A cyclic ratio lower bound involving three symmetric products

Proved

WorkbookSource.base_10878

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

lean-workbooksource-checked

For any positive real numbers $a,\ b$ and $c$ , $\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a} \ge \frac{27abc}{2(a+b+c)(ab+bc+ca)}$

Source: InternLM Lean-Workbook, record lean_workbook_10878 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_10878 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / (a + b) + b / (b + c) + c / (c + a)) ≥ 27 * a * b * c / (2 * (a + b + c) * (a * b + b * c + c * a))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_10878; Apache-2.0

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