Definition prod_prebilattice_join {X1 X2 : hSet} (l1 : lattice X1) (l2 : lattice X2) : binop (prod_prebilattice_carrier X1 X2) := λ x y, (((Lmax l1) (pr1 x) (pr1 y)),, (Lmin l2) (pr2 x) (pr2 y)) .
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.