\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$$f$:sys{-}antecedent(${\it es}$;${\it Sys}$), ${\it chain}$:(E(${\it Sys}$)$\rightarrow$(Id List)).\+
\\[0ex]chain{-}consistent($f$;${\it chain}$)
\\[0ex]$\Rightarrow$ \=($\forall$$a$:E(${\it In}$), $b$:E(${\it Sys}$).\+
\\[0ex](loc($b$) = loc($a$) $\in$ Id)
\\[0ex]$\Rightarrow$ ($\neg$($\uparrow$($b$ $\in_{b}$ ${\it In}$)))
\\[0ex]$\Rightarrow$ ($\uparrow$(${\it isupdate}$(${\it In}$($a$))))
\\[0ex]$\Rightarrow$ ($\neg$(loc($f$($b$)) = loc($b$) $\in$ Id))
\\[0ex]$\Rightarrow$ $b$ $\leq$loc prior(${\it Sys}$)($a$) ))
\-\-
\end{tabbing}