A weighted cyclic pair-product reciprocal lower bound

Proved

WorkbookSource.base_43680

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

lean-workbooksource-checked

If $a,b,c>0$ prove that: $\frac{a}{b(b+2c)}+\frac{b}{c(c+2a)}+\frac{c}{a(a+2b)}\ge\frac{3}{a+b+c}$

Source: InternLM Lean-Workbook, record lean_workbook_43680 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_43680 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (b * (b + 2 * c)) + b / (c * (c + 2 * a)) + c / (a * (a + 2 * b))) ≥ 3 / (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_43680; Apache-2.0

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