 So we have established that \(\mathbf{K}^{*}_N (E)\) is a fixed point of the function \(f_E\) defined by \(f_E (X) = \mathbf{K}^{1}_N (E \cap X). f_E\) has other fixed points. For instance, any contradiction \(B \cap B^c = \varnothing\) is a fixed point of  \(f_E\).[15]  Note also that if \(A \subseteq B\), then \(E \cap A \subseteq E \cap B\) and so