Definition bounded_lattice_set_of_closed_sieves : bounded_lattice set_of_closed_sieves. Proof. use (poset_to_bounded_lattice closed_sieves_poset). - exact closed_sieve_min_operation. - exact closed_sieve_max_operation. - exact closed_sieve_min_el. - exact closed_sieve_max_el. 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.