Definition bounded_prod_prebilattices_to_bounded_prebilattices {X1 X2 : hSet} {l1 : bounded_lattice X1} {l2 : bounded_lattice X2} (b : bounded_prod_prebilattice X1 X2 l1 l2) : bounded_prebilattice (prod_prebilattice_carrier X1 X2) := make_bounded_prebilattice (make_bounded_lattice (pr1 b)) (make_bounded_lattice (pr2 b)) .
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.