
theorem
  for G being edgeless_Graph, e,v1,v2 being object
  holds not e Joins v1,v2,G & not e DJoins v1,v2,G
proof
  let G be edgeless _Graph;
  let e,v1,v2 be object;
  not e Joins v1,v2,G
  proof
    assume e Joins v1,v2,G;
    then e in the_Edges_of G by GLIB_000:def 13;
    hence contradiction;
  end;
  hence thesis by GLIB_000:16;
end;
