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\title{}
\author{}

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\begin{document}
\maketitle


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For each Lemma connected to a LU we require that if it has only one LexemeEntry then the part of speech of the associated Lexeme is the same as the part of speech of the Lemma.

\[
\begin{array}{@{\hspace{5pt}}l}
\forall 
\hspace*{5pt}
\mbox{\em lemma}
^{
\mathsf{Keep}
}
\hspace*{5pt}
{\scriptscriptstyle \in}
\hspace*{5pt}
\mathtt{getAllLemmas}
\left(
\mathtt{fnDB}
\right)
\hspace*{5pt}
\bullet 
\\
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\neg 
\hspace*{2pt}
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{null}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{getLemmaLUs}
\left(
\mathtt{fnDB}
,
\mbox{\em lemma}
\right)
\\
\end{array}
\right)
\\
\\
\end{array}
\\
\implies 
\\
\left(
\begin{array}{@{\hspace{5pt}}l}
\forall 
\hspace*{5pt}
\mbox{\em lexentries}
^{
\mathsf{Keep}
}
\hspace*{5pt}
{\scriptscriptstyle \in}
\hspace*{5pt}
\left[
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{getLemmaLexEntries}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{fnDB}
,
\\
\mbox{\em lemma}
\\
\end{array}
\right)
\\
\end{array}
\right]
\hspace*{5pt}
\bullet 
\\
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{length}
\left(
\mbox{\em lexentries}
\right)
= 
\hspace*{2pt}
\mathsf{1}
\\
\implies 
\\
\left(
\begin{array}{@{\hspace{5pt}}l}
\forall 
\hspace*{5pt}
\mbox{\em lexentry}
^{
\mathsf{Chg}
}
\hspace*{5pt}
{\scriptscriptstyle \in}
\hspace*{5pt}
\mbox{\em lexentries}
\hspace*{5pt}
\bullet 
\\
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{lemmaPartOfSpchRef}
\left(
\mbox{\em lexentry}
\right)
= 
\\
\mathtt{lexemePartOfSpchRef}
\left(
\mbox{\em lexentry}
\right)
\\
\end{array}
\\
\left\{
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\left\{
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{F}
: 
\hspace*{3pt}
\hspace*{3pt}
\mbox{\em lexentry}
. 
\mathtt{lemmaPartOfSpchRef}
\hspace*{3pt}
\rightsquigarrow 
\hspace*{3pt}
\mathtt{lexemePartOfSpchRef}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mbox{\em lexentry}
\\
\end{array}
\right)
\hspace*{3pt}
\\
\end{array}
\right\}
,
\\
\left\{
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mathtt{F}
: 
\hspace*{3pt}
\hspace*{3pt}
\mbox{\em lexentry}
. 
\mathtt{lexemePartOfSpchRef}
\hspace*{3pt}
\rightsquigarrow 
\hspace*{3pt}
\mathtt{lemmaPartOfSpchRef}
\left(
\begin{array}{@{\hspace{1pt}}l@{\hspace{1pt}}}
\mbox{\em lexentry}
\\
\end{array}
\right)
\hspace*{3pt}
\\
\end{array}
\right\}
\\
\end{array}
\right\}
\\
\end{array}
\\
\end{array}
\right)
\\
\end{array}
\\
\end{array}
\right)
\\
\end{array}
\\
\end{array}
\]
\end{document}
