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inc.tex
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inc.tex
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\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage[francais]{babel}
\usepackage[top=3.5cm, bottom=3.5cm, left=3cm, right=3cm]{geometry}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{pgfornament}
\usepackage{amsthm}
\usepackage{stmaryrd} %for \llbracket and \rrbracket
%\usepackage{bbold} %for a nice \mathbb{1}
\usepackage{graphicx}
\usepackage{float}
\usepackage[hidelinks]{hyperref}
\usepackage{bbm}
\usepackage{arcs}
\usepackage{calc}
\renewcommand{\mathbb}[1]{\mathbbm{#1}}
\everymath{\displaystyle}
\usepackage[
leftmargin = 0pt,
innerleftmargin = 1em,
innertopmargin = 0pt,
innerbottommargin = 0pt,
innerrightmargin = 0pt,
rightmargin = 0pt,
linewidth = 3pt,
topline = false,
rightline = false,
bottomline = false,
]{mdframed}
\newcommand{\floor}[1]{\lfloor #1 \rfloor}
\newcommand{\ceil}[1]{\lceil #1 \rceil}
\newcommand{\eps}{\varepsilon} % j'aime pas "eps"
\renewcommand{\epsilon}{\varepsilon}
\renewcommand{\phi}{\varphi}
\newcommand{\dd}{\mathrm{d}}
\newcommand{\der}[2]{\frac{\dd #1}{\dd #2}}
\newcommand{\dern}[3]{\frac{\dd^{#3} #1}{\dd {#2}^{#3}}}
\newcommand{\dpar}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\dparn}[3]{\frac{\partial^{#3} #1}{\partial {#2}^{#3}}}
\newcommand{\infsum}{\sum^{+\infty}}
\newcommand{\infprod}{\prod^{+\infty}}
\newcommand{\sep}{\begin{center} \pgfornament[width=10cm]{88} \end{center}}
\newcommand{\finish}{\begin{center} \pgfornament[width=5cm]{75} \end{center}}
\DeclareMathOperator{\id}{id}
%\linespread{1.1}
%\setlength{\parskip}{1em plus2mm minus2mm}
% _____ _
% |_ _| |__ ___ ___ _ __ ___ _ __ ___ ___
% | | | '_ \ / _ \/ _ \| '__/ _ \ '_ ` _ \/ __|
% | | | | | | __/ (_) | | | __/ | | | | \__ \
% |_| |_| |_|\___|\___/|_| \___|_| |_| |_|___/
\newtheoremstyle{defistyle}{}{}{\normalfont}{}{\bfseries}{\ :}{ }{}
\newtheoremstyle{theostyle}{}{}{\normalfont}{}{\bfseries}{}{ }{}
\newtheoremstyle{axiostyle}{}{}{\normalfont}{}{\bfseries}{}{ }{}
\newtheoremstyle{preuvestyle}{}{}{\normalfont}{}{\normalfont}{\ :}{ }{}
\definecolor{emerald}{rgb}{0.31, 0.78, 0.47}
\newmdenv[
linecolor = emerald!100
]{leftbargreen}
\definecolor{seablue}{rgb}{0.0, 0.412, 0.58}
\newmdenv[
linecolor = seablue!100
]{leftbarblue}
\definecolor{orange}{rgb}{1.0, 0.6, 0.0}
\newmdenv[
linecolor = orange!100
]{leftbarorange}
\definecolor{red}{rgb}{0.9, 0.0, 0.0}
\newmdenv[
linecolor = red!100
]{leftbarred}
\definecolor{violet}{rgb}{0.58, 0.0, 0.83}
\newmdenv[
linecolor = violet!100
]{leftbarviolet}
\definecolor{brown}{rgb}{0.59, 0.29, 0.0}
\newmdenv[
linecolor = brown!100
]{leftbarbrown}
\theoremstyle{defistyle}
\newtheorem{definth}{Définition}[section]
\theoremstyle{theostyle}
\newtheorem{theonth}{Th\'eor\`eme}[subsection]
\newtheorem*{propnth}{Propriété}
\newtheorem*{propsnth}{Propriétés}
\newtheorem{proponth}[theonth]{Proposition}
\newtheorem{cornth}[theonth]{Corollaire}
\newtheorem{lemnth}[theonth]{Lemme}
\newtheorem*{exnth}{Exemple}
\newtheorem*{exsnth}{Exemples}
\theoremstyle{preuvestyle}
\newtheorem*{remnth}{Remarque}
