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$\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]$\Rightarrow$ (E(${\it Out}$) $\subseteq$r E(${\it Sys}$))
\\[0ex]$\Rightarrow$ \=($\forall$$f$:sys{-}antecedent(${\it es}$;${\it Sys}$).\+
\\[0ex]($\forall$$e$:E(${\it In}$). $f$($e$) = $e$ $\in$ E)
\\[0ex]$\Rightarrow$ \=($\forall$${\it chain}$:(E(${\it Sys}$)$\rightarrow$(Id List)).\+
\\[0ex]chain{-}consistent($f$;${\it chain}$)
\\[0ex]$\Rightarrow$ \=($\forall$$x$:E(${\it Sys}$).\+
\\[0ex]effective($x$)
\\[0ex]$\Rightarrow$ \=($\forall$${\it e'}$:E(${\it In}$).\+
\\[0ex]($\uparrow$(${\it isupdate}$(${\it In}$(${\it e'}$))))
\\[0ex]$\Rightarrow$ loc($x$) $<<$ loc(${\it e'}$)
\\[0ex]$\Rightarrow$ ($\exists$\=$e$:E(${\it Sys}$)\+
\\[0ex](loc($e$) = loc(${\it e'}$) $\in$ Id \& ($\neg$(loc($f$($e$)) = loc($e$) $\in$ Id)) \& $x$ is $f$$\ast$($e$)))))))
\-\-\-\-\-
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