"\input only part of a file" and keep numbering

Question

I would like to create an excerpt from a script that I have TeX'ed as a compendium of the most important statements (theorems & definitions).

The question \input only part of a file has an answer by Will Robertson that supposes the usage of catchfilebetweentags. I did that and it is working just fine, but ...

How do you keep the original numbering?

The above mentioned method using the catchfilebetweentags package allows me to make corrections of errors in the main file and the summary at the same time. For the sake of comparability, I would prefer to have the same numbering also. Though the numbering is reset.

---

Note: I could imagine a solution by putting a \setcounter{counter}{value} in front of each statement but inside the tags. However, this is a very inconvenient way as it is inelegant and involves much more work.

---

Edit (MWE):

Taken from this site (by Giacomo Drago)

File that contains tags which should be included

% Equations dictionary
\documentclass[11pt]{article}
\usepackage{amssymb,amsmath}

% Begin document
\begin{document}

%<*eq001>
\begin{equation}
F\left (x_1,\dots,x_n,\frac{\partial u}{\partial x_1},\dots,\frac{\partial u}{\partial x_n},\frac{\partial^2 u}{\partial x_1\partial x_1},\dots,\frac{\partial^2 u}{\partial x_n\partial x_n},\dots
\right)
\end{equation}
%</eq001>

\begin{equation}
    a = b + c
\end{equation}

%<*eq002>
\begin{equation}
u_x=\frac{\partial u}{\partial x}, \quad\quad\quad
u_{xy}=\frac{\partial^2 u}{\partial y \partial x}=\frac{\partial u}{\partial y}\left( \frac{\partial u}{\partial x} \right).
\end{equation}
%</eq002>
% A bunch of other equations...
\end{document}

File that includes

% http://yatb.giacomodrago.com/en/post/3/latex-loading-equations-from-an-external-file.html
\documentclass[a4, 11pt, twoside]{report}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage[T1]{fontenc}

\usepackage{catchfilebetweentags}
\usepackage{blindtext}

\newcommand{\loadeq}[1]{%
   \ExecuteMetaData[equ.tex]{eq#1}%
}


\begin{document}
    \blindtext
    \loadeq{001}
    \blindtext
    \loadeq{002}
    \blindtext
\end{document}

Answer 1

Here is a solution. The idea is to capture almost every thing but display only needed parts

first file (with tags)

\documentclass{amsart}
\usepackage{lipsum}

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\begin{document}
%<*tag>
\lipsum[1]
Here we go
%</tag>
%<*atag> 
\begin{definition}
some bla bla
\end{definition}
\begin{theorem}
more bla bla
\end{theorem}
\begin{definition}
some bla bla
\end{definition}
%</atag>
%<*btag>
\begin{definition}
some bla bla
\end{definition}
\begin{theorem}
more bla bla
\end{theorem}
%</btag>
%<*ctag>
\lipsum[1-2]
%</ctag>
%<*dtag>
\begin{lemma}
more bla bla
\end{lemma}
\begin{theorem}
more bla bla
\end{theorem}
%</dtag>
%<*etag>
\lipsum[1-2]
\begin{example}
some bla bla
\end{example}
%</etag>
\begin{theorem}
more bla bla
\end{theorem}
\end{document}

final file

\documentclass{amsart}
\usepackage{lipsum}

\usepackage{catchfilebetweentags}
\newtoks\temptoken

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\theoremstyle{definition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\begin{document}
\lipsum[1]
\CatchFileBetweenTags\temptoken{file}{tag}% capture part1
\setbox0=\vbox{\the\temptoken}%  skip part1
\CatchFileBetweenTags\temptoken{file}{atag}% capture part2
\the\temptoken % display part2

\CatchFileBetweenTags\temptoken{file}{btag}% capture part3
\setbox0=\vbox{\the\temptoken}%  skip part3
\CatchFileBetweenTags\temptoken{file}{ctag}% capture part4
\setbox0=\vbox{\the\temptoken}%  skip part4

\CatchFileBetweenTags\temptoken{file}{dtag}% capture part5
\the\temptoken%  display part5
\end{document}