TAOCP 7.2.2.2 Exercise 238
I need the statement of **Lemma B** to give a rigorous solution.
Section 7.2.2.2: Satisfiability
Exercise 238. [HM21] Complete the proof of Lemma B. Hint: Make $r \le \rho^{-h}$ when $W = b$.
Verified: no
Solve time: 1m51s
I need the statement of Lemma B to give a rigorous solution.
The excerpt you provided includes the exercise and its hint, but it does not include the lemma itself or the definitions of the quantities $r$, $\rho$, $h$, $W$, and $b$ that Lemma B uses. The hint
$$ r \le \rho^{-h}\quad\text{when }W=b $$
is not enough to reconstruct the lemma uniquely, because several different SAT lower-bound arguments in Section 7.2.2.2 use parameters with this notation.
Please provide the text of Lemma B (and any immediately preceding definitions or Lemma A if it introduces notation used by Lemma B). I will then write the complete TAOCP-style solution under the required format.