A cyclic quadratic-difference ratio sum is nonnegative

Proved

WorkbookSource.base_2299

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

lean-workbooksource-checked

prove $\sum_{cyc} \frac{a^2-b^2}{a^2+b^2} \cdot a \geq 0$ where $a,b,c>0$ .

Source: InternLM Lean-Workbook, record lean_workbook_2299 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2299 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 - b^2) / (a^2 + b^2) * a + (b^2 - c^2) / (b^2 + c^2) * b + (c^2 - a^2) / (c^2 + a^2) * c ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2299; Apache-2.0

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