\newtheorem*{remsnth}{Remarques}
\newtheorem*{pvnth}{Démonstration}
\theoremstyle{axiostyle}
\newtheorem*{axinth}{Axiome}
\newtheorem*{lointh}{Loi}
\newtheorem*{postnth}{Postulat}
\newenvironment{defi}[1]
{\begin{leftbarred}\begin{definth} \textbf{#1}\ \\}
{\end{definth}\end{leftbarred}}
\newenvironment{prop}[1][]
{\begin{leftbarviolet}\begin{proponth} \textbf{#1}\ \\}
{\end{proponth}\end{leftbarviolet}}
\newenvironment{props}[1][]
{\begin{leftbarviolet}\begin{propsnth} \textbf{#1} \begin{enumerate}}
{\end{enumerate}\end{propsnth}\end{leftbarviolet}}
\newenvironment{propo}[1][]
{\begin{leftbarviolet}\begin{proponth} \textbf{#1}\ \\}
{\end{proponth}\end{leftbarviolet}}
\newenvironment{theo}[1]
{\begin{leftbarviolet}\begin{theonth} \textbf{#1}\ \\}
{\end{theonth}\end{leftbarviolet}}
\newenvironment{cor}[1][]
{\begin{leftbarviolet}\begin{cornth} \textbf{#1}\ \\}
{\end{cornth}\end{leftbarviolet}}
\newenvironment{lem}[1][]
{\begin{leftbarviolet}\begin{lemnth} \textbf{#1}\ \\}
{\end{lemnth}\end{leftbarviolet}}
\newenvironment{ex}[1][]
{\begin{leftbarorange}\begin{exnth} \textbf{#1}\ \\}
{\end{exnth}\end{leftbarorange}}
\newenvironment{exs}[1][]
{\begin{leftbarorange}\begin{exsnth} \textbf{#1}\begin{enumerate}}
{\end{enumerate}\end{exsnth}\end{leftbarorange}}
\newenvironment{rem}
{\begin{leftbarbrown}\begin{remnth}}
{\end{remnth}\end{leftbarbrown}}
\newenvironment{rems}
{\begin{leftbarbrown}\begin{remnth}\begin{itemize}}
{\end{itemize}\end{remnth}\end{leftbarbrown}}
\newenvironment{pv}
{\begin{leftbargreen}\begin{pvnth}}
{\hfill$\square$\end{pvnth}\end{leftbargreen}}
\newenvironment{axi}[1][]
{\begin{leftbarblue}\begin{axinth} \textbf{#1}\ \\}
{\end{axinth}\end{leftbarblue}}
\newenvironment{loi}[1][]
{\begin{leftbarblue}\begin{lointh} \textbf{#1}\ \\}
{\end{lointh}\end{leftbarblue}}
\newenvironment{post}[1][]
{\begin{leftbarblue}\begin{postnth} \textbf{#1}\ \\}
{\end{postnth}\end{leftbarblue}}
% ____ _ _ _
% / ___| ___ _ __ ___ _ __ __ _| | _ __ ___ __ _| |_| |__ ___
% | | _ / _ \ '_ \ / _ \ '__/ _` | | | '_ ` _ \ / _` | __| '_ \/ __|
% | |_| | __/ | | | __/ | | (_| | | | | | | | | (_| | |_| | | \__ \
% \____|\___|_| |_|\___|_| \__,_|_| |_| |_| |_|\__,_|\__|_| |_|___/
\renewcommand{\le}{\leqslant}
\renewcommand{\ge}{\geqslant}
\newcommand{\R}{\ensuremath{\mathbb{R}}}
\newcommand{\Rb}{\ensuremath{\overline{\mathbb{R}}}}
\newcommand{\N}{\ensuremath{\mathbb{N}}}
\newcommand{\Q}{\ensuremath{\mathbb{Q}}}
\newcommand{\Z}{\ensuremath{\mathbb{Z}}}
\newcommand{\C}{\ensuremath{\mathbb{C}}}
\newcommand{\U}{\ensuremath{\mathbb{U}}}
\newcommand{\F}{\ensuremath{\mathbb{F}}}
\newcommand{\K}{\ensuremath{\mathbb{K}}}
\newcommand{\imp}{\;\Rightarrow\;}
\newcommand{\pmi}{\;\Leftarrow\;}
\newcommand{\eq}{\;\Leftrightarrow\;}
\newcommand{\tq}{\;|\;}
\newcommand{\et}{\text{ et }}
\newcommand{\ou}{\text{ ou }}
\newcommand{\si}{\text{ si }}
\newcommand{\sinon}{\text{ sinon }}
\newcommand{\eint}[1]{\llbracket #1 \rrbracket}
\newcommand{\app}[3][0cm]{\hspace{-#1} \mbox{\raisebox{#2}{$\begin{aligned}#3
\end{aligned}$}} }
%auto app
\newcommand{\aapp}[2][0cm]{\hspace{-#1} \mbox{\raisebox{- \height+2ex}{$\begin{aligned}#2
\end{aligned}$}} }