Proposition from_eq_in_prod_partial_setoid {Γ : ty H} {t₁ t₂ : tm Γ prod_partial_setoid} {Δ : form Γ} (p : Δ ⊢ t₁ ~ t₂) : Δ ⊢ π₁ t₁ ~ π₁ t₂ ∧ π₂ t₁ ~ π₂ t₂. Proof. use conj_intro. - use eq_in_prod_partial_setoid_l. exact p. - use eq_in_prod_partial_setoid_r. exact p. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Hyperdoctrines.Hyperdoctrine. Require Import UniMath.CategoryTheory.Hyperdoctrines.FirstOrderHyperdoctrine.