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\end{lemma}
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Finally we can state an important lemma about $\mubc$: |
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\begin{lemma}[Polychecking Lemma, \cite{BellantoniThesis}]
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Let $\Phi$ be a class of polymax bounded functions. If $f(\vec u; \vec x)$ is in $\mubc(\Phi)$, then $f$ is a polymax bounded function and a polynomial checking function on $\vec u$.
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Let $\Phi$ be a class of polymax bounded polynomial checking functions. If $f(\vec u; \vec x)$ is in $\mubc(\Phi)$, then $f$ is a polymax bounded function polynomial checking function on $\vec u$.
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\end{lemma}
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