I agree

[embotter]

All physics is about minimising a cost function (free energy, action …). So it is no surprise that the density of the ground state has the lowest energy. Hohenberg-Kohn’s first theorem states that this cofiguration is unique, as expected from general knowledge of physics. So I wouldn’t really say it’s a consequence, but I don’t think it’s worth giving the second theorem its ‘own name’.
Or am I missing something?

[Author]

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