A cyclic fourth-power reciprocal sum bounds a cubed total

Proved

WorkbookSource.base_8483

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

lean-workbooksource-checked

Prove that for any a,b,c >0 we have $\frac{a^4}{b+c} + \frac{b^4}{a+c} + \frac{c^4}{a+b} \geq \frac{1}{18}. (a+b+c)^3$

Source: InternLM Lean-Workbook, record lean_workbook_8483 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_8483 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^4 / (b + c) + b^4 / (a + c) + c^4 / (a + b)) ≥ (1 / 18) * (a + b + c)^3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_8483; Apache-2.0

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