deletions | additions       diff --git a/The_following_theorem_is_the__.tex b/The_following_theorem_is_the__.tex  index 26b7eae..b49a4aa 100644  --- a/The_following_theorem_is_the__.tex  +++ b/The_following_theorem_is_the__.tex 
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$$-\E_{\mu^k \times U^{\R_S(k,j)}}[(t(k,j)S^{kj} + 2 (P^{kj} - f)) S^{kj}] t(k,j) \leq \varepsilon_1(k,j)$$  $$-\E_{\mu^k \times U^{\R_S(k,j)}}[(S^{kj})^2] t(k,j)^2 + 2 \E_{\mu^k \times U^{\R_S(k,j)}}[(P^{kj} - f)) f)  S^{kj}] t(k,j) \leq \varepsilon_1(k,j)$$ Moving $E[Q]t^2$ to the right hand side and dividing both sides by $2|t|=2^{1-a}$ we get