 reserve V for Z_Module;
 reserve W for Subspace of V;
 reserve v, u for Vector of V;
 reserve i for Element of INT.Ring;

theorem HM0:
  for R being Ring
  for X, Y be LeftMod of R, L be linear-transformation of X, Y
  holds L.(0.X) = 0.Y
  proof
    let R be Ring;
    let X,Y be LeftMod of R,
        L be linear-transformation of X, Y;
    thus L.(0.X) = L.(0.R * 0.X) by VECTSP_1:14
    .= 0.R * L.(0.X) by MOD_2:def 2
    .= 0.Y by VECTSP_1:14;
  end;
