Latex- Lemma shows black rectangle at the end

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I am having an issue with my latex document. When I use the lemma by using the below code it shows a small black rectangle at the end of every lemma.

CODE:

 \documentclass{IEEEtran}
    \usepackage{eucal}
    \usepackage{algorithm,algorithmic}
    \begin{document}
    
    \section{ Analysis}
    
    This section discusses essential proofs of some of the properties explained in the earlier,\\
    \newtheorem{theorem}{\textbf{Lemma}}
    
    \begin{theorem}
        Lemma statement 1
    \end{theorem} 
    
    \begin{IEEEproof}
        The body of the lemma.The body of the lemma. The body of the lemma. The body of the lemma.  The body of the lemma.The body of the lemma.The body of the lemma. The body of the lemma.   The body of the lemma.The body of the lemma.The body of the lemma. The body of the lemma.
    \end{IEEEproof}
    
    \newtheorem{theorem2}{\textbf{Lemma}}
    \begin{theorem}
        Lemma statement 2
    \end{theorem} 
    \begin{IEEEproof}
        The body of the lemma. The body of the lemma. The body of the lemma. The body of the lemma. The body of the lemma. The body of the lemma. The body of the lemma. The body of the lemma. The body of the lemma.
    \end{IEEEproof}
    
    \end{document}

The above code shows the below output,

enter image description here

2

There are 2 best solutions below

0
jf_ On BEST ANSWER

As suggested I post my comment as an answer:

This rectangle marks the end of the proof (q.e.d.), as the IEEEproof environment defines. If you don't want to use this proof format you can just make this part a regular paragraph and adjust spacing if needed:

    \begin{theorem}
        Lemma statement 1
    \end{theorem} 
    
\textit{Proof:}
        The body of the lemma.The body of the lemma. The body of the lemma. The body of the lemma.  The body of the lemma.The body of the lemma.The body of the lemma. The body of the lemma.   The body of the lemma.The body of the lemma.The body of the lemma. The body of the lemma.
    

Gives you this:

enter image description here

0
MattAllegro On

I am reading the pdf guide of the package IEEEtran available at this CTAN url.

Section XII A, Proofs, at page 15, explicitly states:

The Q.E.D. symbol is automatically placed at the end of each proof. ... Both the closed (default) and open forms are provided as \IEEEQEDclosed and \IEEEQEDopen, respectively. To change the default from closed to open (some journals and/or authors prefer the open form), just redefine \IEEEQED as desired:

\renewcommand{\IEEEQED}{\IEEEQEDopen}

In the same way, adding

\renewcommand{\IEEEQED}{}

with the second argument left empty, at the end of your preamble, will make the full or empty square disappear form the right end of the last line of each proof.

Hope this helps, happy 2021!!