Theorem TorsorIso_rect {G:gr} {X Y : Torsor G} (P : ActionIso X Y → UU) : (∏ e : X = Y, P (torsor_univalence e)) → ∏ f, P f. Proof. intros ih ?. set (p := ih (invmap torsor_univalence f)). set (h := homotweqinvweq torsor_univalence f). exact (transportf P h p). 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.