
theorem
  for G being edgeless_Graph, e being object, X, Y being set
  holds not e SJoins X,Y,G & not e DSJoins X,Y,G
proof
  let G be edgeless _Graph;
  let e be object, X, Y be set;
  thus not e SJoins X,Y,G
  proof
    assume e SJoins X,Y,G;
    then e in the_Edges_of G by GLIB_000:def 15;
    hence contradiction;
  end;
  thus not e DSJoins X,Y,G
  proof
    assume e DSJoins X,Y,G;
    then e in the_Edges_of G by GLIB_000:def 16;
    hence contradiction;
  end;
end;
