A fifth-degree symmetric product inequality

Proved

WorkbookSource.plus_14843

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that for $a,b,c>0$

2(a^3+b^3+c^3)(ab+bc+ca)\ge3abc(3a^2+3b^2+3c^2-ab-bc-ca)

Source: InternLM Lean-Workbook, record lean_workbook_plus_14843 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_14843 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 2 * (a ^ 3 + b ^ 3 + c ^ 3) * (a * b + b * c + c * a) ≥ 3 * a * b * c * (3 * (a ^ 2 + b ^ 2 + c ^ 2) - (a * b + b * c + c * a))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_14843; Apache-2.0

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