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;
reserve D for non empty Subset of L,
  D9 for non empty Subset of L.:;
reserve D1,D2 for non empty Subset of L,
  D19,D29 for non empty Subset of L.:;

theorem
  p in D implies (.p.> c= (.D.>
proof
  <.p.:.) = (.p.> & <.D.:.) = (.D.> by Th29,Th36;
  hence thesis by FILTER_0:23;
end;
