theorem Th4:
  for PA,PB being a_partition of Y st PA '>' PB & PB '>' PA holds PA = PB
proof
  let PA,PB be a_partition of Y;
  assume PA '>' PB & PB '>' PA;
then  PB c= PA & PA c= PB by Th3;
  hence thesis by XBOOLE_0:def 10;
end;
