reserve A,A1,A2,B,B1,B2,C,O for Ordinal,
      R,S for Relation,
      a,b,c,o,l,r for object;

theorem Th2:
  Games 0 = {[{},{}]}
proof
  consider L be Sequence such that
  A1:Games 0 = L.0 & dom L = succ 0 and
  A2:for O be Ordinal st O in succ 0 holds
    L.O = [:bool union rng (L|O), bool union rng (L|O):] by Def4;
  A3:L.0 = [:bool union rng (L|0), bool union rng (L|0):] by A2,ORDINAL1:6;
  bool union rng (L|0)={{}} by ZFMISC_1:1,2;
  hence thesis by A1,A3,ZFMISC_1:29;
end;
