# How to duplicate the section based autonumbered theorems in section 2, 3, 4 in section 1?

I currently have section based auto-numbering setup for theorems in section 2,3,4 etc via the following environment variables:

\numberwithin{equation}{section}
\newtheorem{definition}{Definition}[section]
\newtheorem{theorem}[definition]{Theorem}

Now I want to duplicate some of these theorems (with labels) in the section 1 (Introduction) as part of the major results.

How do I do that?

Here is a minimum working example. What I want is to change "Theorem 1.1" to "Theorem 2.1", and change "Theorem 1.2" to "Theorem 3.1".

Best regards -mike

%--------------------------
\documentclass[a4paper,12pt,reqno,twoside]{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{color}
\usepackage{ifpdf}
\usepackage{array}

\usepackage{url}
\usepackage{graphicx}
\usepackage{float}
\usepackage{multirow,bigdelim}

\numberwithin{equation}{section}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{conjecture}[theorem]{Conjecture}

\usepackage{hyperref}% http://ctan.org/pkg/hyperref
\usepackage{cleveref}% http://ctan.org/pkg/cleveref
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\usepackage{chngcntr}% http://ctan.org/pkg/lipsum

\newcommand*{\C}{\mathbb{C}}%.............................C
\newcommand*{\R}{\mathbb{R}}%.............................R
\newcommand*{\Q}{\mathbb{Q}}%.............................Q
\newcommand*{\Z}{\mathbb{Z}}%.............................Z
\newcommand*{\N}{\mathbb{N}}%.............................N

\newcommand{\comment}[1]{}

\title[title]%
{title}
\author[A. Author]{Author AUTHOR}
%
\date{Version of \today}
%................................
\subjclass[2000]{11M26, 11M50, 11N64 }
\keywords{}
%
\AtBeginDocument{%
%\mathtoolsset{showonlyrefs,mathic = true}
\begin{abstract}

\end{abstract}
\maketitle
}
%..........................................
\begin{document}
%..........................................
%

\section{Introduction}
\counterwithin{equation}{section}

Here are the major results of this paper:
\begin{theorem}\label{theorem121}
theorem 2.1
\end{theorem}
\begin{theorem}\label{theorem131}
theorem 3.1
\end{theorem}
The proof of these two theorems are given in the subsequent sections.

\section{Implementation, Part I}
\begin{theorem}\label{theorem21}
theorem 2.1
\end{theorem}
\begin{proof}
body of proof of theorem 2.1.
\end{proof}

\begin{theorem}\label{theorem22}
theorem 2.2
\end{theorem}
\begin{proof}
body of proof of theorem 2.2.
\end{proof}

In \cref{theorem21} and \cref{theorem22}, we obtained...

\section{Implementation, Part II}

\begin{theorem}\label{theorem31}
theorem 3.1
\end{theorem}
\begin{proof}
body of proof of theorem 3.1.
\end{proof}

\begin{theorem}\label{theorem32}
theorem 3.2
\end{theorem}
\begin{proof}
body of proof of theorem 3.2.
\end{proof}

In \cref{theorem31} and \cref{theorem32} we obtained...
%---------------------------------------
\end{document}

You can override the \thetheorem command that generates the theorem number. For example, you could do the following in your introduction:

\renewcommand{\thetheorem}{2.1}
\begin{theorem}\label{theorem121}
theorem 2.1
\end{theorem}
\renewcommand{\thetheorem}{3.1}
\begin{theorem}\label{theorem131}
theorem 3.1
\end{theorem}

However, since you have now replaced the actual logic for incrementing the theorem numbers, the rest of the theorems will be numbered incorrectly. So, you need to first backup LaTeX's original logic for theorem numbering:

\let\thetheoremdefault\thetheorem

and restore it after your introduction section:

\let\thetheorem\thetheoremdefault

Here is your updated working example:

\documentclass[a4paper,12pt,reqno,twoside]{amsart}

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{color}
\usepackage{ifpdf}
\usepackage{array}

\usepackage{url}
\usepackage{graphicx}
\usepackage{float}
\usepackage{multirow,bigdelim}

\numberwithin{equation}{section}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{conjecture}[theorem]{Conjecture}

% Backup the original theorem-numbering logic
\let\thetheoremdefault\thetheorem

\usepackage{hyperref}% http://ctan.org/pkg/hyperref
\usepackage{cleveref}% http://ctan.org/pkg/cleveref
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\usepackage{chngcntr}% http://ctan.org/pkg/lipsum

\newcommand*{\C}{\mathbb{C}}%.............................C
\newcommand*{\R}{\mathbb{R}}%.............................R
\newcommand*{\Q}{\mathbb{Q}}%.............................Q
\newcommand*{\Z}{\mathbb{Z}}%.............................Z
\newcommand*{\N}{\mathbb{N}}%.............................N

\newcommand{\comment}[1]{}

\title[title]%
{title}
\author[A. Author]{Author AUTHOR}
%
\date{Version of \today}
%................................
\subjclass[2000]{11M26, 11M50, 11N64 }
\keywords{}
%
\AtBeginDocument{%
%\mathtoolsset{showonlyrefs,mathic = true}
\begin{abstract}

\end{abstract}
\maketitle
}
%..........................................
\begin{document}
%..........................................
%

\section{Introduction}
\counterwithin{equation}{section}

Here are the major results of this paper:
\renewcommand{\thetheorem}{2.1}
\begin{theorem}\label{theorem121}
theorem 2.1
\end{theorem}
\renewcommand{\thetheorem}{3.1}
\begin{theorem}\label{theorem131}
theorem 3.1
\end{theorem}
The proof of these two theorems are given in the subsequent sections.

