A cyclic sixth-degree bound involving triangle factors

Proved

WorkbookSource.base_4843

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

lean-workbooksource-checked

Let $a,b,c>0.$ Prove that $a^4b^2 + b^4c^2 + c^4a^2 \geq ( - a + b + c)(a - b + c)(a + b - c)(a^3 + b^3 + c^3).$

Source: InternLM Lean-Workbook, record lean_workbook_4843 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4843 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^4 * b^2 + b^4 * c^2 + c^4 * a^2 ≥ (- a + b + c) * (a - b + c) * (a + b - c) * (a^3 + b^3 + c^3)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4843; Apache-2.0

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