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Prove SymmetricPolar (openai/math family 087: The Mahler conjectures and symplectic width) in Lean 4 with…

Prove SymmetricPolar (openai/math family 087: The Mahler conjectures and symplectic width) in Lean 4 with…: a task in openai/math as Harbor environments (Harbor dataset). Context: this statement belongs to family 087 of the release, The Mahler conjectures and symplectic width (Convex and metric…

The task

Context: this statement belongs to family 087 of the release, *The Mahler conjectures and symplectic width* (Convex and metric geometry). The family as a whole: Resolves the symmetric and nonsymmetric geometric Mahler conjectures in every dimension, with Hanner polytopes and simplices as the respective volume-product…

Part of raising-heart/openai-math.