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Prove EntropyPhotonNumber (openai/math family 273: The entropy photon-number inequality) in Lean 4 with…

Prove EntropyPhotonNumber (openai/math family 273: The entropy photon-number inequality) in Lean 4 with…: a task in openai/math as Harbor environments (Harbor dataset). Context: this statement belongs to family 273 of the release, The entropy photon-number inequality (Mathematical physics). The…

The task

Context: this statement belongs to family 273 of the release, *The entropy photon-number inequality* (Mathematical physics). The family as a whole: Proves the entropy photon-number inequality for beam-splitter mixing of two independent finite-energy bosonic inputs in any finite number of modes: the…

Part of raising-heart/openai-math.