Let $M$ be a manifold, equipped with a (regular) foliation $\mathcal{F}$. Let $R \subset M \times M$ be an equivalence relation. Godement's theorem states under some conditions, $M/R$ is a smooth manifold. I'm trying to find sufficient conditions for the foliation $\mathcal{F}$ to induce a foliation on $M/R$.
At the moment, I'm not making any progress. A hint would be greatly appreciated.