Definition bounded_prod_prebilattices_to_prod_prebilattices {X1 X2 : hSet} {bl1 : bounded_lattice X1} {bl2 : bounded_lattice X2} (b : bounded_prod_prebilattice X1 X2 bl1 bl2) : prod_prebilattice X1 X2 bl1 bl2 := pr221 (make_bounded_lattice (pr1 b)),, pr221 (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.