Create my own environment with itmize without countering (latex)

Question

I want to create a "recurrence" environment (to create my math lessons). I want this code:

latex
\begin{recurrence}
 \Item $\forall n \in \mathbb{N}, P_n$\\
 \item Initialisation\\
 \item Heredity\\
 \item $\forall n \in \mathbb{N}, P_n$\\
\end{recurrence}

to give:

Answer 1

Personally, I would use a description and manually write the labels

\begin{description}
 \item[Prove:] $\forall n \in \mathbb{N}, P_n$
 \item[Initialisation:]  Initialisation
 \item[Heredity:]  Heredity
 \item[Conclusion:]  $\forall n \in \mathbb{N}, P_n$
\end{description}

but if you insist on your syntax you could jump through some hopes and do:

\documentclass{article}

\usepackage{amsfonts}

\usepackage{getitems}

\makeatletter
\def\doitem#1{%
\ifnum\thecurrentitemnumber=1%
  \item[Prove:]
\fi%
\ifnum\thecurrentitemnumber=2%
  \item[Initialisation:] 
\fi%
\ifnum\thecurrentitemnumber=3%
  \item[Heredity:] 
\fi%
\ifnum\thecurrentitemnumber=4%
  \item[Conclusion:] 
\fi%
#1}%
\makeatother



\usepackage{environ}

\NewEnviron{recurrence}{%
  \expandafter\gatheritems\expandafter{\BODY}%
  \gathereditem{0}%
  \begin{description}%
   \loopthroughitemswithcommand{\doitem}%
  \end{description}
}  



\begin{document}

\begin{recurrence}
 \item $\forall n \in \mathbb{N}, P_n$
 \item Initialisation
 \item Heredity
 \item $\forall n \in \mathbb{N}, P_n$
\end{recurrence}

\end{document}

Answer 2

An easy version using a tabular-like environment:

\documentclass{article}
\usepackage{amssymb,array}

\begin{document}
\begin{tabular}{>{\bf}ll}
Prove~:          & $\forall n\in\mathbb{N}$, $P_n$\\
Initialisation~: & Initialisation\\
Heredity~:       & Heredity\\
Conclusion~:     & $\forall n\in\mathbb{N}$, $P_n$\\
\end{tabular}
\end{document}

The code >{\bf}ll gives a first left-aligned column with contents in bold (>{\bf}l) and a second left-aligned column (l). The tilde characters ~ only serve to implement french spacing (if you really want it, othewise remove them).