Definition torsor_univalence_inv_comp_eval {G:gr} {X Y:Torsor G} (f:ActionIso X Y) (x:X) : castTorsor (invmap torsor_univalence f) x = f x. Proof. intros. unfold torsor_univalence. unfold castTorsor. rewrite invmapweqcomp. unfold weqcomp; simpl. rewrite underlyingAction_injectivity_inv_comp. apply Action_univalence_inv_comp_eval. 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.