Definition is_pullback_subobject_classifier_partial_setoid : isPullback (C := category_of_partial_setoids H) subobject_classifier_partial_setoid_comm. Proof. intros W ψ₁ ψ₂ q. use make_iscontr. - simple refine (_ ,, _ ,, _). + exact (is_pullback_subobject_classifier_partial_setoid_map ψ₁ ψ₂ q). + exact (is_pullback_subobject_classifier_partial_setoid_map_pr1 ψ₁ ψ₂ q). + exact (is_pullback_subobject_classifier_partial_setoid_map_pr2 ψ₁ ψ₂ q). - abstract (intros ζ ; use subtypePath ; [ intro ; apply isapropdirprod ; apply homset_property | ] ; induction ζ as [ ζ [ ζp ζq ]] ; exact (is_pullback_subobject_classifier_partial_setoid_unique _ _ _ ζp)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.SubobjectClassifier.SubobjectClassifier. 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.PartialEqRels.PERs. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERMorphisms. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERCategory. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERTerminal. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERMonomorphisms.