Definition is_complete_set_of_closed_sieve : is_complete_lattice bounded_lattice_set_of_closed_sieves. Proof. use complete_lattice_from_glb. intros I f. refine (closed_sieve_type_intersection I f ,, _). apply is_glb_closed_sieve_type_intersection. 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.