\qed or \qedhere at the end of split environment

Question

While I was trying to improve my latest document with respect to its \qed symbols at the end of amsthm's proof environment i came across an interesting point. Assume the proof ends with some formula, that is finally representing the form the lemma/theorem proposes.

Something like

\documentclass{scrartcl}
\usepackage[fleqn]{amsmath}
\usepackage{amsthm,amstext,amsfonts,bm,amssymb}

\begin{document}
\begin{proof}
...
\begin{equation}
    \begin{split}
        A&= B \\
         &= C\\
         &= D&\qedhere
    \end{split}
\end{equation}
\end{proof}
\end{document}

While using \qedhere just in equation or align would put the symbol below any number (or at least to that side for euqation*), here the symbol is placed far to the left, even with using the additional column with &. Putting it after \end{split} would center it vertically with respect to the three columns, so my question is

How can I get the \qed symbol to the bottom right (text border) of an (equation-)split environment?

Where I would prefer a global solution for all splits where I mention \qedhere at the end.

Answer 1

the best approach in this particular case is to use align*, as that behaves well with \qedhere since each line is treated separately. (any of the multi-line options that treats lines separately should work equally well.)

\documentclass{scrartcl}
\usepackage[fleqn]{amsmath}
\usepackage{amsthm,amssymb}

\begin{document}
\begin{proof}
...
\begin{align*}
        A&= B \\
         &= C\\
         &= D \qedhere
\end{align*}
\end{proof}
\end{document}

this isn't always ideal -- cases, for example, will always force the tombstone to the center vertically -- but the request has been made often enough to place the tombstone on the last line, that it should be considered as a possible option. i am adding it to the formal list of requests.

as noted elsewhere, with flush left equations and equation numbers on the right, there is a built-in conflict. that is why ams document classes default to using equation numbers on the left.

Answer 2

Here is what I'd do if I was using ntheorem instead of amsthm

\documentclass{scrartcl}
\usepackage[fleqn]{amsmath}
\usepackage{amssymb,bm}
\usepackage[ntheorem]{empheq}
\usepackage[amsmath,thmmarks]{ntheorem}
\theoremstyle{nonumberplain}
\theorembodyfont{\normalfont}
\theoremheaderfont{\itshape}
\theoremsymbol{\ensuremath\square}
\theoremseparator{.}
\newtheorem{proof}{Proof}
\begin{document}
\begin{proof}
...
\begin{empheq}{equation}
\begin{split}
A&= B \\
&= C\\
&= D
\end{split}
\end{empheq}
\end{proof}
\end{document}

Answer 3

This is a nice question! I guess that \qedhere is not designed for the purpose you want to achieve. I can only offer a workaround, and it's only simple if you have an odd number of lines. (Since for two lines you won't want to use it anyway, the problem starts with four lines.) The idea: Use the align environment with \nonumber instead of equation and split.

\documentclass{scrartcl}
\usepackage[fleqn]{amsmath}
\usepackage{amsthm}
\begin{document}
\begin{proof}
...
\begin{align}
        A&= B \nonumber \\
         &= C \\
         &= D \nonumber \qedhere
\end{align}
\end{proof}
\end{document}

Answer 4

I noticed an interesting further point. If you are for example using the style provided by Springer svmult.cls, then the \qedhere is not available (haven't checked why though).

Then another approach would be (at least for numberings being at the right side of the page) to use

\tag*{\qeq}

both in split of an equation environment or an align/align* environment.

Nevertheless, compared to my original question, this of course implies, that the last line of the environment is not equipped with a number (or better: not needed to be equipped...)