Definition closed_sieve_intersection (S₁ S₂ : closed_sieve) : closed_sieve. Proof. use make_closed_sieve. - exact (sieve_intersection S₁ S₂). - abstract (intros x C p H ; refine (is_closed_closed_sieve S₁ x C p _ ,, is_closed_closed_sieve S₂ x C p _) ; apply H). Defined.
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.