booleanLattice -- generates the boolean lattice on $n$ elements

i1 : n = 3;

i2 : B = booleanLattice n

o2 = Poset{cache => CacheTable{...13...}                                                                                                                                }
           GroundSet => {000, 001, 010, 011, 100, 101, 110, 111}
           RelationMatrix => | 1 1 1 1 1 1 1 1 |
                             | 0 1 0 1 0 1 0 1 |
                             | 0 0 1 1 0 0 1 1 |
                             | 0 0 0 1 0 0 0 1 |
                             | 0 0 0 0 1 1 1 1 |
                             | 0 0 0 0 0 1 0 1 |
                             | 0 0 0 0 0 0 1 1 |
                             | 0 0 0 0 0 0 0 1 |
           Relations => {{000, 001}, {010, 011}, {000, 010}, {001, 011}, {100, 101}, {110, 111}, {100, 110}, {101, 111}, {000, 100}, {001, 101}, {010, 110}, {011, 111}}

o2 : Poset

i3 : B == poset(subsets n, isSubset)

o3 = true

i4 : B == product(n, i -> chain 2)

o4 = true

i5 : B == divisorPoset (2*3*5)

o5 = true