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Inside a theorem environment I have a numbered list of theorem statements.

Afterward it goes a proof. In the proof I prove every of the above specified numbered statements.

But the order in the proof may be different than the order in the theorem.

Which environment best to use in the proof? I may manually write "1.", "2." or make a definition list with numeric labels, or whatever. Which way is the best?

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5  
You could use a simple enumerate and then use \label and \ref –  cmhughes Sep 24 '12 at 16:52
    
I would a bit oppose @cmhughes 's idea: if there're like 3 points in the theorem and not 20, it might be ok not to use referencing system and say directly something like \begin{description}\item[Proof of claim 3.] blabla \item[Proof of claim 1.] blabla \end{description} –  yo' Sep 24 '12 at 17:20
    
@tohecz manually labelling/referring three (or even two) points can result in inconsistencies or in bad numbering if the order of the points is changed for some reason. –  Gonzalo Medina Sep 24 '12 at 17:38
    
@GonzaloMedina But let's face it: you would (ok, I would) number it as claim1 to claim3 because you don't have to bother to think out some names for them. And then if you switch them, you get a complete confusion if you leave the original labels. –  yo' Sep 24 '12 at 18:39
    
@tohecz I would never use that kind of keys for labels; keys must be descriptive and not be tied to an specific numbering. –  Gonzalo Medina Sep 24 '12 at 18:42

1 Answer 1

As cmhughes suggested in his comment, you can use an enumerate environment with labelled \items to build the theorem, and then use \ref in the proof (this guarantees you consistency and avoids possible errors from manually numbering):

\documentclass{article}
\usepackage{amsthm}
\usepackage{amsmath}

\newtheorem{theorem}{Theorem}

\begin{document}

\begin{theorem}
For a left artin ring $\Lambda$ we have the following.
\begin{enumerate}
\item\label{th:radnil} The radical of $\Lambda$ is nilpotent.
\item\label{th:finsim} There is only a finite number of nonisomorphic simple $\Lambda$-modules.
\item\label{th:leftnoe} $\Lambda$ is left noetherian.
\end{enumerate}
\end{theorem}
\begin{proof}
\ref{th:leftnoe}. Since $\Lambda$ has a finite filtration...\par
\ref{th:radnil}. Let $I$ be an ideal in $\Lambda$...\par
\ref{th:finsim}. If for a $\Lambda$-module $A$ we have...
\end{proof}

\end{document}

enter image description here

Using the enumitem package one can define a customized list-like environment; in the following example the thmclaim environment works as an enumerate environment but using boldfaced labels; inside the proof environment, a description environment was used to refer to the claims (thus keeping consistent use of boldfaced type):

\documentclass{article}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{enumitem}

\newtheorem{theorem}{Theorem}

\newlist{thmclaim}{enumerate}{1}
\setlist[thmclaim,1]{label=\normalfont\textbf{\arabic*.}}

\begin{document}

\begin{theorem}
For a left artin ring $\Lambda$ we have the following.
\begin{thmclaim}
\item\label{th:radnil} The radical of $\Lambda$ is nilpotent.
\item\label{th:finsim} There is only a finite number of nonisomorphic simple $\Lambda$-modules.
\item\label{th:leftnoe} $\Lambda$ is left noetherian.
\end{thmclaim}
\end{theorem}
\begin{proof}
\begin{description}
\item[\ref{th:leftnoe}] Since $\Lambda$ has a finite filtration...\par
\item[\ref{th:radnil}] Let $I$ be an ideal in $\Lambda$...\par
\item[\ref{th:finsim}] If for a $\Lambda$-module $A$ we have...
\end{description}
\end{proof}

\end{document}

enter image description here

And a variation using alphabetical characters:

\documentclass{article}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{enumitem}

\newtheorem{theorem}{Theorem}

\newlist{thmclaim}{enumerate}{1}
\setlist[thmclaim,1]{label=\normalfont\textbf{(\alph*)}}

\begin{document}

\begin{theorem}
For a left artin ring $\Lambda$ we have the following.
\begin{thmclaim}
\item\label{th:radnil} The radical of $\Lambda$ is nilpotent.
\item\label{th:finsim} There is only a finite number of nonisomorphic simple $\Lambda$-modules.
\item\label{th:leftnoe} $\Lambda$ is left noetherian.
\end{thmclaim}
\end{theorem}
\begin{proof}
\begin{description}
\item[\ref{th:leftnoe}] Since $\Lambda$ has a finite filtration...\par
\item[\ref{th:radnil}] Let $I$ be an ideal in $\Lambda$...\par
\item[\ref{th:finsim}] If for a $\Lambda$-module $A$ we have...
\end{description}
\end{proof}

\end{document}

enter image description here

And yet another variation changing also the ref key to automatically add "Proof of claim " (this can be redundant):

\documentclass{article}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{enumitem}

\newtheorem{theorem}{Theorem}

\newlist{thmclaim}{enumerate}{1}
\setlist[thmclaim,1]{label=\normalfont\textbf{\arabic*.},ref=Proof of claim~\arabic*.}

\begin{document}

\begin{theorem}
For a left artin ring $\Lambda$ we have the following.
\begin{thmclaim}
\item\label{th:radnil} The radical of $\Lambda$ is nilpotent.
\item\label{th:finsim} There is only a finite number of nonisomorphic simple $\Lambda$-modules.
\item\label{th:leftnoe} $\Lambda$ is left noetherian.
\end{thmclaim}
\end{theorem}
\begin{proof}
\begin{description}
\item[\ref{th:leftnoe}] Since $\Lambda$ has a finite filtration...\par
\item[\ref{th:radnil}] Let $I$ be an ideal in $\Lambda$...\par
\item[\ref{th:finsim}] If for a $\Lambda$-module $A$ we have...
\end{description}
\end{proof}

\end{document}

enter image description here

share|improve this answer
    
But should I use a description environment inside the proof? Or just manually write labels as yours? –  porton Sep 24 '12 at 17:32
    
A description environment? No need. Since you are using a proof environment, there's no need to repeat "Proof of claim 1", "Proof of claim 2"; it would be redundant; moreover, using the approach suggested by toheca you would be doing the numbering manually and this is clearly error-prone. –  Gonzalo Medina Sep 24 '12 at 17:37
    
But what's about \begin{description}\item[3.] ...? Wouldn't it better than just "3."? –  porton Sep 24 '12 at 17:46
    
@porton Why would it be better? You're manually doing the numbering and that can cause errors if later you decide to modify the order of the claims in the theorem. –  Gonzalo Medina Sep 24 '12 at 17:56
    
Errors with renumbering is rather unlikely, as the list are short and the document is edited by me only without collaborators. I am asking would to use description environment for FORMATTING not numbering. –  porton Sep 24 '12 at 18:13

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