A cyclic quadratic difference ratio at fixed sum three

Proved

WorkbookSource.base_16489

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

lean-workbooksource-checked

The corrected inequality is: For positive numbers $a, b, c$ with $a + b + c = 3$ , prove that: $\frac{a(a+b-2c)}{bc+1}+\frac{b(b+c-2a)}{ca+1}+\frac{c(c+a-2b)}{ab+1} \ge 0$

Source: InternLM Lean-Workbook, record lean_workbook_16489 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_16489 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (a * (a + b - 2 * c) / (b * c + 1) + b * (b + c - 2 * a) / (c * a + 1) + c * (c + a - 2 * b) / (a * b + 1)) ≥ 0  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16489; Apache-2.0

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