Definition sieve_type_intersection (I : UU) (SI : I → sieve) : sieve. Proof. use make_sieve. - exact (λ x, ∀ (i : I), SI i x). - abstract (intros x y p H i ; exact (sieve_downwards_closed (SI i) p (H i))). 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.