Proposition per_subobject_false_laws (Γ : partial_setoid H) : per_subobject_laws (⊥ : form Γ). Proof. split. - use forall_intro. use impl_intro. use weaken_right. use false_elim. simplify. apply hyperdoctrine_hyp. - do 2 use forall_intro. do 2 use impl_intro. use weaken_right. use false_elim. simplify. apply hyperdoctrine_hyp. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseInitial. 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.PERTerminal. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.Logic.SubobjectDispCat.