  Let (X, g) be an arbitrary pseudo-riemannian manifold. A celebrated result by
Lovelock gives an explicit description of all second-order natural
(0,2)-tensors on X, that satisfy the conditions of being symmetric and
divergence-free. Apart from the dual metric, the Einstein tensor of g is the
simplest example.
  In this paper, we give a short and self-contained proof of this theorem,
simplifying the existing one by formalizing the notion of derivative of a
natural tensor.
