\qed for theorems without proofs

Question

It is common to place a \qed-Box at the end of a theorem statement (or lemma, corollary, ...) if we give no proof for that statement.

How can I do this in LaTeX? If I place a qed-box at the end of the statement there is an additional linebreak, which is inacceptable formating.

Answer 1

if you are using amsthm or an ams document class, this problem is addressed by an item in the ams author faq. this in turn links to an example document (that's the input; the output is also present) that covers quite a few of the possible situations in which such a marker could be wanted. the most extreme situations require some manual effort, but i believe that nearly all reasonable possibilities (including the non-proof ending with a display) are covered.

Answer 2

With the theorem packages you would normally use \qed as described in this answer. Without those you use the commands below depending on if you want the filled square or empty.

When the line is too full for a square it will be placed on the new line, but since \hfill only works when there are characters on the line, the square will be placed left. You can precede \hfill by \null\nobreak to fix this. (\null inserts and empty \hbox and \nobreak is necessary to prevent this box from simply being placed on the previous line, where it'd be ineffective)

\documentclass[a4paper]{article}
\usepackage{amssymb} %% <- for \square and \blacksuare

\newcommand*{\QEDA}{\null\nobreak\hfill\ensuremath{\blacksquare}}%
\newcommand*{\QEDB}{\null\nobreak\hfill\ensuremath{\square}}%

\begin{document}

Lorem ipsum \QEDA

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod!?! \QEDB

\end{document}

---

Note:

The \qed command from amsthm employs a few additional tricks. A fully featured version of the above commands (with an optional argument for the symbol to use) would read

\newcommand*{\QED}[1][$\square$]{%
\leavevmode\unskip\penalty9999 \hbox{}\nobreak\hfill
    \quad\hbox{#1}%
}

(\leavevmode makes the command usable outside a paragraph (don't do this, though) \unskip removes a preceding space if there is one, \hbox{} is the same as \null, \penalty9999 ensures that TeX will try its utmost to squeeze the symbol into the same line as the preceding text and \quad separates the symbol from the text by a bit.)

Answer 3

Sometimes it is usefull to create a minimal example:

\documentclass{article}
\usepackage{amsmath,amsthm}
\newtheorem{lem}{Lemma}
\usepackage{lipsum}
\begin{document}
\begin{lem}
Text Text Text\qed
\end{lem}
\end{document}

Leave no space between the end of the text and \qed.

A more complex example.

\documentclass{article}
\usepackage{amsthm}

\newtheorem{theorem}{Theorem}

\begin{document}

\begin{theorem}
This theorem has no proof.\qed
\end{theorem}

\begin{theorem}
This theorem has no proof xxx xxxxx xxx xxxxx xxxx xxx.\qed
\end{theorem}

\begin{theorem}
This theorem has no proof xxx xxxxx xxx xxxxx xxxx xxx xxx.\qed
\end{theorem}

\begin{theorem}
This theorem has no proof xxx xxxxx xxx xxxxx xxxx xxx xxx xx.\qed
\end{theorem}

\begin{theorem}
This theorem has no proof xxx xxxxx xxx xxxxx xxxx xxx xxx xxxx.\qed
\end{theorem}

\end{document}

Answer 4

You could add the \qedsymbol to the end of your theorem automatically. The etoolbox package provides the means to tap into the end of an environment using \AtEndEnvironment{<env>}{<code>}. This adds <code> at \end{<env>}.

\documentclass{article}
\usepackage{amsthm}% http://ctan.org/pkg/amsthm
\usepackage{etoolbox}% http://ctan.org/pkg/etoolbox
\newtheorem{theorem}{Theorem}%
\AtEndEnvironment{theorem}{\null\hfill\qedsymbol}%
\begin{document}
\begin{theorem}
This is an important theorem.
\end{theorem}
\end{document}

However, this is only beneficial if you do not also include a \qedsymbol with your proofs. Moreover, it may cause undesired effects if you end your theorem with an equation. Regardless, you have some options:

• Define a non-proof-theorem environment which adds this automatically; or
• add it manually using some of the other answers provided; or
• provide (say) a starred version of theorem (that is, theorem*) which does the above.

Answer 5

Late to the party, but my answer is as follows:

To insert a QED symbol:

Case 1: Last line of text is to be centre-aligned:

\hfill <last line of code> \hfill $\square$

Case 2: Centre-alignement is not required:

<last line of code> \hfill $\square$

This works inside any environment and even if the last line is an equation, in which case you have to use $\displaystyle <equation>$ instead of \[ \]

Or if you like, use \lozenge instead of $\square$ to have a different QED symbol.

Answer 6

To get the symbol used for typesetting the QED, use \qedsymbol:

\documentclass{minimal}
\usepackage{amsmath,amsthm}
\newtheorem{theorem}{Theorem}
\def\eolqed{\hspace{\stretch1}\ensuremath\qedsymbol}
\begin{document}
\begin{theorem}Foo is a bar.\eolqed
\end{theorem}
\end{document}