
theorem Th9:
  for R being complete reflexive antisymmetric non empty RelStr,
  x being Element of R holds sup waybelow x <= x & x <= inf wayabove x
proof
  let R be complete reflexive antisymmetric non empty RelStr, x be Element
  of R;
  x is_>=_than waybelow x by WAYBEL_3:9;
  hence sup waybelow x <= x by YELLOW_0:32;
  x is_<=_than wayabove x by WAYBEL_3:10;
  hence thesis by YELLOW_0:33;
end;
