
theorem
  for L being non empty reflexive transitive RelStr
  for x,y being Element of L st x << y
  for I being Ideal of L st y <= sup I holds x in I
proof
  let L be non empty reflexive transitive RelStr;
  let x,y be Element of L;
  assume
A1: x << y;
  let I be Ideal of L;
  assume y <= sup I;
  then ex d being Element of L st d in I & x <= d by A1;
  hence thesis by WAYBEL_0:def 19;
end;
