Definition discrete_fiber_runitor_disp_invertible {d d' : D c} (ff : d -->[ id₁ c] d') : disp_invertible_2cell (id2_invertible_2cell (id₁ c)) (local_iso_cleaving_1cell h (ff;;id_disp d') (idempunitor c)) ff. Proof. use tpair. - exact (discrete_fiber_runitor ff). - use tpair. + exact (discrete_fiber_rinvunitor ff). + abstract (split ; apply HD). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat.