A cyclic cubic-over-quadratic sum bounds one third of the total

Proved

WorkbookSource.base_9129

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

lean-workbooksource-checked

Let $a,b,c > 0$ .

\frac {a^3}{2a^2 + b^2} + \frac {b^3}{2b^2 + c^2} + \frac {c^3}{2c^2 + a^2}\geqslant \frac {a + b + c}{3}

Source: InternLM Lean-Workbook, record lean_workbook_9129 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9129 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 / (2 * a^2 + b^2) + b^3 / (2 * b^2 + c^2) + c^3 / (2 * c^2 + a^2)) ≥ (a + b + c) / 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9129; Apache-2.0

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