Lemma disp_lassociator_pstrans_laws : is_disp_pstrans _ _ _ disp_lassociator_pstrans_data. Proof. apply is_disp_pstrans_from_total. pose (PP := lassociator_pstrans (total_psfunctor _ _ _ FF₁) (total_psfunctor _ _ _ FF₂) (total_psfunctor _ _ _ FF₃)). pose (PP2 := pstrans_to_is_pstrans PP). assert (X : pstrans_to_pstrans_data PP = total_pstrans_data _ _ _ disp_lassociator_pstrans_data). - use total2_paths_f. + apply idpath. + apply funextsec. intro x. apply funextsec. intro y. apply funextsec. intro f. use subtypePath. { intro. apply isaprop_is_invertible_2cell. } apply idpath. - exact (transportf is_pstrans X PP2). Qed.
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.