Lemma disp_rwhisker_transport_right {a b c : C} {f : C⟦a,b⟧} {g1 g2 : C⟦b,c⟧} {x x' : g1 ==> g2} (p : x = x') {aa : D a} {bb : D b} {cc : D c} {ff : aa -->[f] bb} (gg1 : bb -->[g1] cc) (gg2 : bb -->[g2] cc) (xx : gg1 ==>[x] gg2) : ff ◃◃ (transportf (λ x, _ ==>[x] _) p xx) = transportf (λ x, _ ==>[x] _) (maponpaths (λ x, f ◃ x) p) (ff ◃◃ xx). Proof. induction p. apply idpath. Defined.
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.