\usepackage{stmaryrd}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{mathtools}
\usepackage{fancybox}
\usepackage{mathrsfs}
\usepackage{mathtools}

\newcommand{\eqdef}{{~\coloneqq~}}

\newcommand{\id}{\operatorname{id}}

% Intervalle discret.
\newcommand{\discrIv}[1]{\llbracket #1 \rrbracket}

% ensembliste
\newcommand{\set}[1]{\left\{ #1 \right\}}
\newcommand{\card}[1]{\left\vert{} #1 \right\vert}
\newcommand{\abs}[1]{\left\vert{} #1 \right\vert}
\newcommand{\interior}[1]{\left({#1}\right)^\circ}
\newcommand{\floor}[1]{\left\lfloor{} #1 \right\rfloor}
\newcommand{\ceil}[1]{\left\lceil{} #1 \right\rceil}

% Abréviations courrantes
\newcommand{\ie}{\textit{ie.}}
\newcommand{\eg}{\textit{eg.}}
\newcommand{\Eg}{\textit{Eg.}}
\newcommand{\wrt}{\textit{wrt.}}
\newcommand{\st}{\textit{st.}}

% Notations à polices étranges
\newcommand{\domain}{\mathcal{D}}
\newcommand{\bigO}{\mathcal{O}}
\newcommand{\calA}{\mathcal{A}}
\newcommand{\calC}{\mathcal{C}}
\newcommand{\calG}{\mathcal{G}}
\newcommand{\calV}{\mathcal{V}}
\newcommand{\calT}{\mathcal{T}}
\newcommand{\calP}{\mathcal{P}}

% Ensembles
\newcommand{\realset}{\mathbb{R}}
\newcommand{\natset}{\mathbb{N}}
\newcommand{\relset}{\mathbb{Z}}
\newcommand{\powerset}{\mathcal{P}}

% Probas
\newcommand{\prob}{\mathbb{P}}
\newcommand{\probP}[1]{\mathbb{P}\left(#1\right)}
\newcommand{\expec}{\mathbb{E}}
\newcommand{\expecP}[1]{\mathbb{E}\left[#1\right]}
\newcommand{\variance}{\mathbb{V}}
\newcommand{\ber}{\mathcal{B}er}
\newcommand{\bin}{\mathcal{B}in}
\newcommand{\poi}{\mathcal{P}oi}

% Suppression des points
\newcommand{\ibar}{\overline{\imath}}
\newcommand{\jbar}{\overline{\jmath}}

% Fonctions
%\newcommand{\functiondef}[4]{\left\lbrace \begin{tabular}{r l} #1 & \rightarrow #2 \\ #3 & \mapsto #4\end{tabular} \right.}
\newcommand{\functiondef}[4]{\begin{cases}
#1 & \to #2 \\
#3 & \mapsto #4
\end{cases}}


% Preuve par équivalence - puces
\newcommand{\impliesbullet}{\ovalbox{$\implies$}}
\newcommand{\impliedbybullet}{\ovalbox{$\impliedby$}}
