  We prove a Poincare lemma for a set of r smooth functions on a 2n-dimensional
smooth manifold satisfying a commutation relation determined by r singular
vector fields associated to a Cartan subalgebra of $\frak{sp}(2r,\mathbb R)$.
This result has a natural interpretation in terms of the cohomology associated
to the infinitesimal deformation of a completely integrable system.
