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Prove OAI.HoneycombForce.maxPartition submultiplicative using the supplied Honeycomb Free Energy source…

Prove OAI.HoneycombForce.maxPartition submultiplicative using the supplied Honeycomb Free Energy source…: a task in openai-math-lemmas (Harbor dataset). Prove this supporting lemma from OpenAI's Honeycomb Free Energy proof in Lean 4. Earlier definitions and already proved lemmas are supplied…

The task

Prove this supporting lemma from OpenAI's Honeycomb Free Energy proof in Lean 4. Earlier definitions and already proved lemmas are supplied below. The only missing proof is `OAI.HoneycombForce.maxPartition_submultiplicative`. Write the complete source below to `/workspace/Submission.lean`, then replace its `by sorry`…

Part of bkhtmm/openai-math-lemmas.