Definition closed_sieve_min_operation : min_operation closed_sieves_poset. Proof. intros S₁ S₂. refine (closed_sieve_intersection S₁ S₂ ,, _ ,, _ ,, _). - abstract (intros x p ; exact (pr1 p)). - abstract (intros x p ; exact (pr2 p)). - abstract (intros S p q x r ; cbn in * ; exact (p x r ,, q x r)). 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.