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theorem - Latex- Lemma shows black rectangle at the end

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}
    egin{document}
    
    section{ Analysis}
    
    This section discusses essential proofs of some of the properties explained in the earlier,\
    
ewtheorem{theorem}{extbf{Lemma}}
    
    egin{theorem}
        Lemma statement 1
    end{theorem} 
    
    egin{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}
    
    
ewtheorem{theorem2}{extbf{Lemma}}
    egin{theorem}
        Lemma statement 2
    end{theorem} 
    egin{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


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1 Answer

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by (71.8m points)

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:

    egin{theorem}
        Lemma statement 1
    end{theorem} 
    
extit{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


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