
theorem
  for L being Z_Lattice holds DualLatMod(L) is Submodule of DivisibleMod(L)
  proof
    let L be Z_Lattice;
    the carrier of DualLatMod(L) = DualSet(L) &
    the addF of DualLatMod(L) = (the addF of DivisibleMod(L)) || DualSet(L) &
    the ZeroF of DualLatMod(L) = 0.DivisibleMod(L) &
    the lmult of DualLatMod(L) = (the lmult of DivisibleMod(L)) |
    [:the carrier of INT.Ring, DualSet(L):] &
    the scalar of DualLatMod(L) = (ScProductDM(L)) | [:DualSet(L), DualSet(L):]
    by defDualMod;
    hence thesis by ZMODLAT2:10;
  end;
