A cyclic seventh-degree mixed-product lower bound

Proved

WorkbookSource.plus_24409

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

lean-workbooksource-checked

Let $a$ , $b$ and $c$ be non-negative numbers. Prove that: $a^6b+b^6c+c^6a\geq abc(a^2b^2+a^2c^2+b^2c^2)$

Source: InternLM Lean-Workbook, record lean_workbook_plus_24409 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_24409 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) : a^6 * b + b^6 * c + c^6 * a ≥ a * b * c * (a^2 * b^2 + a^2 * c^2 + b^2 * c^2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_24409; Apache-2.0

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