Proposition from_eq_in_bot_partial_setoid {Γ : ty H} {Δ : form Γ} {t₁ t₂ : tm Γ bot_partial_setoid} (p : Δ ⊢ t₁ ~ t₂) : Δ ⊢ ⊥. Proof. refine (hyperdoctrine_cut p _). unfold partial_setoid_formula ; cbn. simplify. apply hyperdoctrine_hyp. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Initial. Require Import UniMath.CategoryTheory.Limits.StrictInitial. 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.