 reserve L for AD_Lattice;
 reserve x,y,z for Element of L;
 reserve L for GAD_Lattice;
 reserve x,y,z for Element of L;
reserve L for with_zero GAD_Lattice,
        x,y for Element of L;

theorem   :: Lemma 3.15. (4)
  x "/\" bottom L = bottom L
  proof
    set b1 = bottom L;
A4: b1 "/\" x = b1 by GADL0;
    x "/\" b1 = (x "/\" b1) "/\" x by LATTICES:def 7,A4
             .= (b1 "/\" x) "/\" x by Lem310
             .= b1 "/\" x by GADL0;
    hence thesis by GADL0;
  end;
