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\documentclass{minimal}
\begin{document}
\begin{defn}[Definition 1]
\label{defn:definition_1}
A simple environment with simple contents.
\end{defn}
\begin{figure}[ht] % A standalone figure with label and caption
\centering
%\input{proof}
\caption{Simple figure}
\label{fig:simple_figure}
\end{figure}
\begin{thm}[Example Title of Theorem]
\label{thm:example_title_of_theorem}
Suppose A and B.
\begin{itemize}
\item If C, then D
\item \(A \wedge B \implies D \iff A \wedge B \implies C\)
\end{itemize}
We demonstrate this by the figure.
\begin{figure}[ht] % Comment
\centering
%\input{proof}
\caption{A visual proof of Example Theorem}
\label{fig:visual_theorem}
\end{figure}
\end{thm}
\begin{defn}[Definition 2]
\label{defn:definition_2}
A sample definition.
\caption{A caption for an environment typically without caption}
\end{defn}
\end{document}
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