Lemma disp_mor_transportf_postwhisker (a b : C) {x y z : C⟦a,b⟧} {f f' : x ==> y} (ef : f = f') {g : y ==> z} {aa : D a} {bb : D b} {xx : aa -->[x] bb} {yy} {zz} (ff : xx ==>[f] yy) (gg : yy ==>[g] zz) : (transportf (λ x, _ ==>[x] _) ef ff) •• gg = transportf (λ x, _ ==>[x] _) (maponpaths (λ h, h • g) ef) (ff •• gg). Proof. induction ef; apply idpath. 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.