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Lemma (0.1) Let $\mathfrak{U}$ the phenomenal world and a subjective world filtration $\mathcal{F}_s \subset \mathscr{P}(\mathfrak{U})$. Then for every $x \in U$, there exists a strategy $\mathfrak{m}$, i.e. $\mathfrak{m} \in \mathcal{F}_s$ and $\mathfrak{m}$ does not contain a proper subset in the subjective filtration, such that $x \in \mathfrak{m}$ and $\mathfrak{m} = \sup_{m \in \textbf{strategy}} P(m)$ where $P$ is a functional.

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