reserve G, G1, G2 for _Graph, H for Subgraph of G;

theorem
  for G being loopless connected _Graph
  holds G is GraphUnion of G.allSpanningTrees()
proof
  let G be loopless connected _Graph;
  set H = the removeLoops of G;
  A1: G == H by GLIB_009:58;
  H is GraphUnion of G.allSpanningTrees() by Th185;
  hence thesis by A1, GLIB_014:22;
end;
