Prove2Me

A cyclic linear-product quadratic ratio bound

Proved
WorkbookSource.base_3528

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

lean-workbooksource-checked

Prove that for all positive reals a,b,ca,b,c

∑cyca(b+c)a2+(b+c)2≤65\sum_{cyc}\frac{a(b+c)}{a^2+ (b+c)^2} \leq \frac{6}{5}

Source: InternLM Lean-Workbook, record lean_workbook_3528 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_3528 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a * (b + c) / (a ^ 2 + (b + c) ^ 2) + b * (c + a) / (b ^ 2 + (c + a) ^ 2) + c * (a + b) / (c ^ 2 + (a + b) ^ 2)) ≤ 6 / 5  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3528; Apache-2.0

View graph