$\forall$${\it es}$:ES, $P$:(E$\rightarrow\mathbb{P}$), $R$:(E$\rightarrow$E$\rightarrow\mathbb{P}$), $f$:(\{$e$:E$\mid$ $P$($e$)\} $\rightarrow$E). $f$ is $R${-}pre{-}preserving on $P$ $\in$ $\mathbb{P}$