Proposition h_valued_morphism_unique_im (x : X) (y₁ y₂ : Y) : ((f x y₁ ∧ f x y₂) ≤ y₁ ~_{Y} y₂)%heyting. Proof. refine (@partial_setoid_mor_unique_im _ _ _ f unitset (λ _, f x y₁ ∧ f x y₂)%heyting (λ _, x) (λ _, y₁) (λ _, y₂) _ _ tt) ; cbn ; unfold prodtofuntoprod ; cbn ; intro. - apply cha_min_le_l. - apply cha_min_le_r. 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.