Vertical line & list environment

Question

I would like to make a good looking environment for my proofs. Some are spread on two pages so i thought of the list environment.

\documentclass{article}
\usepackage[francais]{babel}
\usepackage{lipsum}

\begin{document}

\lipsum[1]

\begin{list}{\underline{Proof} :}{\leftmargin=0.6cm \setlength{\labelwidth}{10pt}}
\item \lipsum
\end{list}

\lipsum[2]

\end{document}

What i want is a vertical line starting approximatively under the 'r' of proof and that continue on the second page.

In fact It is quite similar to this question Vertical line enclosing items in itemize wich unfortunately didn't find no answer.

Answer 1

I suggest you to turn it into an environment; for large first lines one can do some manual adjustment:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[francais]{babel}
\usepackage{lipsum}
\usepackage{mdframed}

\newenvironment{Proof}[1][1.9ex]
  {\par\bigskip\vspace{#1}
   \begin{mdframed}[outerlinewidth=2,leftmargin=10,%
     rightmargin=-10pt,backgroundcolor=white,hidealllines=true,leftline=true,%
     innertopmargin=0pt,splittopskip=\topskip,skipbelow=\baselineskip,innerbottommargin=0pt%
     skipabove=\baselineskip]%
     \vspace{-#1}\hspace{-12.2mm}\underline{Proof} : \ignorespaces}
  {\end{mdframed}}

\begin{document}

\lipsum[1]

\begin{Proof}
\lipsum
\end{Proof}

\lipsum[2]

\begin{Proof}[2.1ex]
abc$\sum$\lipsum
\end{Proof}

\lipsum[2]

\end{document}

In the optional argument you put the necessary adjustment if the first line has descenders or ascenders that go beyond the underlined "Proof".

Answer 2

Thanks to egreg for the indication. After some trys i got what i wanted, that is :

\documentclass{article}
\usepackage[francais]{babel}
\usepackage{lipsum}
\usepackage{mdframed}

\newcommand{\Proof}[1]{%
\bigskip\bigskip
\begin{mdframed}[outerlinewidth=2,leftmargin=10,%
rightmargin=-10pt,backgroundcolor=white,hidealllines=true,leftline=true,%
innertopmargin=0pt,splittopskip=\topskip,skipbelow=\baselineskip,innerbottommargin=0pt%
skipabove=\baselineskip]%
\vspace{-3mm}\hspace{-12.2mm}\underline{Proof} : #1
\end{mdframed}
}

\begin{document}

\lipsum[1] \Proof\lipsum \lipsum[2]

\end{document}

Unfortunately it won't work if the first line height is bigger than usual ..