State the Cauchy Integral Formula for a disc. If $f: D\left(z_{0} ; r\right) \rightarrow \mathbb{C}$ is a holomorphic function such that $|f(z)| \leqslant\left|f\left(z_{0}\right)\right|$ for all $z \in D\left(z_{0} ; r\right)$, show using the Cauchy Integral Formula that $f$ is constant.