For a pair formula_126 and formula_127, we wish to combine the two structures into a single structure. In order for the result to be well labelled, this requires some relabelling of the atoms in formula_128 and formula_129. We will restrict our attention to relabellings that are consistent with the order of the original labels. Note that there are still multiple ways to do the relabelling; thus, each pair of members determines not a single member in the product, but a set of new members. The details of this construction are found on the page of the Labelled enumeration theorem.