How access document class's normal paragraph indent size?

Question

I want to modify the standard amsthm environment proof so that its beginning, including the word "Proof", is indented by the same amount as any normal text paragraph.

How do I refer to the size of a normal text paragraph's indentation so that I can use it as a length with \hskip, as in:

\makeatlatter
\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  \item[\hskip\SOMETHING       %% WHAT GOES IN PLACE OF "SOMETHING"
      \itshape
    #1\@addpunct{.}]\ignorespaces
}{%
  \popQED\endtrivlist\@endpefalse
} 
\makeatother    

I'd like this to be independent of any particular documentclass or the class's base font-size option, which is why I want to refer to the size of the normal paragraph indentation rather than specify something specific (looking at the code for the documentclass) like 10pt or 2em, or whatever.

Important I do not want to indent the entire proof, including the first line that contains "Proof" — just that first line.

Minimal example:

\documentclass{memoir}

\usepackage{amsthm}
\newtheorem{thm}{Theorem}

\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  \item[\hskip\labelsep % WHAT GOES IN PLACE OF \labelsep??
        \itshape
    #1\@addpunct{.}]\ignorespaces
}{%
  \popQED\endtrivlist\@endpefalse
}
\makeatother

\begin{document}

Lots of text here.

\begin{thm}
This is true.
\end{thm}

\begin{proof}
It's ovvious!
\end{proof}

\end{document}

On the output I've indicated graphically what I want to move.

Answer 1

Add a new length that's set to \parindent at begin document, so it will be available inside lists (that may reset \parindent).

\documentclass{memoir}

\usepackage{amsthm}
\newtheorem{thm}{Theorem}

\makeatletter
\newlength{\normalparindent}
\AtBeginDocument{\setlength{\normalparindent}{\parindent}}
\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \topsep6\p@\@plus6\p@\relax
  \trivlist
  \item[\hskip\labelsep\hskip\normalparindent
        \itshape
    #1\@addpunct{.}]\ignorespaces
}{%
  \popQED\endtrivlist\@endpefalse
}
\makeatother

\begin{document}

Lots of text here.

\begin{thm}
This is true.
\end{thm}

\begin{proof}
It's obvious!
\end{proof}

\end{document}

A more compact version using xpatch:

\documentclass{memoir}

\usepackage{amsthm,xpatch}
\newtheorem{thm}{Theorem}

\newlength{\normalparindent}
\AtBeginDocument{\setlength{\normalparindent}{\parindent}}
\xpatchcmd{\proof}{\hskip\labelsep}{\hskip\labelsep\hskip\normalparindent}{}{}

\begin{document}

Lots of text here.

\begin{thm}
This is true.
\end{thm}

\begin{proof}
It's obvious!
\end{proof}

\end{document}

Answer 2

I'd imagine you can just set the proof as a regular paragraph, not as part of a list.

\documentclass{memoir}

\usepackage{amsthm}
\newtheorem{thm}{Theorem}

\newlength{\storeparindent}
\AtBeginDocument{\setlength{\storeparindent}{\parindent}}

\makeatletter
\renewenvironment{proof}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \vspace{6\p@\@plus6\p@}%
  {\itshape #1\@addpunct{.}}\hspace*{\labelsep}%
  \ignorespaces
}{%
  \popQED
  \@endpefalse
}
\makeatother

\begin{document}

Lots of text here.

\begin{thm}
This is true.
\end{thm}

\begin{proof}
It's obvious!
\end{proof}

\end{document}

This will ensure that the "proof paragraph" will indent the same way other paragraphs should. Also, if the document class resets \parindent, the proof environment will follow suit.

You may wish to play a little with the post-proof spacing, since lists do have that.