A cyclic sixth-degree comparison with triple-product corrections

Proved

WorkbookSource.base_55749

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

lean-workbooksource-checked

Let $a,b,c\in\mathbb{R}_+$ . Prove that $11(a^6+b^6+c^6)+40abc(ab^2+bc^2+ca^2)\geq 51abc(a^2b+b^2c+c^2a)$ .

Source: InternLM Lean-Workbook, record lean_workbook_55749 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_55749 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 11 * (a^6 + b^6 + c^6) + 40 * a * b * c * (a * b^2 + b * c^2 + c * a^2) ≥ 51 * a * b * c * (a^2 * b + b^2 * c + c^2 * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_55749; Apache-2.0

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