title: Proving that no minimum spanning tree contains the maximum weighted edge
body: <p>Let's say there's Graph G such that it all its edges have weights that correspond to distinct integers. So no two edge has the same weight.
  Let E be all the edges of G. Let emax be an edge in E with the maximum weight.
  Another property of  Graph G is that every edge e belongs to some cycle in G.</p>
  
  <p>I have to prove that no minimum spanning tree of G contains the edge emax.</p>
  
  <p>I can see why this is true, since all edges are distinct and every edge belongs to a cycle, the minimum spanning tree algorithm can simply choose the edge with lower weight in the cycle that contains emax.
  But I'm not sure how to concretely prove it.</p>