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如何将证明很好地分成不同的部分？

tag-icon • tag-icon page-breaking environments theorems
如何将证明很好地分成不同的部分？

我经常将长篇校样分成小段，以便于阅读和理解。我通过添加fbox“第 X 部分：...”来实现这一点。然而，这种方法并不总是奏效：方框和校样的相应部分可以通过分页符来分割，如下面代码所示。

\documentclass{article}

\usepackage{amsthm}
\usepackage{lipsum}

\parskip 12pt
\parindent 0pt
\newtheorem{theorem}{Theorem}

\begin{document}
    \lipsum[1-4]
    \begin{theorem}
        This is my theorem.
    \end{theorem}
    \begin{proof}
        Let's cut this long proof into little pieces.

        \fbox{Part 1: firstly}

        This is part 1.

        \fbox{Part 2: secondly}

        This is part 2.
    \end{proof}
\end{document}

有没有办法可以防止这种情况发生？是否有可能创建一个新的环境来防止分裂，并使添加这样的子证明更容易（我厌倦了\fbox{Part X: ...}重新输入）？我正在寻找允许我输入的东西

\begin{proof}
  Let's cut this long proof into little pieces.
  \begin{subproof}{Title of subproof 1}
    (subproof 1)
  \end{subproof}
  \begin{subproof}{Title of subproof 2}
    (subproof 2)
  \end{subproof}
\end{proof}

这将导致

带有子证明的证明

或许校样中的零件编号可以帮助自动对子证明进行编号。

答案1

您可以使用与章节标题相同的机制：

\documentclass{article}

\usepackage{amsthm}
\usepackage{lipsum}

\newtheorem{theorem}{Theorem}

\makeatletter
\newcommand{\proofpart}[2]{%
  \par
  \addvspace{\medskipamount}%
  \noindent\emph{Part #1: #2}\par\nobreak
  \addvspace{\smallskipamount}%
  \@afterheading
}
\makeatother

\begin{document}
\lipsum[1-4]

\begin{theorem}
This is my theorem.
\end{theorem}

\begin{proof}
Let's cut this long proof into little pieces.

\proofpart{1}{firstly}

This is part 1.

\proofpart{2}{secondly}

This is part 2.

\proofpart{3}{thirdly}

This is part 3.
\end{proof}

\end{document}

抱歉，但我无法忍受看到非零 parskip 文档，我觉得这浪费纸张，对清晰度和可读性没有任何帮助。

“第 1 部分：首先”周围的框架很刺眼，我建议只使用斜体，就像“证明”一样。老实说，我不会在证明部分标题后添加换行符，但这是个人喜好。

自动对校样部件进行编号的变体。

\documentclass{article}

\usepackage{amsthm,xpatch}
\usepackage{lipsum}

\newtheorem{theorem}{Theorem}

\makeatletter
\newcounter{proofpart}
\xpretocmd{\proof}{\setcounter{proofpart}{0}}{}{}
\newcommand{\proofpart}[1]{%
  \par
  \addvspace{\medskipamount}%
  \stepcounter{proofpart}%
  \noindent\emph{Part \theproofpart: #1}\par\nobreak\smallskip
  \@afterheading
}
\makeatother

\begin{document}

\lipsum[1-4]

\begin{theorem}
This is my theorem.
\end{theorem}

\begin{proof}
Let's cut this long proof into little pieces.

\proofpart{firstly}

This is part 1.

\proofpart{secondly}

This is part 2. \lipsum*[1]

\proofpart{thirdly}

This is part 3. \lipsum*[1]
\end{proof}

\end{document}

答案2

如果证明部分不需要描述，则可以使用该enumitem包并使用此代码：

\documentclass{article}

\usepackage{amsthm}
\usepackage{lipsum}
\usepackage{enumitem}

\newtheorem{theorem}{Theorem}

\begin{document}
\lipsum[1]

\begin{theorem}
This is my theorem.
\end{theorem}

\begin{proof}
Let's cut this long proof into little pieces.

\begin{enumerate}[label={{Part} \arabic*.}, leftmargin=*]
    \item This is part 1.
    \item This is part 2.
    \item This is part 3.
\end{enumerate}
\end{proof}

\end{document}

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