Bound pair states beyond the condensate for Fermi systems below T_c: the pseudogap as a necessary condition

As is known, the 1/q^2 theorem of Bogoliubov asserts that the mean density of the fermion pair states with the total momentum q obeys the inequality n_q > C/q^2 (q \to 0) in the case of the Fermi system taken at nonzero temperature and in the superconducting state provided the interaction term of its Hamiltonian is locally gauge invariant. With the principle of correlation weakening it is proved in this paper that the reason for the mentioned singular behaviour of n_q is the presence of the bound states of particle pairs with nonzero total momenta. Thus, below the temperature of the superconducting phase transition there always exist the bound states of the fermion couples beyond the pair condensate. If the pseudogap observed in the normal phase of the high-T_c superconductors is stipulated by the presence of the electron bound pairs, then the derived result suggests, in a model-independent manner, that the pseudogap survives below T_c.