theorem Th41:
  L + ZeroLC(V) = L & ZeroLC(V) + L = L
proof
  thus L + ZeroLC(V) = L
  proof
    let v;
    thus (L + ZeroLC(V)).v = L.v + ZeroLC(V).v by Def10
      .= L.v + 0 by Th20
      .= L.v;
  end;
  hence thesis;
end;
