Lemma boolset_lattice : lattice boolset. Proof. use make_lattice. - exact andb. - exact orb. - apply make_dirprod; [apply make_dirprod|apply make_dirprod; [apply make_dirprod|apply make_dirprod]]. + intros ? ? ?; apply andb_is_associative. + intros ? ?; apply andb_is_commutative. + intros ? ? ?; apply orb_is_associative. + intros ? ?; apply orb_is_commutative. + intros b1 b2; abstract (induction b1, b2; reflexivity). + intros b1 b2; abstract (induction b1, b2; reflexivity). Defined.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.MoreFoundations.Bool. 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.