
theorem Th97:
  for G1, G2, G3 being _Graph, G4 being GraphComplement of G1
  st G1 == G2 & G3 == G4 holds G3 is GraphComplement of G2
proof
  let G1, G2, G3 be _Graph, G4 be GraphComplement of G1;
  assume A1: G1 == G2 & G3 == G4;
  consider G9 being LGraphComplement of G1 such that
    A2: G4 is removeLoops of G9 by Def9;
  G9 is LGraphComplement of G2 & G3 is removeLoops of G9
    by A1, A2, Th62, GLIB_009:59;
  hence thesis by Def9;
end;
