  The Green function (GF) equation of motion technique for solving the
effective two-band Hubbard model of high-T_c superconductivity in cuprates
[N.M. Plakida et al., Phys. Rev. B, v. 51, 16599 (1995); JETP, v. 97, 331
(2003)] rests on the Hubbard operator (HO) algebra. We show that, if we take
into account the invariance to translations and spin reversal, the HO algebra
results in invariance properties of several specific correlation functions. The
use of these properties allows rigorous derivation and simplification of the
expressions of the frequency matrix (FM) and of the generalized mean field
approximation (GMFA) Green functions (GFs) of the model.
  For the normal singlet hopping and anomalous exchange pairing correlation
functions which enter the FM and GMFA-GFs, an approximation procedure based on
the identification and elimination of exponentially small quantities is
described. It secures the reduction of the correlation order to GMFA-GF
expressions.
