
theorem Th12:
  for L being complemented' join-commutative meet-commutative
  upper-bounded' lower-bounded' join-idempotent distributive distributive' non
  empty LattStr holds L is upper-bounded
proof
  let L be complemented' join-commutative meet-commutative upper-bounded'
lower-bounded' join-idempotent distributive distributive' non empty LattStr;
  ex c being Element of L st for a being Element of L holds c"\/"a = c & a
  "\/"c = c
  proof
    take Top' L;
    let a be Element of L;
    thus thesis by Th4;
  end;
  hence thesis;
end;
