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

theorem Th14:
  for G being non edgeless _Graph, e being Edge of G
  holds e DJoins (the_Source_of G).e,(the_Target_of G).e,createGraph(e)
proof
  let G be non edgeless _Graph, e be Edge of G;
  A1: e DJoins (the_Source_of G).e,(the_Target_of G).e,G by GLIB_000:def 14;
  the_Edges_of createGraph(e) = {e} by Th13;
  then e in the_Edges_of createGraph(e) by TARSKI:def 1;
  hence thesis by A1, GLIB_000:73;
end;
