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Lemma 34.3

If L1, L2$\subseteq$ {0,1}*, and \(L_1 \;\leq_P\; L_2\), then L2$\in$ P implies L1$\in$ P.

For any instance of L1
$\;\;\;\;\;$map to L2 (poly time)
$\;\;\;\;\;$solve L2 (poly time)

Thus if we can solve L2 in poly time we can solve L1 in poly time.


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