A cyclic ratio sum with a pairwise-product correction

Proved

WorkbookSource.base_4627

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

lean-workbooksource-checked

Let $a,b,c>0 .$ $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{24abc}{(b+c)(c+a)(a+b)}\geq 6$

Source: InternLM Lean-Workbook, record lean_workbook_4627 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_4627 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / b + b / c + c / a + 24 * a * b * c / (b + c) / (c + a) / (a + b)) ≥ 6  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4627; Apache-2.0

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