
theorem Th5:
  REAL+ misses [:{{}},REAL+:]
proof
  assume REAL+ meets [:{{}},REAL+:];
  then consider x being object such that
A1: x in REAL+ and
A2: x in [:{{}},REAL+:] by XBOOLE_0:3;
  consider x1,x2 being object such that
A3: x1 in {{}} and
  x2 in REAL+ and
A4: x = [x1,x2] by A2,ZFMISC_1:84;
  x1 = {} by A3,TARSKI:def 1;
  hence contradiction by A1,A4,ARYTM_2:3;
end;
