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second Hohenberg-Kohn theorem

Not surprisingly, after the first follows the second Hohenberg-Kohn theorem:

Someone tells you: “To me it looks like the 2nd theorem is a natural consequence of the 1st one, and not a separate independent theorem.” Do you agree? Explain the arguments you have to support your opinion in this forum:

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If you want to dig deeper (now or later), you may study this pedagogical lecture by Mel Levy on (mainly) the Hohenberg-Kohn theorems (part of the CECAM school on Teaching the Theory in DFT):

expected time: 20m
report time spent (page code AW03B)

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