\begin{tabbing}
$\forall$${\it es}$:ES, ${\it Cmd}$:Type, ${\it In}$:AbsInterface(${\it Cmd}$), ${\it isupdate}$:(${\it Cmd}$$\rightarrow\mathbb{B}$), ${\it Sys}$, ${\it Out}$:AbsInterface(Top).
\\[0ex](E(${\it In}$) $\subseteq$r E(${\it Sys}$))
\\[0ex]$\Rightarrow$ \=($\forall$$f$:sys{-}antecedent(${\it es}$;${\it Sys}$).\+
\\[0ex]fifo{-}antecedent(${\it es}$;${\it Sys}$;$f$)
\\[0ex]$\Rightarrow$ ($\forall$$e$:E(${\it In}$). $f$($e$) = $e$ $\in$ E)
\\[0ex]$\Rightarrow$ ($\forall$${\it chain}$:(E(${\it Sys}$)$\rightarrow$(Id List)). chain{-}consistent($f$;${\it chain}$) $\Rightarrow$ sys{-}order(${\it es}$; ${\it Sys}$; $f$)))
\-
\end{tabbing}