Definition cleaving_of_opcleaving_lift_2cell_data : disp_nat_trans_data (pr1 α) (pr11 Lh : disp_functor _ _ _) (pr11 Lh' : disp_functor _ _ _). Proof. intros x xx. simple refine (transportf (λ z, _ -->[ z ] _) _ (pr1 (pr112 Lh) x xx ;; pr11 αα x xx ;; inv_mor_disp_from_z_iso (disp_bicat_of_opcleaving_disp_invertible_2cell_pointwise_inv _ (pr2 Lh') (pr22 Lh') xx))%mor_disp). abstract (cbn ; unfold precomp_with ; cbn ; rewrite !id_left, id_right ; apply idpath). Defined.
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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Reindexing. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Opposite. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DispBicatOfDispCats.