Definition interlaced_prebilattice_to_prod {X : hSet} (b : interlaced_prebilattice X) : ∑ (X1 X2 : hSet) (l1 : lattice X1) (l2 : lattice X2) , prod_prebilattice X1 X2 l1 l2 := setquotinset (rel_same_SW2NE b),, setquotinset (rel_same_SE2NW b),,lattice_SW2NE b,,lattice_SE2NW b,,make_prod_prebilattice (lattice_SW2NE b) (lattice_SE2NW 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.