Definition fiberwise_exponentials_h_valued_sets : fiberwise_exponentials fiberwise_binproducts_h_valued_sets. Proof. use make_fiberwise_exponentials_locally_propositional. - exact locally_propositional_h_valued_sets. - exact (λ (X : hSet) (P Q : X → H) (x : X), P x ⇒ Q x). - abstract (intros X P Q x ; cbn ; rewrite cha_min_comm ; apply cha_exp_eval). - abstract (intros X P Q R p x ; cbn in * ; use cha_to_le_exp ; rewrite cha_min_comm ; exact (p x)). - abstract (intros X Y f P Q x ; cbn ; apply cha_le_refl). 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.