
theorem
  for L being upper-bounded Lattice holds Top L = Top LattPOSet L
proof
  let L be upper-bounded Lattice;
  set x = %Top LattPOSet L;
  now
    let a be Element of L;
    a% <= x% by YELLOW_0:45;
    then a [= x by LATTICE3:7;
    hence x"\/"a = x & a"\/"x = x by LATTICES:def 3;
  end;
  hence thesis by LATTICES:def 17;
end;
