Prove that T is an MST for G0 , whose edge weights are given by w 0 .

Gru gives you a graph G, a set of edge weights w. and an MST T of G. He would like to know if T is also an MST of G'. where G' is formed by decreasing the weight of exactly one of the edges in T. In other words, denote the edge chosen to be (x, y) elementof T, k be a positive number representing the decreased edge weight, and a weight function defined as w'(u, upsilon) = {w(u, upsilon) if (u, upsilon) notequalto (x, y) w(x, y) - k if (u, upsilon) = (x, y) Prove that T is an MST for G', whose edge weights are given by w