Suppose that \(f:\mathbb {D}\to \mathbb {D}\) is holomorphic and zero at points \(z_1,\ldots ,z_n\in \mathbb {D}\) counted with multiplicity. Show that
\[ |f(z)|\le |\psi _{z_1}(z)|\cdots |\psi _{z_n}(z)|\text { in }\mathbb {D} \]
where
\[ \psi _\alpha (z)=\frac {\alpha -z}{1-\bar {\alpha }z}. \]