theorem
  for R being comRing for V being RightMod of R for L being
  Linear_Combination of V holds L + ZeroLC(V) = L & ZeroLC(V) + L = L
proof
  let R be comRing;
  let V be RightMod of R;
  let L be Linear_Combination of V;
  thus L + ZeroLC(V) = L
  proof
    let v be Vector of V;
    thus (L + ZeroLC(V)).v = L.v + ZeroLC(V).v by Def9
      .= L.v + 0.R by Th18
      .= L.v by RLVECT_1:4;
  end;
  hence thesis by Th39;
end;
