  It is demonstrated that the original reductio ad absurdum proof of the
generalization of the Hohenberg-Kohn theorem for ensembles of fractionally
occupied states for isolated many-electron Coulomb systems with Coulomb-type
external potentials by Gross et al. [Phys. Rev. A 37, 2809 (1988)] is
self-contradictory since the to-be-refuted assumption (negation) regarding the
ensemble one-electron densities and the assumption about the external
potentials are logically incompatible to each other due to the Kato
electron-nuclear cusp theorem. It is however proved that the Kato theorem
itself provides a satisfactory proof of this theorem.
