A cyclic fourth-power ratio sum bounds the triple product

Proved

WorkbookSource.base_11149

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

lean-workbooksource-checked

Prove that $\frac{a^4 + b^4}{b+c}+\frac{b^4 + c^4}{c+a}+\frac{c^4 + a^4}{a+b}\geq3abc$ For all positive reals $a$ , $b$ , and $c$ .

Source: InternLM Lean-Workbook, record lean_workbook_11149 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_11149 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^4 + b^4)/(b + c) + (b^4 + c^4)/(c + a) + (c^4 + a^4)/(a + b) ≥ 3 * a * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_11149; Apache-2.0

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