Definition Action_univalence_inv_comp {G:gr} {X Y:Action G} (f:ActionIso X Y) : path_to_ActionIso (Action_univalence_inv f) = f. Proof. intros. unfold Action_univalence_inv, Action_univalence. apply (homotweqinvweq Action_univalence f). 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.