$\forall$$T$:Type, $L$:($T$ List), $P$:($T$$\rightarrow\mathbb{B}$).
\\[0ex]l\_all($L$; $T$; $x$.($\uparrow$$P$($x$))) $\Leftarrow\!\Rightarrow$ ($\uparrow$reduce(($\lambda$$x$,$y$. band($P$($x$); $y$)); tt; $L$))