$\forall$$T$:Type, $R$, ${\it R'}$:($T$$\rightarrow$$T$$\rightarrow\mathbb{P}$).
\\[0ex]($\forall$$x$, $y$:$T$. $R$($x$,$y$) $\Leftarrow\!\Rightarrow$ ${\it R'}$($x$,$y$)) $\Rightarrow$ (Trans($T$;$y$,$x$.$R$($x$,$y$)) $\Leftarrow\!\Rightarrow$ Trans($T$;$y$,$x$.${\it R'}$($x$,$y$)))