  We confirm the Hanna Neumann conjecture for topologically finitely generated
closed subgroups $U$ and $W$ of a nonsolvable Demushkin group $G$. Namely, we
show that \begin{equation*} \sum_{g \in U \backslash G/W} \bar d(U \cap
gWg^{-1}) \leq \bar d(U) \bar d(W) \end{equation*} where $\bar d(K) =
\max\{d(K) - 1, 0\}$ and $d(K)$ is the least cardinality of a topological
generating set for the group $K$.
