  We show that the differential structure of the orbit space of a proper action
of a Lie group on a smooth manifold is continuously reflexive. This implies
that the orbit space is a differentiable space in the sense of Smith, which
ensures that the orbit space has an exterior algebra of differenial forms,
which statisfies Smith's version of de Rham's theorem. Because the orbit space
is a locally closed subcartesian space, it has vector fields and their flows.
