A cyclic cubic reciprocal-sum comparison

Proved

WorkbookSource.base_231

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

lean-workbooksource-checked

Let $a$ , $b$ and $c$ be positive numbers. Prove that: $\frac{a^{3}}{b+2c}+\frac{b^{3}}{c+2a}+\frac{c^{3}}{a+2b}\geq\frac{a^{3}+b^{3}+c^{3}}{a+b+c}$

Source: InternLM Lean-Workbook, record lean_workbook_231 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_231 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 / (b + 2 * c) + b^3 / (c + 2 * a) + c^3 / (a + 2 * b)) ≥ (a^3 + b^3 + c^3) / (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_231; Apache-2.0

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