A product of three quadratic forms bounds a cubic symmetric product

Proved

WorkbookSource.base_30032

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

oh yes . Why don't I think it early? >So, can you prove that this inequality $(a^2+ab+b^2)(b^2+bc+c^2)(c^2+ca+a^2)\ge abc(a+b+c)^3$

Source: InternLM Lean-Workbook, record lean_workbook_30032 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_30032 (a b c : ℝ) : (a^2 + b * a + b^2) * (b^2 + c * b + c^2) * (c^2 + a * c + a^2) ≥ a * b * c * (a + b + c)^3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30032; Apache-2.0

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