A cyclic ratio sum with a normalized triple-product correction

Proved

WorkbookSource.base_46701

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

lean-workbooksource-checked

If $a,b,c>0$ then: $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}\ge\frac{7}{2}-\frac{4abc}{(b+c)(c+a)(a+b)}$

Source: InternLM Lean-Workbook, record lean_workbook_46701 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_46701 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / b + b / c + c / a) ≥ 7 / 2 - 4 * a * b * c / (b + c) / (c + a) / (a + b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_46701; Apache-2.0

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