A cyclic product reciprocal lower bound

Proved

WorkbookSource.base_3633

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

lean-workbooksource-checked

Let $a, b, c>0$ .

\frac{1}{b(a+b)}+\frac{1}{c(b+c)}+\frac{1}{a(a+c)}\geq \frac{9}{2(ab+bc+ca)}.

Source: InternLM Lean-Workbook, record lean_workbook_3633 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3633 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (1 / (b * (a + b)) + 1 / (c * (b + c)) + 1 / (a * (a + c))) ≥ 9 / (2 * (a * b + b * c + c * a))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3633; Apache-2.0

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