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Time complexity of decision problems or relations among time-bounded complexity classes. (Use the [analysis-of-algorithms] tag for the time taken by particular algorithms.)

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Calculation on Sparsification and critical clauses in SAT

First part: $2^{h(\delta)n}+2^{\epsilon n}+2^{\epsilon n}2^{(s_k+ \epsilon)(1-(\delta/ek))n} \leq 2^{(s_\infty(1-d/k)+2\epsilon)n}$ $\implies2^{(s_\infty/2)n} + 2^{(s_k+ \epsilon)(1-(\delta/ek))n +\ep …
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Calculation on Sparsification and critical clauses in SAT

I followed from this question. I need to prove, the final result $s_k \leq (1 − \Omega(k^{−1}))s_{\infty}.$ But before prove the final result first I need to prove the $s_k \leq (1 − d/k))s_{\infty}$. …
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