A squared cyclic ratio sum with a triple-product correction

Proved

WorkbookSource.base_4237

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

lean-workbooksource-checked

Prove that all positive real number a,b,c

$\left(\frac {a}{b + c}\right)^2 + \left(\frac {b}{c + a}\right)^2 + \left(\frac {c}{a + b}\right)^2 + 10\cdot\frac {abc}{(a + b)(b + c)(c + a)}\geq2$

Source: InternLM Lean-Workbook, record lean_workbook_4237 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4237 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (b + c))^2 + (b / (c + a))^2 + (c / (a + b))^2 + 10 * (a * b * c) / ((a + b) * (b + c) * (c + a)) ≥ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4237; Apache-2.0

View graph