\relax +
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\ifx\hyper@anchor\@undefined+
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\global \let \oldcontentsline\contentsline+
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\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}+
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\global \let \oldnewlabel\newlabel+
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\gdef \newlabel#1#2{\newlabelxx{#1}#2}+
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\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}+
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\AtEndDocument{\let \contentsline\oldcontentsline+
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\let \newlabel\oldnewlabel}+
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\else+
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\global \let \hyper@last\relax +
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\fi+
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+
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\@writefile{toc}{\contentsline {section}{\numberline {1}Preliminary definitions}{1}{section.1}}+
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\@writefile{toc}{\contentsline {section}{\numberline {2}Direction \emph  {\it  finite\ partition\ {\emph  {$\Rightarrow $}}\ regular\ language}}{5}{section.2}}+
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\newlabel{example_eqns}{{1}{5}{Direction \isa {finite\ partition\ {\isasymRightarrow }\ regular\ language}\relax }{equation.1}{}}+
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\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Proof for this direction}{9}{subsection.2.1}}+
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\@writefile{toc}{\contentsline {section}{\numberline {3}Direction: \emph  {\it  regular\ language\ {\emph  {$\Rightarrow $}}finite\ partition}}{21}{section.3}}+
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.2}A small theory for list difference}{22}{subsection.3.2}}+
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.3}Lemmas for basic cases}{23}{subsection.3.3}}+
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.4}The case for \emph  {\it  SEQ}}{24}{subsection.3.4}}+
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.5}The case for \emph  {\it  ALT}}{26}{subsection.3.5}}+
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.6}The case for \emph  {\it  STAR}}{27}{subsection.3.6}}+
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\@writefile{toc}{\contentsline {subsection}{\numberline {3.7}The main lemma}{29}{subsection.3.7}}+
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