Definition disp_pstrans_comp_law : UU := ∏ (x y z : B₁) (f : B₁ ⟦ x, y ⟧) (g : B₁ ⟦ y, z ⟧) (xx : D₁ x) (yy : D₁ y) (zz : D₁ z) (ff : xx -->[ f] yy) (gg : yy -->[ g] zz), (ααdata x xx ◃◃ disp_psfunctor_comp D₁ D₂ F₂ FF₂ ff gg) •• disp_psnaturality_of ααdata (ff;; gg) = transportb (λ p, _ ==>[p] _) (pstrans_comp α f g) (((((disp_lassociator (ααdata x xx) (disp_psfunctor_mor D₁ D₂ F₂ FF₂ ff) (disp_psfunctor_mor D₁ D₂ F₂ FF₂ gg) •• (disp_psnaturality_of ααdata ff ▹▹ disp_psfunctor_mor D₁ D₂ F₂ FF₂ gg)) •• disp_rassociator (disp_psfunctor_mor D₁ D₂ F₁ FF₁ ff) (ααdata y yy) (disp_psfunctor_mor D₁ D₂ F₂ FF₂ gg)) •• (disp_psfunctor_mor D₁ D₂ F₁ FF₁ ff ◃◃ disp_psnaturality_of ααdata gg)) •• disp_lassociator (disp_psfunctor_mor D₁ D₂ F₁ FF₁ ff) (disp_psfunctor_mor D₁ D₂ F₁ FF₁ gg) (ααdata z zz)) •• (disp_psfunctor_comp D₁ D₂ F₁ FF₁ ff gg ▹▹ ααdata z zz)).
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.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Transformations.Examples.Whiskering. Require Import UniMath.Bicategories.Transformations.Examples.Unitality. Require Import UniMath.Bicategories.Transformations.Examples.Associativity. Require Import UniMath.Bicategories.DisplayedBicats.DispPseudofunctor. Import PseudoFunctor.Notations.