
theorem Th115:
for G, H being SimpleGraph, n be Nat
  holds (MycielskianSeq G).(n+1) = Mycielskian (MycielskianSeq G).n
proof
 let G, H be SimpleGraph, n be Nat;
 set H = (MycielskianSeq G).n;
 consider myc being Function such that
A1: MycielskianSeq G = myc and myc.0 = G and
A2: for k being Nat, G being SimpleGraph
        st G = myc.k holds myc.(k+1) = Mycielskian G by Def26;
 thus (MycielskianSeq G).(n+1) = Mycielskian H by A1,A2;
end;
