\begin{tabbing}
$\forall$\=${\it es}$:ES, $P_{1}$, $P_{2}$:(E$\rightarrow\mathbb{P}$), $Q_{1}$, $Q_{2}$, $Q_{3}$:(E$\rightarrow$E$\rightarrow\mathbb{P}$), $f_{1}$:(\{$e$:E$\mid$ $P_{1}$($e$)\} $\rightarrow$\{$e$:E$\mid$ $P_{2}$($e$)\} ),\+
\\[0ex]$f_{2}$:(\{$e$:E$\mid$ $P_{2}$($e$)\} $\rightarrow$E).
\-\\[0ex]$f_{1}$ is $Q_{2}${-}$Q_{3}${-}pre{-}preserving on $P_{1}$
\\[0ex]$\Rightarrow$ $f_{2}$ is $Q_{1}${-}$Q_{2}${-}pre{-}preserving on $P_{2}$
\\[0ex]$\Rightarrow$ $f_{2}$ o $f_{1}$ is $Q_{1}${-}$Q_{3}${-}pre{-}preserving on $P_{1}$
\end{tabbing}