reserve L for Lattice,
  p,q,r for Element of L,
  p9,q9,r9 for Element of L.:,
  x, y for set;
reserve I,J for Ideal of L,
  F for Filter of L;

theorem
  {p} is Ideal of L implies L is lower-bounded
proof
  assume {p} is Ideal of L;
  then {p} is Filter of L.: by Th20;
  then L.: is upper-bounded by FILTER_0:13;
  hence thesis by LATTICE2:48;
end;
