-\newtheorem{Def}{\underline{Définition}}
-\newtheorem{Lemma}{\underline{Lemme}}
-\newtheorem{Theo}{\underline{Théorème}}
+\newtheorem{Def}{\underline{Definition}}
+\newtheorem{Lemma}{\underline{Lemma}}
+\newtheorem{Theo}{\underline{Theorem}}
% \theoremheaderfont{\sc}
% \theorembodyfont{\upshape}
% \theoremstyle{nonumberplain}
% \theoremseparator{}
% \theoremsymbol{\rule{1ex}{1ex}}
% \theoremheaderfont{\sc}
% \theorembodyfont{\upshape}
% \theoremstyle{nonumberplain}
% \theoremseparator{}
% \theoremsymbol{\rule{1ex}{1ex}}
-\newtheorem{Proof}{Preuve :}
-\newtheorem{xpl}{Exemple illustratif :}
+\newtheorem{Proof}{Proof}
+\newtheorem{proposition}{Proposition}
+\newtheorem{xpl}{Running Example}
\newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}}
%\newcommand{\ie}{\textit{i.e.}}
\newcommand{\vectornorm}[1]{\ensuremath{\left|\left|#1\right|\right|_2}}
%\newcommand{\ie}{\textit{i.e.}}