  We prove the absence of a direct quantum phase transition between a
superfluid and a Mott insulator in a bosonic system with generic, bounded
disorder. We also prove compressibility of the system on the
superfluid--insulator critical line and in its neighborhood. These conclusions
follow from a general {\it theorem of inclusions} which states that for any
transition in a disordered system one can always find rare regions of the
competing phase on either side of the transition line. Quantum Monte Carlo
simulations for the disordered Bose-Hubbard model show an even stronger result,
important for the nature of the Mott insulator to Bose glass phase transition:
The critical disorder bound, $\Delta_c$, corresponding to the onset of
disorder-induced superfluidity, satisfies the relation $\Delta_c > E_{\rm
g/2}$, with $E_{\rm g/2}$ the half-width of the Mott gap in the pure system.
