  Using the variational Monte-Carlo method we find that a relatively weak
long-range electron-phonon interaction induces a d-wave superconducting state
of doped Mott-Hubbard insulators and/or strongly-correlated metals with a
condensation energy significantly larger than can be obtained with Coulomb
repulsion only. Moreover, the superconductivity is shown to exist for infinite
on-site Coulomb repulsion, removing the requirement for additional mechanisms
such as spin fluctuations to mediate d-wave superconductivity. We argue that
the superconducting state is robust with respect to a more intricate choice of
the trial function and that the true origin of high-temperature
superconductivity lies in a proper combination of strong electron-electron
correlations with poorly screened Froehlich electron-phonon interaction.
