Redefining proof environment so that it won't affect lists within the environment

Question

As part of my topology course, we filled in a book/course notes on Overleaf. As such I did not write the front matter of the book (my only contribution to it was adding in the verbatim package for multiline comments). The professor defined a new proof environment as follows:

\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{$\qedsymbol$}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \list{}
{\leftmargin=1.25mm\itemindent=20pt\linewidth=0.975\textwidth%
  \item[\hskip\labelsep
      \bfseries
  #1\@addpunct{.}]\ignorespaces}
}{%
  \popQED\endlist\@endpefalse
}

However this definition is causing issues within the book whenever someone uses a list within a proof. The first item is not labeled (I assume that's the \hskip\labelsep but I'm not sure) and the second item has a bolded label. Is there a way I can rewrite the proof environment so it was the same layout, but does not impact lists within proofs? I would prefer to not have to rewrite the proofs with lists.

EDIT: Things were getting clustered so I removed the image and code snippet.

This should run (worked on Overleaf and TeX Works).

\documentclass[letterpaper,twoside]{tufte-book}

\usepackage{amsmath}
\usepackage{amsthm}
\usepackage[inline]{enumitem}
\usepackage{amssymb}

\setlist[enumerate]{label=(\arabic*)}

\renewcommand{\qedsymbol}{\square}% PLEASE NOTE: this is in the AMS symbols font.
\makeatletter

\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{$\qedsymbol$}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \list{}{\leftmargin=1.25mm\itemindent=20pt\linewidth=0.975\textwidth%
  \item[\hskip\labelsep
        \bfseries
   #1\@addpunct{.}]\ignorespaces}
}{%
  \popQED\endlist\@endpefalse
}
\makeatother

\begin{document}
\begin{proof} Stuff
\begin{enumerate}
\item Item 1
\item Item 2
\item Item 3
\end{enumerate}
\end{proof}
\end{document}

Answer 1

Your professor is much better of by just reusing the amsthm original and not using \list to define it. The tombstone placement is all wrong in this example

If all the processor want is boldface instead of italics then use

\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  \item[\hskip\labelsep
        %\itshape
        \bfseries   
    #1\@addpunct{.}]\ignorespaces
}{%
  \popQED\endtrivlist\@endpefalse
}

Alternatively make sure the \list definition ends before \item i.e.

\list{}{\leftmargin=1.25mm\itemindent=20pt\linewidth=0.975\textwidth}%
\item[\hskip\labelsep
      \bfseries
 #1\@addpunct{.}]\ignorespaces

Then the list also works as expected. It is the \item inside the \list argument that is causing trouble