
theorem
  for Y being set, k being Nat st Y = REAL \ {k} holds
    Y is Event of Borel_Sets
proof
  let Y be set,k be Nat;
  assume A1: Y = REAL \ {k};
  reconsider Exx = k as Element of REAL by ORDINAL1:def 12,NUMBERS:19;
  reconsider Z = {Exx} as Subset of REAL;
  Z` is Element of Borel_Sets by PROB_1:15,Th1;
  hence thesis by A1;
end;
