Defining a double star (**) for theorem environment

Question

This is a follow-up question of QED symbol after statements without proof, and I am really not sure whether this is the right approach to solve the problem raised there. But it seems to solve all situations I encounter perfectly, so I will try...

The theorem environment has the usual version with numbering and a *'ed version without numbering. I would now like to have another **'ed (or something similar) version that puts something around the theorem environment.

Here is what I currently need to do:

\documentclass{amsart}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\begin{document}
\begin{proof}[\unskip\nopunct]
\begin{theorem}
    $e^{2\pi i} = 1$. \qedhere
\end{theorem}
\end{proof}

\begin{proof}[\unskip\nopunct]
\begin{corollary}[{myref}]
    The expression $e^{2\pi i} - 1$ equals $0$. Moreover, there is more text to actually add here. \qedhere
\end{corollary}
\end{proof}
\end{document}

and I want to avoid adding the \begin{proof}[\unskip\nopunct] and the \end{proof} myself, but get this automatically using a double star in both situations.

It might actually be better to interchange the order of the proof and the theorem environment, so a solution that provides that version would also be appreciated!

That is

\begin{myXYZ**}[...]
    ...
\end{myXYZ**}

(with myXYZ defined as a theorem environment in the header) should simply translate into

\begin{proof}[\unskip\nopunct]
\begin{myXYZ}[...]
    ...
\end{myXYZ}
\end{proof}

Is this (or the ** replaced with something else, independent of using theorem or lemma or proposition) possible?

Answer 1

Maybe this solves your problem. I define a \varnewtheorem command with the same syntax as \newtheorem, but that creates four variants for each label we call. So with \varnewtheorem{foo}{Foo} we create the four environments

• foo (theorem, proof follows)
• foo* (unnumbered theorem, proof follows)
• foo+ (theorem, no proof)
• foo*+ (unnumbered theorem, no proof)

The syntax accepts the optional arguments as usual.

\documentclass{amsbook}
\usepackage{amsthm}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\varnewtheorem}{momo}
 {
  \IfValueTF{#4}
   {\newtheorem{#1}{#3}[#4]}
    {
     \IfValueTF{#2}
      {\newtheorem{#1}[#2]{#3}}
      {\newtheorem{#1}{#3}}
    }
  \newtheorem*{#1*}{#3}
  \newenvironment{#1+}
   {\pushQED{\qed}\begin{#1}}
   {\popQED\end{#1}}
  \newenvironment{#1*+}
   {\pushQED{\qed}\begin{#1*}}
   {\popQED\end{#1*}}
 }
\ExplSyntaxOff

\varnewtheorem{theorem}{Theorem}[chapter]
\varnewtheorem{proposition}[theorem]{proposition}

\begin{document}

\chapter{Test}

\begin{theorem}
A standard theorem statement
\end{theorem}

\begin{theorem*}
A standard unnumbered theorem statement
\end{theorem*}

\begin{theorem+}
A theorem statement without proof
\end{theorem+}

\begin{theorem*+}
An unnumbered theorem statement without proof
\end{theorem*+}


\begin{proposition}
A standard theorem statement
\end{proposition}

\begin{proposition*}
A standard unnumbered theorem statement
\end{proposition*}

\begin{proposition+}
A theorem statement without proof
\end{proposition+}

\begin{proposition*+}
An unnumbered theorem statement without proof
\end{proposition*+}

\end{document}

Answer 2

For each \newtheorem{X}, you can call the below function \doublestarenv{X} to create an X** environment:

\documentclass{amsart}

\newcommand{\doublestarenv}[1]{%
  \newenvironment{#1**}[1][]
    {\proof[\unskip\nopunct]
     \csname #1\endcsname[##1]}
    {\csname end#1\endcsname
     \endproof}%
}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}

\doublestarenv{theorem}
\doublestarenv{corollary}

\begin{document}

\begin{proof}[\unskip\nopunct]
\begin{theorem}
    $e^{2\pi i} = 1$. \qedhere
\end{theorem}
\end{proof}

\begin{proof}[\unskip\nopunct]
\begin{corollary}[{myref}]
    The expression $e^{2\pi i} - 1$ equals $0$. Moreover, there is more text to actually add here. \qedhere
\end{corollary}
\end{proof}

\begin{theorem**}
    $e^{2\pi i} = 1$. \qedhere
\end{theorem**}

\begin{corollary**}[{myref}]
    The expression $e^{2\pi i} - 1$ equals $0$. Moreover, there is more text to actually add here. \qedhere
\end{corollary**}

\end{document}

---

You can automate this process by updating \newtheorem to automatically execute \doublestarenv:

\newcommand{\doublestarenv}[1]{%
  \newenvironment{#1**}[1][]
    {\proof[\unskip\nopunct]
     \csname #1\endcsname[##1]}
    {\csname end#1\endcsname
     \endproof}%
}

\usepackage{xparse}

\let\oldnewtheorem\newtheorem
\RenewDocumentCommand{\newtheorem}{ m o m o }{%
  \IfValueTF{#2}
    {\edef\x{\noexpand\oldnewtheorem{#1}[#2]{#3}}}
    {\IfValueTF{#4}
       {\edef\x{\noexpand\oldnewtheorem{#1}{#3}[#4]}}
       {\edef\x{\noexpand\oldnewtheorem{#1}{#3}}}%
    }%
  \x\doublestarenv{#1}%
}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}

Answer 3

Here is @egreg's theorem+ approach done with the package create-theorem. Take the environment theorem as an example, it begins by creating theorem and its starred variant via the key create starred version, and then uses copy existed to copy their definitions respectively and qed to add the QED symbol.

You may of course name the theorem+ as theorem** and theorem*+ as theorem***, it's your call.

\documentclass{book}
\usepackage{amsthm}
\usepackage{create-theorem}
\CreateTheorem { theorem } { parent counter = chapter, create starred version }
\CreateTheorem { theorem+ } { copy existed = theorem, qed }
\CreateTheorem { theorem+ } { copy existed = theorem, qed }
\CreateTheorem { proposition } { shared counter = theorem, create starred version }
\CreateTheorem { proposition+ } { copy existed = proposition, qed }
\CreateTheorem { proposition+ } { copy existed = proposition, qed }
\begin{document}
\chapter{Test}
\begin{theorem}
A standard theorem statement
\end{theorem}
\begin{theorem}
A standard unnumbered theorem statement
\end{theorem}
\begin{theorem+}
A theorem statement without proof
\end{theorem+}
\begin{theorem+}
An unnumbered theorem statement without proof
\end{theorem+}
\begin{proposition}
A standard theorem statement
\end{proposition}
\begin{proposition}
A standard unnumbered theorem statement
\end{proposition}
\begin{proposition+}
A theorem statement without proof
\end{proposition+}
\begin{proposition+}
An unnumbered theorem statement without proof
\end{proposition+}
\end{document}

Note that create-theorem does not work very well with amsbook, in that:

1. The \qedsymbol in amsbook somehow shows as \Lambda. This is not a big issue through, you can explicitly write the option as qed = \square (provided that \square is defined, for example via amssymb).
2. The big issue is that create-theorem loads cleveref internally, which is known to be incompatible with the class amsbook. A workaround can be seen in this answer -- however, the theorem styles would be broken.