  We show that if a smooth multiplicative subbundle $S\subseteq TG$ on a
groupoid $G\rr P$ is involutive and satisfies completeness conditions, then its
leaf space $G/S$ inherits a groupoid structure over the space of leaves of
$TP\cap S$ in $P$.
  As an application, a special class of Dirac groupoids is shown to project by
forward Dirac maps to Poisson groupoids.
