theorem
  for R being Ring
  for V be LeftMod of R, v be Element of V holds (ZeroLC(V)).v = 0.R
  proof
    let R be Ring;
    let V be LeftMod of R, v be Element of V;
    Carrier (ZeroLC(V)) = {} & not v in {} by VECTSP_6:def 3;
    hence thesis;
  end;
