Theorem disp_lunitor_runitor_identity {C : bicat} {D : disp_bicat C} (a : C) (aa : D a) : disp_lunitor (id_disp aa) = cell_transportb (lunitor_runitor_identity a) (disp_runitor (id_disp aa)). Proof. set (TT := fiber_paths (lunitor_runitor_identity (C := total_bicat D) (a ,, aa))). cbn in TT. apply cell_transportf_to_b. etrans. 2: now apply TT. unfold cell_transportf. apply maponpaths_2. apply cellset_property. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence.