Definition disp_psfunctor_invmap_1_comp_eq (HB₁ : is_univalent_2_1 B₁) (HD₂ : disp_univalent_2_1 D₂) {x : B₁} {xx yy zz : D₁ x} (f : FF x xx -->[ id₁ (F x) ] FF x yy) (g : FF x yy -->[ id₁ (F x) ] FF x zz) : transportf (λ z, _ -->[ z ] _) (isotoid_2_1 HB₁ (linvunitor_invertible_2cell (id₁ _))) (disp_psfunctor_invmap_1 (transportf (λ z, _ -->[ z ] _) (isotoid_2_1 HB₂ (lunitor_invertible_2cell (id₁ _))) (f ;; g)%mor_disp)) = (disp_psfunctor_invmap_1 f ;; disp_psfunctor_invmap_1 g)%mor_disp.
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.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.TransportLaws. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. 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. Require Import UniMath.Bicategories.DisplayedBicats.DispTransportLaws.