 Duplication  \(x\) is a duplicate of \(y\) if and only if there is a bijective function \(f\) from the parts of \(x\) to the parts of \(y\), such that for any any perfectly natural \(n\)-ary property \(R\) and any sequence \(x_1,\ldots,x_n\) of parts of \(x\), \(x_1,\ldots,x_n\) instantiate \(R\) just in case \(f(x_1),\ldots,f(x_n)\) instantiate  \(R\).[16] 