(\(I^*\)) For all \(x\) and \(y\), and all \(\langle R_{i}\rangle\) and \(\langle R_{i}^*\rangle\) in the domain of \(f\), if for all \(i: xR_{i}y\) if and only if \(xR^*_{i}y\), then \(x f\langle R_{i}\rangle y\) if and only if \(x f\langle R_{i}^*\rangle y\).