Definition underlyingAction_injectivity_inv_comp {G:gr} {X Y:Torsor G} (f:underlyingAction X = underlyingAction Y) : maponpaths underlyingAction (invmap underlyingAction_injectivity f) = f. Proof. intros. apply (homotweqinvweq underlyingAction_injectivity 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.