Proposition per_subobject_forall_form_eq {Γ : ty H} {Δ : form Γ} (b : tm Γ B) (p : Δ ⊢ per_subobject_forall_form [ b ]) : Δ ⊢ b ~ b. Proof. refine (hyperdoctrine_cut p _). unfold per_subobject_forall_form. simplify_form. use weaken_left. rewrite partial_setoid_subst. simplify. apply hyperdoctrine_hyp. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentSums. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DualBeckChevalley. Require Import UniMath.CategoryTheory.Limits.Pullbacks. 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.Logic.SubobjectDispCat. Require Import UniMath.CategoryTheory.Hyperdoctrines.PartialEqRels.Logic.Existential.