Definition lam_partial_setoid_eq : form (Z ×h exp_partial_setoid X Y) := let z := π₁ (π₁ (π₁ (tm_var (((Z ×h ℙ (X ×h Y)) ×h X) ×h Y)))) in let f := π₂ (π₁ (π₁ (tm_var (((Z ×h ℙ (X ×h Y)) ×h X) ×h Y)))) in let x := π₂ (π₁ (tm_var (((Z ×h ℙ (X ×h Y)) ×h X) ×h Y))) in let y := π₂ (tm_var (((Z ×h ℙ (X ×h Y)) ×h X) ×h Y)) in (∀h ∀h (φ [ ⟨ ⟨ x , z ⟩ , y ⟩ ] ⇔ ⟨ x , y ⟩ ∈ f)).
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. 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.PERBinProducts. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.ExponentialPER.