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It is shown that in the Bose-Fermi-Hubbard model which is used for adescription of the ultracold atomic boson-fermion mixture in the opticallattice, the $n_\text{B}\leqslant 2$ restriction enables one to analyze a moregeneral case of separated lobes Mott insulator in comparison with the case of$n_\text{B} \leqslant 1$ (hard-core bosons). It also showed that therestriction to no more than 2 bosons on site is enough to comprehend thestructure of $(\mu, |t_0|)$ diagrams at arbitrary $n^\text{b}$ values with anaccount of a possibility of the 1st order phase transition.

Bose-Fermi-Hubbard model in the truncated Hilbert space limit