
theorem Th2:
  for x being Element of REAL+ st x <> {} holds [{},x] in REAL
proof
  let x be Element of REAL+ such that
A1: x <> {};
A2: now
    assume [{},x] in {[{},{}]};
    then [{},x] = [{},{}] by TARSKI:def 1;
    hence contradiction by A1,XTUPLE_0:1;
  end;
  {} in {{}} by TARSKI:def 1;
  then [{},x] in [:{{}},REAL+:] by ZFMISC_1:87;
  then [{},x] in REAL+ \/ [:{{}},REAL+:] by XBOOLE_0:def 3;
  hence thesis by A2,XBOOLE_0:def 5;
end;
