Theorem disp_runitor_lunitor_identity {C : bicat} {D : disp_bicat C} {a : C} (aa : D a) : disp_runitor (id_disp aa) = transportb (λ x, disp_2cells x _ _) (runitor_lunitor_identity a) (disp_lunitor (id_disp aa)). Proof. apply (transportf_transpose_right (P := (λ x, disp_2cells x _ _))). apply pathsinv0. etrans. 1: now apply disp_lunitor_runitor_identity. unfold cell_transportb. apply maponpaths_2, 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.