Set version of Menger theorem

For vertex sets $A,B$, the maximum number of pairwise vertex-disjoint $A$-$B$ paths equals the minimum size of a vertex set meeting every $A$-$B$ path.

In a $k$-connected graph, for a vertex $x$ and a set $Y$ of at least $k$ other vertices, there are $k$ paths from $x$ to distinct vertices of $Y$ that meet only at $x$. This follows from the Set version of Menger theorem by separating $x$ from $Y$.