  A classical result in differential geometry states that for a free and proper
Lie group action, the quotient map to the orbit space induces an isomorphism
between the de Rham complex of differential forms on the orbit space and the
basic differential forms on the original manifold. In this paper, this result
is generalized to the case of a proper Lie groupoid, in which the orbit space
is equipped with the quotient diffeological structure. As an application of
this, we obtain a de Rham theorem for the de Rham complex on the orbit space.
