Definition disp_psfunctor_lassociator_law : UU := ∏ (a b c d : B₁) (f : B₁ ⟦ a, b ⟧) (g : B₁ ⟦ b, c ⟧) (h : B₁ ⟦ c, d ⟧) (aa : D₁ a) (bb : D₁ b) (cc : D₁ c) (dd : D₁ d) (ff : aa -->[ f] bb) (gg : bb -->[ g] cc) (hh : cc -->[ h] dd), ((disp_psfunctor_mor FFdata ff ◃◃ disp_psfunctor_comp FFdata gg hh) •• disp_psfunctor_comp FFdata ff (gg;; hh)) •• disp_psfunctor_cell FFdata (disp_lassociator ff gg hh) = transportb (λ p, _ ==>[p] _) (psfunctor_lassociator F f g h) ((disp_lassociator (disp_psfunctor_mor FFdata ff) (disp_psfunctor_mor FFdata gg) (disp_psfunctor_mor FFdata hh) •• (disp_psfunctor_comp FFdata ff gg ▹▹ disp_psfunctor_mor FFdata hh)) •• disp_psfunctor_comp FFdata (ff;; gg) hh).
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.