A cyclic linear difference reciprocal sum upper bound

Proved

WorkbookSource.plus_33926

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

lean-workbooksource-checked

Let $a,b,c$ be positive reals. Then $\sum_{cycl}\frac{a+b-c}{a^2+ab+b^2} \le \frac{3}{a+b+c}$

Source: InternLM Lean-Workbook, record lean_workbook_plus_33926 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_33926 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b - c) / (a ^ 2 + a * b + b ^ 2) + (b + c - a) / (b ^ 2 + b * c + c ^ 2) + (c + a - b) / (c ^ 2 + c * a + a ^ 2) ≤ 3 / (a + b + c)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_33926; Apache-2.0

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