demo_external_appendix.tex

\documentclass{article}

\usepackage{amsmath}
\usepackage{xparse} % Not needed with recent LaTeX
\usepackage{amsthm}

% Create new theorems, or use ntheorem/thmtools/...
\newtheorem{thm}{Theorem}[section]
% Default uses autoref, but you can also use cleveref, see the documentation.
% Say to autoref that "thm" are Theorems.
\newcommand{\thmautorefname}{Theorem}

%% Load the library. createShortEnv automatically creates the shortcuts
%% thmE, theoremE, lemmaE, propositionE, corollaryE, proofE. See \newEndThm for more details.
%% The "external appendix" option is used to ensure theorem are restatable with the auxiliary file is
%% opened inside another file (do load the xr package for crossreferences)
\usepackage[createShortEnv,conf={external appendix}]{proof-at-the-end}
\usepackage{hyperref}
\usepackage{cleveref}
\begin{document}

\section{Theorems}\label{sec:theorems}

%% If you don't have any title, leave an empty bracket like \begin{thmE}[][end]
\begin{thmE}[My title][end, restate]
  I am a theorem:
  \begin{align}
    1+1 &= 2 \label{eq:nontrivialfact}
  \end{align}
\end{thmE}
\begin{proofE}
  And I am a trivial proof: $1+1=2$.
\end{proofE}

\begin{thmE}[][all end]
  I'm only in Appendix.
\end{thmE}
\begin{proofE}
  Check the first file, you will see.
\end{proofE}

\section{Proofs}

In this document, we made the choice to display the appendix in another file.  Compile \verb|demo_external_appendix_part2.tex| now ;)

\end{document}