implied by N ( n, 2, z ), is

$$\frac{1}{6}\alpha+O\big{(}\frac{1}{n}\big{)}.\tag{4.21}$$  Without loss of generality, assume that $T_{2}=\big{\{}x\lor y\lor u,x\lor y\lor\bar{u}\big{\}}$ and $T_{1}=\big{\{}x\lor y\lor u,\bar{x}\lor y\lor\bar{u}\big{\}}$.  
Since w is implied by N ( n , 2 , z ), there is a local fitness function g = g ( | x | , | y | , | u | ) that implies T 2 . The conditional probability that T 1 is implied, is less than or equal to P 1 + P 2 where P 1 is the conditional probability that g also implies the clause ¯ V y V ¯ given that g implies T 2 , and P 2 is the conditional probability that the clause x V y V ū is implied by other local fitness functions. By the definition of N ( n, 2, z ), we have that P 1 = f α. Since a local fitness function implies x V y V v only if it has the same variables with g = g(|x|,|y|,|u|), we have that P 2 = O( ). The claim is proved. It follows that, for sufficiently large n,

 -  $P r\left\{\bar{w}\ |\ w\right\}\leq c\left(\frac{3+\sqrt{5}}{2}p_0\right)^{t-q}\cdot1^{q_1}\cdot\left(\frac{1}{6}\alpha\right)^{q_2}$  Lemma 4.3 and $\alpha$ is a fixed constant. 
$$(4\,,22)$$
where po is defined in Lemma 4.3 and c is a fixed constant.

Let AQ,q,q 2 (w) be the set of t-3-modules that share Q clauses with w such that these Q
clauses are distributed over q different 3-modules. As before, q 1 is the number of 3-modules whose two clauses are both shared and q 2 = q - q 1 the number of 3-modules that only has one clause shared. We claim that

$$\left|A_{Q,q,q_{2}}(w)\right|=\left|A_{2q,q,0}(w)\right|6^{q_{2}}.$$
$$(4.23)$$

where A2q,q,0(w) is the set of t-3-modules that share all the 2q clauses in the q 3-modules with w. Let M = { M 1 , . . , M i } be a t-3-module in which all the clauses M i , 1 ≤ i ≤ q are shared with w. Let M = { M 1 , . . , M i } be a t-3-module in which all the clauses in M i , 1 ≤ i ≤ q 1 are shared and each of the 3-modules M i , q 1 + 1 ≤ q 1 + q 2 has only one clause shared. Since for each of the q2 3-modules, we have 6 ways to choose the non-shared clauses, there are 692 such t-3-modules M in AQ,g,g,(w) that correspond to one t-3-module M in A 29.9.0. The claims follow. From formula (55) and (56) in (Franco & Gelder, 1998)
and (4.23), it follows that

$$A_{Q,q,q_{2}}(w)|<\begin{cases}\frac{O(l)}{n^{2}}2^{l-q}n^{2\,(l-q)}6^{q_{2}}&,q\leq p+1,\\ \frac{O(1)}{n}2^{l-q}n^{2\,(l-q)}6^{q_{2}}&,q>p+1.\end{cases}\tag{4.24}$$
Let r = α) + H α), and write po 'hen, we have (4.25) [A t }(2(3 + V5)r ))-q, q < p + 3