Definition exp_partial_setoid_eq : form (ℙ (X ×h Y) ×h ℙ (X ×h Y)) := let f := π₁ (π₁ (π₁ (tm_var (((ℙ (X ×h Y) ×h ℙ (X ×h Y)) ×h X) ×h Y)))) in let g := π₂ (π₁ (π₁ (tm_var (((ℙ (X ×h Y) ×h ℙ (X ×h Y)) ×h X) ×h Y)))) in let x := π₂ (π₁ (tm_var (((ℙ (X ×h Y) ×h ℙ (X ×h Y)) ×h X) ×h Y))) in let y := π₂ (tm_var (((ℙ (X ×h Y) ×h ℙ (X ×h Y)) ×h X) ×h Y)) in (∀h ∀h ((⟨ x , y ⟩ ∈ f) ⇔ (⟨ x , y ⟩ ∈ g))).
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.