Definition subset_bounded_lattice : bounded_lattice (subtype_set X). Proof. use make_bounded_lattice. - exact subset_lattice. - exact (emptysubtype X). - exact (totalsubtype X). - exact subset_lattice_is_bounded. 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.