Definition equalizer_per_form : form (X ×h X) := let x := π₁ (tm_var (X ×h X)) in let x' := π₂ (tm_var (X ×h X)) in let y := π₂ (tm_var ((X ×h X) ×h Y)) in x ~ x' ∧ (∃h (φ [ ⟨ x [ π₁ (tm_var _) ]tm , y ⟩ ] ∧ ψ [ ⟨ x [ π₁ (tm_var _) ]tm , y ⟩ ])).
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Hyperdoctrines.Hyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.FirstOrderHyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERs. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERMorphisms. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERCategory.