Incremental network design with minimum spanning trees

Given an edge-weighted graph G=(V,E) and a set E₀⊂E, the incremental network design problem with minimum spanning trees asks for a sequence of edges e′₁,…,e′_T∈E∖E₀ minimizing [formula could not be replicated] where w(Xt) is the weight of a minimum spanning tree X_t for the subgraph (V,E₀∪{e′₁,…,e′_t}) and T=|E∖E₀|. We prove that this problem can be solved by a greedy algorithm.