$\forall$$A$:Type, $P$:($A$$\rightarrow$Prop), $L$:$A$ List, $x$:$A$. ($\forall$$x$$\in$$L$. $P$($x$)) $\Rightarrow$ \{($x$ $\in$ $L$) $\Rightarrow$ ($x$ $\in$ $L$)\}