$\forall$$T$:Type, $P$:($T$$\rightarrow\mathbb{B}$), $L$:($T$ List), $x$:$T$. ($x$ $\in$ filter($P$; $L$)) $\Leftarrow\!\Rightarrow$ (($x$ $\in$ $L$) $\wedge$ ($\uparrow$($P$($x$))))