Definition partial_setoid_mor_eq_defined_law (φ : form (X ×h Y)) : UU := let x₁ := π₂ (π₁ (π₁ (π₁ (tm_var _)))) : tm ((((𝟙 ×h X) ×h X) ×h Y) ×h Y) X in let x₂ := π₂ (π₁ (π₁ (tm_var _))) : tm ((((𝟙 ×h X) ×h X) ×h Y) ×h Y) X in let y₁ := π₂ (π₁ (tm_var _)) : tm ((((𝟙 ×h X) ×h X) ×h Y) ×h Y) Y in let y₂ := π₂ (tm_var _) : tm ((((𝟙 ×h X) ×h X) ×h Y) ×h Y) Y in ⊤ ⊢ (∀h ∀h ∀h ∀h (x₁ ~ x₂ ⇒ y₁ ~ y₂ ⇒ φ [ ⟨ x₁ , y₁ ⟩ ] ⇒ φ [ ⟨ x₂ , y₂ ⟩ ])).
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.