Definition partial_setoid_comp_morphism_form : form (X ×h Z) := let x := π₁ (π₁ (tm_var _)) : tm ((X ×h Z) ×h Y) X in let y := π₂ (tm_var _) : tm ((X ×h Z) ×h Y) Y in let z := π₂ (π₁ (tm_var _)) : tm ((X ×h Z) ×h Y) Z in (∃h (φ₁ [ ⟨ x , y ⟩ ] ∧ φ₂ [ ⟨ y , z ⟩ ])).
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.PartialEqRels.PERs. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERMorphisms.