
theorem Th113:
for G being SimpleGraph holds (MycielskianSeq G).0 = G
proof
 let G be SimpleGraph;
 consider myc being Function such that
A1: MycielskianSeq G = myc and
A2: myc.0 = G and
      for k being Nat, G being SimpleGraph
        st G = myc.k holds myc.(k+1) = Mycielskian G by Def26;
 thus (MycielskianSeq G).0 = G by A1,A2;
end;
