Definition disp_psfunctor_cell_transportf {B₁ B₂ : bicat} {F : psfunctor B₁ B₂} {D₁ : disp_bicat B₁} {D₂ : disp_bicat B₂} (FF : disp_psfunctor D₁ D₂ F) {x y : B₁} {f g : x --> y} {φ ψ : f ==> g} (p : φ = ψ) {xx : D₁ x} {yy : D₁ y} {ff : xx -->[ f ] yy} {gg : xx -->[ g ] yy} (φφ : ff ==>[ φ ] gg) : disp_psfunctor_cell _ _ _ (pr1 FF) (transportf (λ z, ff ==>[ z ] gg) p φφ) = transportf (λ z, _ ==>[ z ] _) (maponpaths (## F) p) (disp_psfunctor_cell _ _ _ (pr1 FF) φφ).
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.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.Initial. Require Import UniMath.Bicategories.Core.Examples.Final. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.FiberCategory. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Import PseudoFunctor.Notations.