$a$.$f$($a$) is c$\leq$ preserving on $e$.$P$($e$) $\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$$\forall$$e$, ${\it e'}$:\{$e$:E$\mid$ $P$($e$)\} . $e$ c$\leq$ ${\it e'}$ $\Rightarrow$ $f$($e$) c$\leq$ $f$(${\it e'}$)