Definition discrete_fiber_rinvunitor {d d' : D c} (ff : d -->[ id₁ c] d') : ff ==>[ id₂ (id₁ c) ] (local_iso_cleaving_1cell h (ff;;id_disp d') (idempunitor c)). Proof. set (PP := disp_inv_cell (disp_local_iso_cleaving_invertible_2cell h (ff;; id_disp d') (idempunitor c))). assert (Heq : rinvunitor (identity c) • (idempunitor c)^-1 = id2 (identity c)). { unfold idempunitor. cbn. abstract (rewrite lunitor_runitor_identity, rinvunitor_runitor ; reflexivity). } exact (transportf (λ x, _ ==>[x] _) Heq (disp_rinvunitor ff •• PP)). 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.