The fourth-power sum bounds a cyclic cubic ratio sum

Proved

WorkbookSource.plus_77676

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

lean-workbooksource-checked

THQ146.Let $a,b,c$ be positive real numbers . Prove that $a^4+b^4+c^4\ge \frac{a^3(b^2+c^2)}{b+c}+\frac{b^3(c^2+a^2)}{c+a}+\frac{c^3(a^2+b^2)}{a+b}$

Source: InternLM Lean-Workbook, record lean_workbook_plus_77676 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_77676 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^4 + b^4 + c^4 ≥ a^3 * (b^2 + c^2) / (b + c) + b^3 * (c^2 + a^2) / (c + a) + c^3 * (a^2 + b^2) / (a + b)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_77676; Apache-2.0

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