
theorem
  for L being lower-bounded Lattice holds Bottom L = Bottom LattPOSet L
proof
  let L be lower-bounded Lattice;
  set x = %Bottom LattPOSet L;
  now
    let a be Element of L;
    a% >= x% by YELLOW_0:44;
    then x [= a by LATTICE3:7;
    hence x"/\"a = x & a"/\"x = x by LATTICES:4;
  end;
  hence thesis by LATTICES:def 16;
end;
