theorem
  x in rng p implies rng(p -| x) misses {x}
proof
  assume x in rng p;
  then not x in rng(p -| x) by Th37;
  then for y being object st y in rng(p -| x) holds not y in {x}
     by TARSKI:def 1;
  hence thesis by XBOOLE_0:3;
end;
