Let $\kappa$ a infinite cardinal with uncountable cofinality and $S\subset\kappa$. We can find a normal function $f$ from $\operatorname{cf}(\kappa)$ on $\kappa$ such that $\sup(\operatorname{rg}(f))=\kappa$. I try to prove the equivalence :
$S$ stationary in $\kappa$ iff $\{\xi<\operatorname{cf}\kappa : f(\xi)\in S\}$ is stationary in $cf\kappa$
$(\Rightarrow)$ : it's ok by supposing the contrary. I can find a club $Y$ in $\kappa$ that doesn't intersect $S$.
$(\Leftarrow)$ : can somebody give me an indication ? it seems to be evident but ...
Thanks.