Proposition h_valued_morphism_dom_defined (x : X) (y : Y) : (f x y ≤ x ~_{X} x)%heyting. Proof. refine (@partial_setoid_mor_dom_defined _ _ _ f unitset (λ _, f x y) (λ _, x) (λ _, y) _ tt). intro ; cbn ; unfold prodtofuntoprod ; cbn. apply cha_le_refl. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Lattice.CompleteHeyting. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifier. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.ElementaryTopos. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.HValuedPredicates. Require Import UniMath.CategoryTheory.Hyperdoctrines.Hyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.FirstOrderHyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.Tripos. Require Import UniMath.CategoryTheory.Hyperdoctrines.GenericPredicate. Require Import UniMath.CategoryTheory.Hyperdoctrines.TriposToTopos.