A weighted fourth-power ratio bounds the cubic mean

Proved

WorkbookSource.base_29201

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

lean-workbooksource-checked

If $a, b, c>0$ prove that $\frac{a^4}{3a+b+c}+\frac{b^4}{3b+c+a}+\frac{c^4}{3c+a+b}\ge\frac{a^3+b^3+c^3}{5}$

Source: InternLM Lean-Workbook, record lean_workbook_29201 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_29201 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^4 / (3 * a + b + c) + b^4 / (3 * b + c + a) + c^4 / (3 * c + a + b)) ≥ (a^3 + b^3 + c^3) / 5  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_29201; Apache-2.0

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