Definition all_functor_democratic_iso : z_iso (F [] & comp_cat_type_functor F [] (is_democratic_ty D₁ Γ)) (F [] & (is_democratic_ty D₂ (F Γ) [[TerminalArrow [] (F [])]])) := z_iso_comp (z_iso_comp (z_iso_inv (comp_cat_functor_extension F [] (is_democratic_ty D₁ Γ))) (z_iso_comp (functor_on_z_iso F (z_iso_inv (is_democratic_iso D₁ Γ))) (is_democratic_iso D₂ (F Γ)))) (z_iso_inv (comp_cat_extend_over_iso _ _ (comp_cat_functor_empty_context_is_z_iso F))).
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.FullyFaithfulDispFunctor. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat. Require Import UniMath.Bicategories.ComprehensionCat.CompCatNotations.