
theorem Th11:
  for L1 be up-complete non empty Poset st L1 is finite for x be
  Element of L1 holds x in compactbelow x
proof
  let L1 be up-complete non empty Poset;
  assume
A1: L1 is finite;
  let x be Element of L1;
A2: x <= x;
  x is compact by A1,WAYBEL_3:17;
  hence thesis by A2;
end;
