A sixth-degree product inequality for three alternating quadratic factors

Proved

WorkbookSource.base_24900

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

lean-workbooksource-checked

Let $a,b,c$ be real numbers. Prove the inequality:

3(a^2-ab+b^2)(b^2-bc+c^2)(c^2-ac+a^2)\geq a^3b^3+b^3c^3+c^3a^3

Source: InternLM Lean-Workbook, record lean_workbook_24900 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_24900 (a b c : ℝ) : 3 * (a^2 - a * b + b^2) * (b^2 - b * c + c^2) * (c^2 - c * a + a^2) ≥ a^3 * b^3 + b^3 * c^3 + c^3 * a^3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_24900; Apache-2.0

View graph