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$\forall$${\it poss}$:(ES\{i\}$\rightarrow\mathbb{P}$\{i'\}), $R$:(possible{-}event\{i:l\}(${\it poss}$)$\rightarrow$possible{-}event\{i:l\}(${\it poss}$)$\rightarrow\mathbb{P}$\{i'\}).
\\[0ex]Trans(possible{-}event\=\{i:l\}\+
\\[0ex](${\it poss}$);$a$,$b$.$R$($a$,$b$))
\-\\[0ex]$\Rightarrow$ \=($\forall$$P$:(possible{-}event\{i:l\}(${\it poss}$)$\rightarrow\mathbb{P}$\{i'\}), $e$:possible{-}event\{i:l\}(${\it poss}$).\+
\\[0ex]es{-}knows\=\{i:l\}\+
\\[0ex](${\it poss}$; $R$; $P$; $e$)
\-\\[0ex]$\Rightarrow$ es{-}knows\=\{i:l\}\+
\\[0ex](${\it poss}$; $R$; ($\lambda$$e$.es{-}knows\{i:l\}(${\it poss}$; $R$; $P$; $e$)); $e$))
\-\-
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