Is the statement of Iwasawa's theorem that for every number field $K$ there are $\mu$, $\lambda$ and $\nu$ such that for every $\mathbb{Z}_p$ extension $K_{\infty}$, the class number of any big enough level, say $n$, is $\lambda n+ \mu p^n +\nu$?
Or is the statement that for every $\mathbb{Z}_p$ extension $K_{\infty}$ there are $\mu$ $\lambda$ and $\nu$?