Critical values of the n-th iteration of a Rational map

Question

I am looking at Alan Beardon's Iteration of Rational Maps and I am a bit stuck on the proof of the following theorem:

Let $R:\widetilde{\mathbb{C}} \rightarrow \widetilde{\mathbb{C}}$ be a rational map and $C$ be it's set of critical points. Then the set of critical values of $R^n$ is: $R(C) \cup ... \cup R^n (C)$.

Note: Here $R^n$ denotes the n-th iteration of $R$.

If anyone could help break down his version of the proof, or provide an alternative, that would be greatly appreciated.

Thanks.