Definition discrete_fiber_linvunitor {d d' : D c} (ff : d -->[ id₁ c] d') : ff ==>[id₂ (id₁ c) ] (local_iso_cleaving_1cell h (id_disp d;; ff) (idempunitor c)). Proof. set (PP := disp_inv_cell (disp_local_iso_cleaving_invertible_2cell h (id_disp d;; ff) (idempunitor c))). assert (Heq : linvunitor (identity c) • (idempunitor c)^-1 = id2 (identity c)). { abstract (apply linvunitor_lunitor). } exact (transportf (λ x, _ ==>[x] _) Heq (disp_linvunitor 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.