Definition disp_bicat_cat_with_terminal_cleaving : disp_bicat bicat_cat_with_terminal_disp_cat. Proof. use disp_subbicat. - exact (λ C, cleaving (disp_cat_of_types C)). - exact (λ C₁ C₂ D₁ D₂ F, is_cartesian_disp_functor (comp_cat_type_functor F)). - abstract (intros X fibX x y f xx yy ff p ; exact p). - abstract (intros X Y Z F G fibX fibY fibZ cartF cartG x y f xx yy ff p ; simpl ; apply cartG ; apply cartF ; exact p). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. 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.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Equivalences. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat.DispCatTerminal. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sub1Cell.