Y) Action_univalence). } destruct X as [X x], Y as [Y y]; simpl. intro p. destruct p; simpl. exact (idweq _). 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.