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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]$\Rightarrow$ \=($\forall$$f$:sys{-}antecedent(${\it es}$;${\it Sys}$), ${\it chain}$:(E(${\it Sys}$)$\rightarrow$(Id List)).\+
\\[0ex]chain{-}consistent($f$;${\it chain}$)
\\[0ex]$\Rightarrow$ ($\forall$$e$, ${\it e'}$:E(${\it Sys}$). loc($e$) $<<$ loc(${\it e'}$) $\vee$ (loc($e$) = loc(${\it e'}$) $\in$ Id) $\vee$ loc(${\it e'}$) $<<$ loc($e$)))
\-
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