A cyclic quadratic difference ratio sum is nonnegative

Proved

WorkbookSource.base_16078

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

lean-workbooksource-checked

Let $a,b,c> 0$ Prove that: $\sum \frac{(2a-b-c)(b+c)}{b^2+c^2} \ge 0$

Source: InternLM Lean-Workbook, record lean_workbook_16078 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_16078 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (2 * a - b - c) * (b + c) / (b * b + c * c) + (2 * b - c - a) * (c + a) / (c * c + a * a) + (2 * c - a - b) * (a + b) / (a * a + b * b) ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16078; Apache-2.0

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