reserve x1, x2, x3, x4, x5, x6, x7 for set;

theorem Th56:
  for a, b being Real holds IRRAT (a, b) misses RAT (a, b)
proof
  let a, b be Real;
  assume IRRAT (a, b) meets RAT (a, b);
  then consider x being object such that
A1: x in IRRAT (a, b) and
A2: x in RAT (a, b) by XBOOLE_0:3;
  thus thesis by A1,A2,Th29;
end;
