
theorem
  for R being non empty RelStr, x,y being Element of R holds
  y in (uparrow x)` iff not x <= y
proof
  let R be non empty RelStr, x,y be Element of R;
  (uparrow x)` = (the carrier of R) \ uparrow x by SUBSET_1:def 4;
  then y in (uparrow x)` iff not y in uparrow x by XBOOLE_0:def 5;
  hence thesis by WAYBEL_0:18;
end;
