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