\documentclass[12pt]{article}
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\usepackage{amssymb}
\usepackage{amsbsy,natbib}
\usepackage{amsthm}
\usepackage{amsfonts,amsmath,bm}
\usepackage[dvipsone]{epsfig}
\usepackage{color}
\usepackage{epic}
\RequirePackage{graphics,epsf}

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% \'Enonc\'es
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\newtheorem{proposition}{Proposition}
\newtheorem{theorem}{Theorem}
\newtheorem{remark}{Remark}
\newtheorem{lemma}{Lemma}
\newtheorem{definition}{Definition}

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\def\A{{\mathcal A}}
\def\B{{\mathbb B}}
\def\K{{\mathbb K}}
\def\L{{\mathcal L}}
\def\F{{\mathbb F}}
\def\N{{\mathbb N}}
\def\C{{\mathbb C}}
\def\R{{\mathbb R}}
\def\Z{{\mathbb Z}}
\def\Q{{\mathbb Q}}
\def\X{{\mathbb X}}
\def\al{\alpha}
\def\be{\beta}
\def\ga{\gamma}
\def\ep{\epsilon}
\def\S{{\Sigma}}
\def\Q{{\mathbb Q}}
\def\SG{{\goth S}}
\def\mref#1{(\ref{#1})}

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\begin{document}
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\begin{theorem}

Let $\Phi = \{\al\} \cup \Phi^+$ be a data stucture with a
bi-variate statistics
$$ \Phi \rightarrow \N\times X\ ;\ p \mapsto s(p) = (n,k)$$
($X$ is set of labels) such that
$$ s(\Phi^+) \subset \N^+ \times X$$
Set $\Phi_n=\{p\in \Phi|pr_1(s(p))=n\}$ and $l(p)=pr_2(s(p))$ ``label of $p$''. 
We suppose that there exists a function ``return to the father'' 
$$ 
d : \Phi_{n+1} \rightarrow \Phi_n
$$ 
such that $p\mapsto (d(p),l(p))$ is into. Then, for $p\in \Phi_n$, the code 
$$(l(p),l(d(p)),l(d^2(p)), \cdots l(d^{n-1}(p)))$$
is into.
\end{theorem}
\end{document}