 reserve Exx for Real;

theorem
  REAL is Event of Borel_Sets
proof
  reconsider A = {1} as Subset of REAL;
W1: A in Borel_Sets by Th1;
  A` in Borel_Sets by Th1,PROB_1:15; then
  A \/ A` in Borel_Sets by W1,PROB_1:3;
  then [#]REAL in Borel_Sets by SUBSET_1:10;
  hence thesis;
end;
