Bad screening and applicability of Migdal's theorem to layered cuprates

A proof is presented, that in the model of high-Tc layered cuprates with long-range phonon-mediated attraction, due to bad screening of Coulomb forces, the “Migdal's theorem”, permitting to neglect vertex corrections, still holds, despite the absence of the small “adiabatic parameter”. The calculation of the superconducting critical temperature for this model permits to explain the high values of Tc observed in experiment.