QED box after equation inside lemma

Question

In a mathematical text, I have a lemma which I will just state and not proof. I want to give it a QED box at the end. Usually, I can just put the command \qed at the end of the lemma. See the following example:

\documentclass{amsart}
\theoremstyle{plain}
\newtheorem{lemma}{Lemma}
\begin{document}
  The reader is familiar with the following statement:
\begin{lemma}
    If $a, b, c$ denote the sides of a rectangular triangle, and if $a$ denotes the longest side, then
    %
    \begin{equation}
      a^2 = b^2+c^2.
    \end{equation}
    \qed
  \end{lemma}
\end{document}

It produces a PDF-file which almost fits my desires:

$Output with \qed after the equation environment$

My problem is that the QED-symbol is too low. This happens because of the equation environment. The same problem appears in the proof environment, but in the proof environment it can be remedied by putting qedhere inside the equation environment.
Naively, I tried putting \qedhere inside my equation inside the lemma. The command had no effect, i. e. no QED box appeared. When I put \qed inside the equation environment like

\begin{equation*}
  a^2 = b^2+c^2. \qed
\end{equation*}

then I get the following, which I also dislike:

$Output with \qed inside the equation environment$

Is there an analogue of the \qedhere command that works in other environments than proof? If not, is there an easy way to get what I want?

I conferred these two posts:
QED symbol after statements without proof
How to make qed box inside alignment environment
But it seems that they both don't address my problem.

Why are you adding qed symbols inside lemmas in the first place? IMO they only belong at the end of proofs — daleif, Sep 09 '21 at 10:40
Hi @daleif, I do so because I want to indicate that this lemma will not be proven. This post carries the spirit of my consideration: https://tex.stackexchange.com/questions/334082/qed-symbol-after-statements-without-proof I am aware that this is a question of choice, so you may dislike my preferences. — NerdOnTour, Sep 09 '21 at 16:00
I would write that in words instead of confusing the reader. — daleif, Sep 09 '21 at 16:04
One way to diminish the vertical space between the equation and the qed sign, in this situation, is to add a \[-1ex] at the end of the equation, but inside the equation environment. Something like a^2 = b^2+c^2. \[-1ex] — Daniel N, Jan 27 '22 at 13:07

score 1 · Answer 1 · answered Feb 09 '24 at 19:13

You can use thmtools to define a qedlemma environment that always ends with a qed symbol, then use \qedhere inside the equation*.

\documentclass{amsart}
\usepackage{thmtools}
\declaretheorem{lemma}
\declaretheorem[qed,name=Lemma,sibling=lemma]{qedlemma}
\begin{document}
The reader is familiar with the following statement:
\begin{qedlemma}
If $a, b, c$ denote the sides of a rectangular triangle, and if $a$ denotes the longest side, then
%
\begin{equation}
  a^2 = b^2+c^2. \qedhere
\end{equation}
\end{qedlemma}
\end{document}

score 1 · Answer 2 · answered Feb 09 '24 at 20:51

You can define a wrapper environment noproof for statements that don't need a proof. You still need \qedhere if the statement ends with a display. You can use it with lemmas, propositions and even theorems.

\documentclass{amsart}
\theoremstyle{plain}
\newtheorem{lemma}{Lemma}
\NewDocumentEnvironment{noproof}{m}{% #1 is the inner environment
  \par\pushQED{\qed}\UseName{#1}%
}{\popQED\UseName{end#1}}
\begin{document}
The reader is familiar with the following 
statements \ref{test1}~and~\ref{test2}.
\begin{noproof}{lemma}\label{test1}
If $a, b, c$ denote the sides of a rectangular triangle, and if 
$a$ denotes the longest side, then
\begin{equation}
  a^2 = b^2+c^2.\qedhere
\end{equation}
\end{noproof}
\begin{noproof}{lemma}\label{test2}
All animals are equal.
\end{noproof}
\begin{lemma}
This is unreferenced.
\end{lemma}
\begin{proof}
Easy exercise.
\end{proof}
\end{document}

QED box after equation inside lemma

2 Answers2