A cyclic rational difference sum at fixed sum three is nonnegative

Proved

WorkbookSource.plus_3930

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

lean-workbooksource-checked

Let a,b,c>0 such that $a + b + c = 3$ . Prove that $\sum {\frac{{a\left( {c - b} \right)}}{{ab + 1}}} \ge 0$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_3930 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_3930 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : a * (c - b) / (a * b + 1) + b * (a - c) / (b * c + 1) + c * (b - a) / (c * a + 1) ≥ 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_3930; Apache-2.0

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