Definition cleaving_h_valued_sets : cleaving disp_cat_h_valued_sets. Proof. intros Y X f Q. simple refine ((λ x, Q(f x)) ,, _ ,, _). - abstract (intro ; apply cha_le_refl). - intros W g R p. use iscontraprop1. + abstract (use isaproptotal2 ; [ | intros ; apply locally_propositional_h_valued_sets ] ; intro ; apply disp_cat_h_valued_sets). + abstract (refine (p ,, _) ; apply locally_propositional_h_valued_sets). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Lattice.CompleteHeyting. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseTerminal. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseInitial. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseCoproducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseCartesianClosed. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentSums. Require Import UniMath.CategoryTheory.Hyperdoctrines.Hyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.FirstOrderHyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.Tripos.