A cyclic ratio sum has a normalized quadratic refinement

Proved

WorkbookSource.base_32348

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

lean-workbooksource-checked

Let $a,b,c$ be positive numbers. Prove that: $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \ge \frac{14(a^2+b^2+c^2)}{(a+b+c)^2}-2$

Source: InternLM Lean-Workbook, record lean_workbook_32348 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_32348 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / b + b / c + c / a) ≥ (14 * (a ^ 2 + b ^ 2 + c ^ 2)) / (a + b + c) ^ 2 - 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_32348; Apache-2.0

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