A cyclic sixth-degree inequality with a triple-product factor

Proved

WorkbookSource.base_30699

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers prove the following inequality

a^2 b^4 +b^2c^4+ c^2 a^4 +6 a^2 b^2 c^2 \geq 3a b c \left(a b^2+b c^2 +c a^2\right)

Source: InternLM Lean-Workbook, record lean_workbook_30699 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_30699 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^2 * b^4 + b^2 * c^4 + c^2 * a^4 + 6 * a^2 * b^2 * c^2 ≥ 3 * a * b * c * (a * b^2 + b * c^2 + c * a^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30699; Apache-2.0

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