
theorem LmZMtoZL1:
  for V being Z_Module,
  sc being Function of [: the carrier of V, the carrier of V :],
  the carrier of F_Real holds
  GenLat (V,sc) is Submodule of V
  proof
    let V be Z_Module,
    sc be Function of [: the carrier of V, the carrier of V :],
    the carrier of F_Real;
    set L = GenLat (V,sc);
    A2: 0.L = 0.V;
    A3: the addF of L = (the addF of V) || the carrier of L;
    the lmult of L = (the lmult of V) |
    [:the carrier of INT.Ring, the carrier of L:];
    hence thesis by A2,A3,VECTSP_4:def 2;
  end;
