Definition disp_psfunctor_mor_transportb {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} (p : f = g) {xx : D₁ x} {yy : D₁ y} (gg : xx -->[ g ] yy) : disp_psfunctor_mor _ _ _ FF (transportb (λ z, xx -->[ z ] yy) p gg) = transportb (λ z, _ -->[ z ] _) (maponpaths (#F) p) (disp_psfunctor_mor _ _ _ FF gg).
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.