Let be $\Omega$ a compact subset of $H(D)$, i.e., the holomorphic functions in the open set $D$. If $z_0 \in D$, then there exists a function $g \in \Omega$ such that:
$|g'(z_0)| \geq |f'(z_0)|$ for every $f \in \Omega$
Why? I think it must be a consequence of Montel's Theorem, but I don't know how.