Definition term_partial_setoid_morphism {H : first_order_hyperdoctrine} {X Y : ty H} (t : tm X Y) : partial_setoid_morphism (eq_partial_setoid X) (eq_partial_setoid Y). Proof. use make_partial_setoid_morphism. - exact (term_partial_setoid_morphism_form t). - exact (term_partial_setoid_morphism_laws t). Defined.
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. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.PERCategory.