A cyclic ratio sum with a pairwise correction

Proved

WorkbookSource.base_51471

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

lean-workbooksource-checked

If $a,b,c>0 ,$ $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\geq \frac{9}{2}-\left(\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a} \right)$

Source: InternLM Lean-Workbook, record lean_workbook_51471 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_51471 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / b + b / c + c / a) ≥ 9 / 2 - (a / (a + b) + b / (b + c) + c / (c + a))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_51471; Apache-2.0

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