\def \ts {\tau_{\rm stop}}
-\newtheorem{Def}{Definition}
-%\newtheorem{Lemma}{\underline{Lemma}}
-\newtheorem{Theo}{Theorem}
-\newtheorem{Corollary}{Corollary}
-\newtheorem{Lemma}{Lemma}
-\newtheorem{proposition}{Proposition}
\newtheorem*{xpl}{Running Example}
\newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}}