Funes el memorioso

\documentclass{report}

\usepackage{amsthm,amsmath,amssymb}
\newtheorem{theorem}{Theorem}[chapter]
\newtheorem{claim}[theorem]{Claim}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}

\begin{document}
\tableofcontents
\chapter{first}
\begin{claim}
Mountain dew rocks.
\end{claim}
\section{1}

\section*{Proof}

\begin{lemma}[Dr. Strangelove's last line.]
Mein F\"uhrer, I can walk!
\end{lemma}

\begin{appendix}
  \chapter{First Appendix}
  \begin{theorem}
    Halo!
  \end{theorem}
  \begin{lemma}
    world!
  \end{lemma}
\end{appendix}
\end{document}