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