A cyclic power-ratio comparison

Proved

WorkbookSource.base_31228

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

lean-workbooksource-checked

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

Source: InternLM Lean-Workbook, record lean_workbook_31228 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_31228 {a b c : ℝ} (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 / b^3 + b^2 / c^3 + c^2 / a^3) ≥ (a / b^2 + b / c^2 + c / a^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_31228; Apache-2.0

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