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\documentclass[10pt]{book}
% generated by Madoko, version 1.0.3
%mdk-data-line={1}
\newcommand\mdmathmode{plain}
\newcommand\mdmathrender{png}
\usepackage[heading-base={2},section-num={false},bib-label={true}]{madoko2}
\usepackage[margin=1in]{geometry}


\begin{document}


\begin{mdSnippets}
%mdk-data-line={8}
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\begin{mdInlineSnippet}[44c29edb103a2872f519ad0c9a0fdaaa]%mdk
$P$\end{mdInlineSnippet}%mdk
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\begin{mdInlineSnippet}[4be60c01260fad068dd84cb934d15c36]%mdk
$A_1$\end{mdInlineSnippet}%mdk
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\begin{mdInlineSnippet}[e7fb081e7d6a49314607f263a85eef3c]%mdk
$A_2$\end{mdInlineSnippet}%mdk
%mdk-data-line={258}
\begin{mdInlineSnippet}[44c29edb103a2872f519ad0c9a0fdaaa]%mdk
$P$\end{mdInlineSnippet}%mdk
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\begin{mdInlineSnippet}[4af9cb7140eff406f917e3b6d2ad8bb3]%mdk
$P'$\end{mdInlineSnippet}%mdk
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\begin{mdInlineSnippet}[44c29edb103a2872f519ad0c9a0fdaaa]%mdk
$P$\end{mdInlineSnippet}%mdk
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$A_3$\end{mdInlineSnippet}%mdk
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$P'$\end{mdInlineSnippet}%mdk
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$A_3$\end{mdInlineSnippet}%mdk
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\begin{mdInlineSnippet}[cfa262363bd8ba06eb741b5b69ad4819]%mdk
$p = \{ o_1, o_2, \dots, o_i \}$\end{mdInlineSnippet}%mdk
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\begin{mdInlineSnippet}[0c84573d3953d7242cd6612b4fd50f39]%mdk
$p' = p \cup \{o_{i + 1}\}$\end{mdInlineSnippet}%mdk
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\begin{mdInlineSnippet}[405af36463d007c116a0712d93d380f4]%mdk
$o_{i + 1}$\end{mdInlineSnippet}%mdk
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$n+1$\end{mdInlineSnippet}%mdk
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$n$\end{mdInlineSnippet}%mdk
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$n$\end{mdInlineSnippet}%mdk
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\end{document}