$\forall$$T$:Type, $R$:($T$$\rightarrow$$T$$\rightarrow\mathbb{P}$), $x$, $y$:$T$. ($x$ ($R$$^{\mbox{\scriptsize $\ast$}}$) $y$) $\Leftarrow\!\Rightarrow$ ($\exists$$L$:$T$ List. rel{-}path{-}between($T$;$R$;$x$;$y$;$L$))