How can I eliminate the vertical extra space before and after the proof-environment?

Question

consider the following code:

\documentclass{scrartcl}
\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{enumerate}

\theoremstyle{plain}
\newtheorem{thm}{Theorem}
\theoremstyle{definition}
\newtheorem{rmk}[thm]{Remark}


\begin{document}

\begin{thm}
Normal theorem.
\end{thm}
\begin{proof}
Normal proof.
\end{proof}

%%%%%%%%%%%%%%%%%%%%%%

\begin{rmk}
\begin{enumerate}[(a)]
\item Some remark.
\begin{proof}
Proof for that remark. %!!!
\end{proof}
\item Other information.
\end{enumerate}
\end{rmk}


\end{document}

I want to introduce (best via newenvironment) a new kind of proof environment that I can use for remarks and that does not have additional vertical space before and after the proof other than the usual vertical line spacing.

So, the above example looks like

and I want to get rid of the extra space around the second Beweis.

Answer 1

You can define a new environment, duplicating proof:

\makeatletter
\newenvironment{proof*}[1][\proofname]{\par
  \pushQED{\qed}%
  \normalfont \partopsep=\z@skip \topsep=\z@skip
  \trivlist
  \item[\hskip\labelsep
        \itshape
    #1\@addpunct{.}]\ignorespaces
}{%
  \popQED\endtrivlist\@endpefalse
}
\makeatother

Now you can input the "inner" proof as

\begin{proof*}
This is a proof without additional vertical space
\end{proof*}