theorem Th167:
  dom(R \ (R|A)) = dom R \ A
proof
  R \ (R|A) = R|(dom R \ A) by Th166;
  hence dom(R \ (R|A)) = dom R /\ (dom R \ A) by Th55
      .= (dom R /\ dom R) \ A by XBOOLE_1:49
      .= dom R \ A;
end;
