Bad Screening and Applicability of Migdal's Theorem to Layered Cuprates

A proof is presented, that in the model of high-T$_{c }$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 T$_{c}$ observed in experiment. This work was supported by the Department of Energy under the contracts {\#} W-31-109-ENG-38.