. Since the cardinality of \(\mathcal {S}_{f, T}\) is bounded by \(\sum _{i \le f}\left( {\begin{array}{c}|E_T|\\ i\end{array}}\right) = O(n^{f})\), by the union bound argument, we conclude that \(|\partial _{E_{i+1}}(S)| > 0\)...