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\begin{proposition}\label{first_proposition}
$a = a$.
\end{proposition}
\begin{proposition}\label{second_proposition}
$b = b$.
\end{proposition}
\begin{proposition}\label{third_proposition}
$c = c$.
\end{proposition}
\begin{proof}
Follows by \ref{first_proposition}. % Should filter out second_proposition
\end{proof}
\begin{proposition}\label{fourth_proposition}
$e = e$.
\end{proposition}
\begin{proof}
For all $d$ we have $d = d$ by \ref{first_proposition}.
\end{proof}
\begin{proposition}\label{fifth_proposition}
$f = f$.
\end{proposition}
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