PosetMap Thing -- applies a poset map to a poset element

i1 : f = map(product(chain 2, chain 2), chain 2, {{1,1},{1,2}})

o1 = PosetMap{1 => {1, 1}                           }
              2 => {1, 2}
              source => Relation Matrix: | 1 1 |
                                         | 0 1 |
              target => Relation Matrix: | 1 1 1 1 |
                                         | 0 1 0 1 |
                                         | 0 0 1 1 |
                                         | 0 0 0 1 |

o1 : PosetMap

i2 : f 1

o2 = {1, 1}

o2 : List

i3 : f 2

o3 = {1, 2}

o3 : List