Definition proof_to_partial_setoid_morphism_form {Γ₁ Γ₂ : ty H} {Δ : form Γ₁} {φ : form Γ₂} {s : tm Γ₁ Γ₂} (q : Δ ⊢ φ [ s ]) : form (formula_to_partial_setoid Δ ×h formula_to_partial_setoid φ) := let x := π₁ (tm_var (Γ₁ ×h Γ₂)) in let y := π₂ (tm_var (Γ₁ ×h Γ₂)) in Δ [ x ] ∧ φ [ y ] ∧ y ≡ s [ x ]tm.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.MonoCodomain. Require Import UniMath.CategoryTheory.DisplayedCats.MonoCodomain.FiberMonoCod. 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. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERConstantObjects.