Definition bounded_islatticeop_prod_t {X1 X2 : hSet} (bl1 : bounded_lattice X1) (bl2 : bounded_lattice X2) : bounded_latticeop (make_lattice (islatticeop_prod_t bl1 bl2)) (prod_prebilattice_false bl1 bl2) (prod_prebilattice_true bl1 bl2) . Proof. use make_dirprod; intro; use dirprod_paths; [use islunit_Lmax_Lbot | use islunit_Lmin_Ltop | use islunit_Lmin_Ltop | use islunit_Lmax_Lbot]. Defined.
Require Import UniMath.OrderTheory.Prebilattice.Prebilattice. Require Import UniMath.OrderTheory.Prebilattice.Interlaced. Require Import UniMath.OrderTheory.Prebilattice.PrebilatticeDisplayedCat. Require Import UniMath.MoreFoundations.Equivalences. Require Import UniMath.Foundations.Sets. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.OrderTheory.Lattice.Bounded. Require Import UniMath.CategoryTheory.Core.Prelude.