Proposition eq_sieve {S₁ S₂ : sieve} (H₁ : ∏ (x : X), S₁ x → S₂ x) (H₂ : ∏ (x : X), S₂ x → S₁ x) : S₁ = S₂. Proof. use subtypePath ; [ intro ; apply propproperty | ]. use funextsec ; intro x. use hPropUnivalence. - apply H₁. - apply H₂. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.OrderTheory.Lattice.Bounded. Require Import UniMath.OrderTheory.Lattice.Distributive. Require Import UniMath.OrderTheory.Lattice.Heyting. Require Import UniMath.OrderTheory.Lattice.CompleteHeyting. Require Import UniMath.OrderTheory.Lattice.Examples.FromPartialOrder.