Definition disp_psfunctor_vcomp2_alt (H : is_disp_psfunctor) (a b : B₁) (f g h : B₁ ⟦a, b⟧) (η : f ==> g) (φ : g ==> h) (aa : D₁ a) (bb : D₁ b) (ff : aa -->[f] bb) (gg : aa -->[g] bb) (hh : aa -->[h] bb) (ηη : ff ==>[η] gg) (φφ : gg ==>[φ] hh) : transportf (λ p : # F f ==> # F h, disp_psfunctor_mor FFdata ff ==>[ p] disp_psfunctor_mor FFdata hh) (psfunctor_vcomp F η φ) (disp_psfunctor_cell FFdata (ηη •• φφ)) = disp_psfunctor_cell FFdata ηη •• disp_psfunctor_cell FFdata 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.