Definition complete_heyting_algebra_sieves : complete_heyting_algebra. Proof. use make_complete_heyting_algebra. - exact set_of_sieves. - exact bounded_lattice_set_of_sieves. - exact is_complete_set_of_sieve. - exact exponential_set_of_sieves. 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.