  Let $G=(V,E)$ be a complete $n$-vertex graph with distinct positive edge
weights. We prove that for $k\in\{1,2,...,n-1\}$, the set consisting of the
edges of all minimum spanning trees (MSTs) over induced subgraphs of $G$ with
$n-k+1$ vertices has at most $nk-\binom{k+1}{2}$ elements. This proves a
conjecture of Goemans and Vondrak \cite{GV2005}. We also show that the result
is a generalization of Mader's Theorem, which bounds the number of edges in any
edge-minimal $k$-connected graph.
