
theorem Th9:
  for a, b being Real st a <> b holds Cl [.a,b.[ = [.a,b.]
proof
  let a, b be Real;
A1: Cl [.a,b.[ c= [.a,b.] by MEASURE6:57,XXREAL_1:24;
A2: Cl ].a,b.[ c= Cl [.a,b.[ by MEASURE6:62,XXREAL_1:22;
  assume a <> b;
  then [.a,b.] c= Cl [.a,b.[ by A2,JORDAN5A:26;
  hence thesis by A1,XBOOLE_0:def 10;
end;
