  The mean field Green function solution of the two-band singlet-hole Hubbard
model for high-$T\sb{c}$ superconductivity in cuprates (Plakida, N.M. et al.,
Phys. Rev. B51, 16599 (1995), JETP 97, 331 (2003)) involves expressions of
higher order correlation functions describing respectively the singlet hopping
and the superconducting pairing. Rigorous derivation of their values is
reported based on the finding that specific invariant classes of polynomial
Green functions in terms of the Wannier overlap coefficients $\nu\sb{ij}$
exist.
