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Fix typos <noupdate>
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\item[Exhaustive decomposition] \marginnote{Exhaustive decomposition}
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Given a category $c$ and a set of categories $S$, $S$ is an exhaustive decomposition of $c$ iff
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any element in $c$ belongs to at least a category in $S$:
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\[ \texttt{exhaustiveDecomposition($S$, $c$)} \iff (\forall o \in c \iff \exists c_2 \in S: o \in c_2) \]
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\[ \texttt{exhaustiveDecomposition($S$, $c$)} \iff \forall o: (o \in c \iff \exists c_2 \in S: o \in c_2) \]
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\item[Partition] \marginnote{Partition}
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Given a category $c$ and a set of categories $S$, $S$ is a partition of $c$ when:
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