A cyclic fourth-power ratio bounds half the cubic sum

Proved

WorkbookSource.base_57256

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

lean-workbooksource-checked

Prove that $\frac{a^4}{a+b}+\frac{b^4}{b+c}+\frac{c^4}{c+a}\geq \frac{a^3+b^3+c^3}{2}$ . $\forall a,b,c> 0$

Source: InternLM Lean-Workbook, record lean_workbook_57256 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_57256 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^4 / (a + b) + b^4 / (b + c) + c^4 / (c + a) ≥ (a^3 + b^3 + c^3) / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_57256; Apache-2.0

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