Projection and support

For the projection $\pi :Y\times Z\to Y$, fiber integration of $h\in {\mathcal{D}}^{\prime }(Y\times Z)$ is defined when $\pi {|}_{\mathrm{supp}h}$ is proper. Its wavefront bound is

See BDHoperations (Theorem 6.3). Properness is a support requirement, not a wavefront transversality requirement.