
theorem Th16:
  for G1 being _Graph, G2 being DGraphComplement of G1
  holds the_Edges_of G1 = G1.loops() iff G2 is Dcomplete
proof
  let G1 be _Graph, G2 be DGraphComplement of G1;
  consider G9 being DLGraphComplement of G1 such that
    A1: G2 is removeLoops of G9 by GLIB_012:def 8;
  hereby
    assume the_Edges_of G1 = G1.loops();
    then G9 is Dcomplete by Th14;
    hence G2 is Dcomplete by A1;
  end;
  assume G2 is Dcomplete;
  then G9 is Dcomplete by A1;
  hence thesis by Th14;
end;
