
theorem
  for L being up-complete non empty Poset st L is finite
  for x being Element of L holds x is isolated_from_below
proof
  let L be up-complete non empty Poset such that
A1: the carrier of L is finite;
  let x be Element of L, D be non empty directed Subset of L;
  assume x <= sup D;
  hence thesis by A1,Th16;
end;
