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Definition: For prime $p$: $$n \uparrow p \iff (\exists a > 0, n = ap) \lor (\exists b > 1, b \perp p \land \exists m \uparrow p, n = b^m)$$ Lemma: For prime $p$, if $L' \vdash L$ and $\exists x \in L, x \uparrow p$, then $\exists x' \in L', x' \uparrow p$.
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Sat, 16 Dec 2017 23:38 GMT