
theorem Th79:
  for G1, G2, G3 being _Graph, G4 being DGraphComplement of G1
  st G1 == G2 & G3 == G4 holds G3 is DGraphComplement of G2
proof
  let G1, G2, G3 be _Graph, G4 be DGraphComplement of G1;
  assume A1: G1 == G2 & G3 == G4;
  consider G9 being DLGraphComplement of G1 such that
    A2: G4 is removeLoops of G9 by Def8;
  G9 is DLGraphComplement of G2 & G3 is removeLoops of G9
    by A1, A2, Th45, GLIB_009:59;
  hence thesis by Def8;
end;
