$\forall$$T$:Type, $R$:($T$$\rightarrow$$T$$\rightarrow\mathbb{P}$), $P$:($T$$\rightarrow\mathbb{P}$). Trans($T$;$x$,$y$.$R$($x$,$y$)) $\Rightarrow$ Trans($T$;$x$,$y$.$R$$\mid$$P$($x$,$y$))