% Restore the original theorem-numbering logic
\let\thetheorem\thetheoremdefault

\section{Implementation, Part I}
\begin{theorem}\label{theorem21}
theorem 2.1
\end{theorem}
\begin{proof}
body of proof of theorem 2.1.
\end{proof}

\begin{theorem}\label{theorem22}
theorem 2.2
\end{theorem}
\begin{proof}
body of proof of theorem 2.2.
\end{proof}

In \cref{theorem21} and \cref{theorem22}, we obtained...

\section{Implementation, Part II}

\begin{theorem}\label{theorem31}
theorem 3.1
\end{theorem}
\begin{proof}
body of proof of theorem 3.1.
\end{proof}

\begin{theorem}\label{theorem32}
theorem 3.2
\end{theorem}
\begin{proof}
body of proof of theorem 3.2.
\end{proof}

In \cref{theorem31} and \cref{theorem32} we obtained...
%---------------------------------------
\end{document}
• Thanks a lot for the detailed answer!
– mike
Sep 9 '19 at 14:25

There are other ways to repeat statements. A hand-made one for just a couple of them can be done as follows.

The idea is to have an unnumbered theorem type, which receives the right header as an argument to the reptheorem environment.

The mandatory argument is the label assigned to the statement in the main part. Labeling the repeated theorem is not supported and it wouldn't make sense. By using \Cref we ensure that the number in the repeated theorem is a link when hyperref is loaded.

\documentclass[a4paper,12pt,reqno,twoside]{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{color}
\usepackage{ifpdf}
\usepackage{array}

\usepackage{url}
\usepackage{graphicx}
\usepackage{float}
\usepackage{multirow,bigdelim}

\usepackage{hyperref}% http://ctan.org/pkg/hyperref
\usepackage{cleveref}% http://ctan.org/pkg/cleveref
%\usepackage{lipsum}% http://ctan.org/pkg/lipsum

\calclayout % <--- YES

\numberwithin{equation}{section}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{conjecture}[theorem]{Conjecture}

\newcommand{\reptheoremname}{}
\newtheorem*{reptheoreminner}{\reptheoremname}
\newenvironment{reptheorem}[1]
{\renewcommand{\reptheoremname}{\cref{#1}}\reptheoreminner}
{\endreptheoreminner}

\newcommand*{\C}{\mathbb{C}}%.............................C
\newcommand*{\R}{\mathbb{R}}%.............................R
\newcommand*{\Q}{\mathbb{Q}}%.............................Q
\newcommand*{\Z}{\mathbb{Z}}%.............................Z
\newcommand*{\N}{\mathbb{N}}%.............................N

\newcommand{\comment}[1]{}

\title[title]%
{title}
\author[A. Author]{Author AUTHOR}
%
\date{Version of \today}
%................................
\subjclass[2000]{11M26, 11M50, 11N64 }
\keywords{}
%
\AtBeginDocument{%
%\mathtoolsset{showonlyrefs,mathic = true}
\begin{abstract}

\end{abstract}
\maketitle
}
%..........................................
\begin{document}
%..........................................
%

\section{Introduction}
\counterwithin{equation}{section}

Here are the major results of this paper:
\begin{reptheorem}{theorem21}
theorem 2.1
\end{reptheorem}
\begin{reptheorem}{theorem31}
theorem 3.1
\end{reptheorem}
The proof of these two theorems are given in the subsequent sections.

\section{Implementation, Part I}
\begin{theorem}\label{theorem21}
theorem 2.1
\end{theorem}
\begin{proof}
body of proof of theorem 2.1.
\end{proof}

\begin{theorem}\label{theorem22}
theorem 2.2
\end{theorem}
\begin{proof}
body of proof of theorem 2.2.
\end{proof}

In \cref{theorem21} and \cref{theorem22}, we obtained...

\section{Implementation, Part II}

\begin{theorem}\label{theorem31}
theorem 3.1
\end{theorem}
\begin{proof}
body of proof of theorem 3.1.
\end{proof}

\begin{theorem}\label{theorem32}
theorem 3.2
\end{theorem}
\begin{proof}
body of proof of theorem 3.2.
\end{proof}

In \cref{theorem31} and \cref{theorem32} we obtained...
%---------------------------------------
\end{document}

I've made some adjustments to your document preamble; avoid setting \oddsidemargin and \evensidemargin and prefer the amsart specific \calclayout command.