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causal{-}order{-}preserving(${\it es}$;$a$.$f$($a$);$e$.$P$($e$))
\\[0ex]$\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$\=$\forall$$e$:\{$e$:es{-}E(${\it es}$)$\mid$ $P$($e$)\} , ${\it e'}$:\{$e$:es{-}E(${\it es}$)$\mid$ $P$($e$)\} .\+
\\[0ex]es{-}causl(${\it es}$; $e$; ${\it e'}$) $\Rightarrow$ es{-}causl(${\it es}$; $f$($e$); $f$(${\it e'}$))
\-
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