Proposition to_per_subobject_forall_form {Γ : ty H} {Δ : form Γ} {b : tm Γ B} (p : Δ ⊢ b ~ b) (q : Δ ⊢ ∀h (φ [ ⟨ π₂ (tm_var _) , b [π₁ (tm_var _)]tm ⟩] ⇒ ψ [π₂ (tm_var _)])) : Δ ⊢ per_subobject_forall_form [ b ]. Proof. unfold per_subobject_forall_form. simplify_form. rewrite partial_setoid_subst. simplify. use conj_intro. - exact p. - simplify. exact q. 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.