
theorem Th5:
  for T being non empty RelStr, x being Element of T,
  A being upper Subset of T st not x in A holds A misses downarrow x
proof
  let T be non empty RelStr, x be Element of T,
  A be upper Subset of T such that
A1: not x in A;
  assume A meets downarrow x;
  then consider y being object such that
A2: y in A and
A3: y in downarrow x by XBOOLE_0:3;
  reconsider y as Element of T by A2;
  y <= x by A3,WAYBEL_0:17;
  hence contradiction by A1,A2,WAYBEL_0:def 20;
end;
