Definition proof_to_partial_setoid_morphism {Γ₁ Γ₂ : ty H} {Δ : form Γ₁} {φ : form Γ₂} {s : tm Γ₁ Γ₂} (q : Δ ⊢ φ [ s ]) : partial_setoid_morphism (formula_to_partial_setoid Δ) (formula_to_partial_setoid φ). Proof. use make_partial_setoid_morphism. - exact (proof_to_partial_setoid_morphism_form q). - exact (proof_to_partial_setoid_morphism_laws q). Defined.
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.