A cyclic quadratic ratio bounds a normalized cubic sum

Proved

WorkbookSource.base_14423

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

lean-workbooksource-checked

Prove that for positives $a$ , $b$ , and $c$ : $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \ge \frac{3(a^3 + b^3 + c^3)}{a^2 + b^2 + c^2}$

Source: InternLM Lean-Workbook, record lean_workbook_14423 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_14423 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 / b + b^2 / c + c^2 / a) ≥ (3 * (a^3 + b^3 + c^3)) / (a^2 + b^2 + c^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_14423; Apache-2.0

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