$.  **Lemma 0**: $P_{OptSample}(T, L) \geq {P_{0-Sample}(T, L)}$.     We continue to use the definition of $p$, $q$, $k$, $r$, $s$, $l$, and $t$ in the proof of Lemma 0. For convenience, in the following proof, we abbreviate $P_{OptSample}(T, L)$ to $P_{0}(T, L)$ and $P_{