theorem
  for L being 0_Lattice holds L is H_Lattice iff for x,z being Element
  of L ex y being Element of L st x "/\" y [= z & for v being Element of L st x
  "/\" v [= z holds v [= y
proof
  let L be 0_Lattice;
  L is H_Lattice iff L is I_Lattice;
  hence thesis by FILTER_0:def 6;
end;
