$\forall$$T$:Type, $P$:($T$$\rightarrow\mathbb{P}$), $L_{1}$, $L_{2}$:($T$ List). ($\exists$$x$$\in$$L_{1}$ @ $L_{2}$.$P$($x$)) $\Leftarrow\!\Rightarrow$ (($\exists$$x$$\in$$L_{1}$.$P$($x$)) $\vee$ ($\exists$$x$$\in$$L_{2}$.$P$($x$)))