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 Th70:
  for a,b being Real holds [.b,a.] is Element of Ext_Borel_Sets
proof
 let a,b be Real;
 B1: [.-infty,a.] is Element of Ext_Borel_Sets by Th3;
 [.-infty,a.] /\ [.b,+infty.] is Element of Ext_Borel_Sets
 proof
  Intersection ext_half_open_sets(b) = [.b,+infty.] by Th60;
  then [.b,+infty.] is Element of Ext_Borel_Sets by Th50;
 hence thesis by B1,PROB_1:19;
 end;
 hence thesis by CrossTh;
end;
