Solution
= Solution
<Fodor lemma> says that if $\lambda$ is a regular uncountable <cardinal>, $S\subseteq\lambda$ is stationary, and $f:S\to\lambda$ is regressive, then
$$
\boxed{\exists\xi<\lambda\quad\{\alpha\in S:f(\alpha)=\xi\}\text{ is stationary}.}
$$
Here a <regressive function> satisfies $f(\alpha)<\alpha$ at every nonzero $\alpha\in S$; removing $0$ has no effect on stationarity. Both regularity and stationarity are part of the hypotheses.