We discuss the predictions of the Simple equation for the ground state energy, condensate fraction, two-point correlation function and momentum distribution. We prove that the ground state energy coincides with that of the many-body Bose gas at low and at high densities. Furthermore, we prove that the condensate fraction agrees with Bogolyubov theory in the low-density regime, which shows that the Simple equation predicts Bose-Einstein condensation. We state theorems that show that two-point correlation function decays at the same rate as that predicted by Bogolyubov theory, and the momentum distribution agrees with the prediction of Bogolyubov theory in a certain range of momenta.