定理：权利要求的编号及其证明

Question

我正在尝试创建一个声明环境以ntheorem在证明环境中使用。我尝试使用以下代码

\documentclass{article}


\usepackage{ntheorem}

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}

\theoremheaderfont{\normalfont\itshape}
\newtheorem{claim}{Claim}
\theoremsymbol{\ensuremath{\blacksquare}} % \theoremsymbol{\ensuremath{_\square}}
\newtheorem{claimproof}{Proof of Claim}[claim]

\theoremstyle{nonumberplain}
\newtheorem{proof}{Proof}


\begin{document}
\begin{theorem}
asdjas aasdj adj 
\end{theorem}
\begin{proof}
\begin{claim}
some claim
\end{claim}
\begin{claimproof}
asdasd asdasd
\end{claimproof}

\begin{claim} some other claim \end{claim}
\begin{claimproof}proof of claim\end{claimproof}
\end{proof}

\begin{lemma}
some lemma
\end{lemma}
\begin{proof}
asdlasd
\begin{claim} claim for lemma\end{claim}
\begin{claimproof}
askl adlksd
\end{claimproof}
\begin{claim} asdljkd
\end{claim}
\begin{claimproof}
asd aspdok
\end{claimproof}
\end{proof}

\end{document}

这种方法确实可行。但结果如下：

Theorem 1
...
Proof
...
Claim 1
Proof of Claim 1.1
..

Claim 2
Proof of Claim 2.1

但我想得到类似的东西

Theorem 1
...
Proof
...
Claim 1
Proof of Claim 1
..

Claim 2
Proof of Claim 2

更好的方法是将证明中引用的定理或引理的子编号作为编号，但我想这会让一切变得更加复杂

Theorem 1
...
Proof
...
Claim 1.1
Proof of Claim 1.1
..

Claim 1.2
Proof of Claim 2.1

Lemma 3
Proof
Claim 3.1
Proof of Claim 3.1
...

Answer 1

理解的可选参数非常重要\newtheorem。

\newtheorem{claim}{Claim}

在整个文档中生成编号为 1、2、3、... 的“声明”。最后一个可选参数

\newtheorem{claimproof}{Proof of claim}[claim]

产生数字 X.1​​、X.2、X.3、...，其中 X 是前一个索赔的编号。

为了正确编号你的索赔，你需要类似

\newtheorem{claim}{Claim}[theorem]

因此根据先前的定理，索赔获得子数。

对于您对声明的证明，我认为您的要求是错误的，但我将在下面的第二个示例中说明如何执行您的要求。一般来说，人们希望能够自由地以与声明呈现顺序不同的顺序进行声明的证明；此外，声明陈述之后立即进行的声明证明实际上不需要用数字标记；如果证明距离较远或顺序不同，则使用 LaTeX 的\label/\ref机制提供正确的编号会更合适。

以下是一个例子：

\documentclass{article}

\usepackage[thmmarks]{ntheorem}
\usepackage{amssymb}

\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}

\newtheorem{claim}{Claim}[theorem]

\theoremstyle{nonumberplain}
\theoremsymbol{\ensuremath{\Box}}
\newtheorem{proof}{Proof}

\makeatletter
\newtheoremstyle{nonumberplainnobrackets}%
  {\item[\theorem@headerfont\hskip\labelsep ##1\theorem@separator]}%
  {\item[\theorem@headerfont\hskip \labelsep ##1\ ##3\theorem@separator]}
\makeatother

\theoremstyle{nonumberplainnobrackets}
\theoremsymbol{\ensuremath{\blacksquare}} 
\newtheorem{claimproof}{Proof of claim}
\begin{document}

\begin{lemma}
  A theorem.
\end{lemma}

\begin{proof}
  Proof starts.
  \begin{claim}
    A claim.
  \end{claim}
  \begin{claimproof}
    Proof of claim.
  \end{claimproof}
  Proof ends.
\end{proof}

\begin{theorem}
  A theorem.
\end{theorem}

\begin{proof}
  Proof starts.
  \begin{claim}
    A claim.
  \end{claim}
  \begin{claimproof}
    Proof of claim.
  \end{claimproof}
  Proof continues.
  \begin{claim}
    \label{claim:one}
    One claim.
  \end{claim}
  \begin{claim}
    \label{claim:another}
    Another claim.
  \end{claim}
  \begin{claimproof}[\ref{claim:another}]
    Proving another claim.
  \end{claimproof}
  Text.
  \begin{claimproof}[\ref{claim:one}]
    Proving claim one.
  \end{claimproof}
  Finally the end.
\end{proof}

\end{document}

注意，我引入了一种新的定理样式来应对证明数量声明所需的排版。

如果你真的确定claimproofs 不会以与声明不同的顺序出现，那么你可以使用以下方式进行设置

\theoremstyle{nonumberplain}
\theoremsymbol{\ensuremath{\blacksquare}} 
\newtheorem{claimproof}{Proof of claim \theclaim}

完整的例子是

\documentclass{article}

\usepackage[thmmarks]{ntheorem}
\usepackage{amssymb}

\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}

\newtheorem{claim}{Claim}[theorem]

\theoremstyle{nonumberplain}
\theoremsymbol{\ensuremath{\Box}}
\newtheorem{proof}{Proof}

\theoremsymbol{\ensuremath{\blacksquare}} 
\newtheorem{claimproof}{Proof of claim \theclaim}

\begin{document}

\begin{lemma}
  A theorem.
\end{lemma}

\begin{proof}
  Proof starts.
  \begin{claim}
    A claim.
  \end{claim}
  \begin{claimproof}
    Proof of claim.
  \end{claimproof}
  Proof ends.
\end{proof}

\begin{theorem}
  A theorem.
\end{theorem}

\begin{proof}
  Proof starts.
  \begin{claim}
    A claim.
  \end{claim}
  \begin{claimproof}
    Proof of claim.
  \end{claimproof}
  Proof continues.
  \begin{claim}
    \label{claim:one}
    One claim.
  \end{claim}
  Text.
  \begin{claimproof}
    Proving claim one.
  \end{claimproof}
  Finally the end.
\end{proof}

\end{document}