A cyclic quadratic difference ratio sum is at most three

Proved

WorkbookSource.base_12820

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

lean-workbooksource-checked

if $a,b,c$ are positive number,then $\sum_{cyc}\frac {4a^2 - b^2 - c^2}{a(b + c)} \leq 3$

Source: InternLM Lean-Workbook, record lean_workbook_12820 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12820 {a b c : ℝ} (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (4 * a ^ 2 - b ^ 2 - c ^ 2) / (a * (b + c)) + (4 * b ^ 2 - c ^ 2 - a ^ 2) / (b * (c + a)) + (4 * c ^ 2 - a ^ 2 - b ^ 2) / (c * (a + b)) ≤ 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12820; Apache-2.0

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