reserve Omega for non empty set;
reserve Sigma for SigmaField of Omega;
reserve S for non empty Subset of REAL;
reserve r for Real;
reserve T for Nat;
reserve I for TheEvent of r;

theorem
  I is Event of Borel_Sets
proof
 per cases;
 suppose S1: r<=0;
   [.0,+infty.[ is Element of Borel_Sets by FINANCE1:3;
   hence thesis by S1,Def555;
 end;
 suppose S1: r>0;
   [.0,r.] is Element of Borel_Sets by FINANCE1:8;
   hence thesis by S1,Def555;
 end;
end;
