Definition subobject_classifier_partial_setoid_map_form : form (Y ×h omega_partial_setoid) := let x := π₂ (tm_var ((Y ×h Ω) ×h X)) in let y := π₁ (tm_var (Y ×h Ω)) in let ω := π₂ (tm_var (Y ×h Ω)) in y ~ y ∧ (∃h (φ [ ⟨ x , y [ π₁ (tm_var _) ]tm ⟩ ]) ⇔ Prf [ ω ]).
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.