
theorem ZMtoZL3:
  for V being finite-rank free Z_Module,
      sc being Function of [: the carrier of V, the carrier of V :],
         the carrier of F_Real holds
    GenLat (V,sc) is finite-rank
  proof
    let V be finite-rank free Z_Module,
    sc be Function of [: the carrier of V, the carrier of V :],
    the carrier of F_Real;
    set L = GenLat (V,sc);
    L is Submodule of V by LmZMtoZL1;
    hence thesis;
  end;
