☰

具有任意顺序的编号列表

tag-icon • tag-icon lists theorems enumerate
具有任意顺序的编号列表

在定理环境中，我有一个编号的定理陈述列表。

之后是证明。在证明中，我证明了上面每个指定编号的陈述。

但证明中的顺序可能与定理中的顺序不同。

在证明中最好使用哪种环境？我可以手动写下“1”、“2”，或者用数字标签制作定义列表，或者其他方式。哪种方式最好？

答案1

作为 休斯他在评论中建议，您可以使用enumerate带有标签\items 的环境来构建定理，然后\ref在证明中使用（这可以保证一致性并避免手动编号可能出现的错误）：

\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}

在此处输入图片描述

使用该enumitem包，可以定义自定义的列表式环境；在下面的例子中，该thmclaim环境用作enumerate环境，但使用粗体标签；在proof环境内部，description使用环境来引用声明（从而保持粗体类型的一致使用）：

\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}

在此处输入图片描述

还有一种使用字母字符的变体：

\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}

在此处输入图片描述

还有另一种变化，也改变了ref键以自动添加“索赔证明”（这可能是多余的）：

\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}

在此处输入图片描述

相关内容