Please write in your own word with detailed explanration.

Given a graph G and a minimum spanning tree T, suppose that we decrease the weight of one of the edges in T. Show that T is still a minimum spanning tree for G. More formally, let T be a minimum spanning tree for G with edge weights given by weight function w. Choose one edge (x, y) T and a positive number k and define the weight function w by w(u, v u'(1. v) =le(x,y)-k if (u, v) (x, y) . Show that T is a minimum spanning tree for G with edge weights given by w