Definition is_boolean : hProp. Proof. use make_hProp. - refine (∑ is_distr : is_distributive L, _). use make_hProp. + exact (complemented_structure L). + apply impred; intro. apply distributive_lattice_complements_are_unique; auto. - abstract (apply isaprop_total2). Defined.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.Algebra.Monoids. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.OrderTheory.Lattice.Bounded. Require Import UniMath.OrderTheory.Lattice.Complement. Require Import UniMath.OrderTheory.Lattice.Distributive. Require Import UniMath.OrderTheory.Lattice.Heyting.