
theorem Th7:
  for G1 being _Graph, G2 being DSimpleGraph of G1
  holds G1 is Dcomplete iff G2 is Dcomplete
proof
  let G1 be _Graph, G2 be DSimpleGraph of G1;
  consider G9 being removeDParallelEdges of G1 such that
    A1: G2 is removeLoops of G9 by GLIB_009:120;
  hereby
    assume G1 is Dcomplete;
    then G9 is Dcomplete by Th6;
    hence G2 is Dcomplete by A1, Th5;
  end;
  assume G2 is Dcomplete;
  then G9 is Dcomplete by A1, Th5;
  hence thesis by Th6;
end;
