Definition intersection_binop : binop (subtype_set X). Proof. apply infinitary_op_to_binop; exact (@subtype_intersection X). Defined.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Sets. 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.Complement. Require Import UniMath.OrderTheory.Lattice.Boolean.