
theorem Th4:
  for L be non empty reflexive RelStr for x,y be Element of L holds
  y in compactbelow x iff x >= y & y is compact
proof
  let L be non empty reflexive RelStr;
  let x,y be Element of L;
  thus y in compactbelow x implies x >= y & y is compact
  proof
    assume y in compactbelow x;
    then ex z be Element of L st z = y & x >= z & z is compact;
    hence thesis;
  end;
  assume x >= y & y is compact;
  hence thesis;
end;
