 reserve Exx for Real;

theorem Th41:
  RAT is Event of Borel_Sets
proof
  reconsider mym = 1 as Element of REAL by Ko1;
  consider myp being Element of REAL such that A10: myp=-mym;
A0: Union GoCross_Union(mym) \/ Union GoCross_Union(myp) = RAT by A10,Th3;
A1: Union GoCross_Union(mym) is Event of Borel_Sets by PROB_1:17;
  Union GoCross_Union(myp) is Event of Borel_Sets by PROB_1:17;
  hence thesis by A1,PROB_1:21,A0;
end;
