Definition is_pullback_subobject_classifier_partial_setoid_map_form : form (W ×h X) := let w := π₁ (π₁ (tm_var ((W ×h X) ×h Y))) in let x := π₂ (π₁ (tm_var ((W ×h X) ×h Y))) in let y := π₂ (tm_var ((W ×h X) ×h Y)) in (∃h (φ [ ⟨ x , y ⟩ ] ∧ ψ₁ [ ⟨ w , y ⟩ ])).
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.