Definition transportf_prewhisker_1cell {B : bicat} {D : disp_bicat B} {x y z : B} {xx : D x} {yy : D y} {zz : D z} {f₁ f₂ : x --> y} {g : y --> z} (p : f₁ = f₂) (ff : xx -->[ f₁ ] yy) (gg : yy -->[ g ] zz) : (transportf (λ z, xx -->[ z ] yy) p ff ;; gg = transportf (λ z, xx -->[ z ] zz) (maponpaths (λ z, z · _) p) (ff ;; gg))%mor_disp. Proof. induction p ; cbn. apply idpath. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor.