A cyclic ratio sum has a product lower bound at fixed sum three

Proved

WorkbookSource.base_39559

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

lean-workbooksource-checked

If $a, b, c >0, a+b+c=3$ , then $\frac{a}{b}+ \frac{b}{c}+ \frac{c}{a} \ge \frac{12}{3abc+1}$

Source: InternLM Lean-Workbook, record lean_workbook_39559 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_39559 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a / b + b / c + c / a ≥ 12 / (3 * a * b * c + 1)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_39559; Apache-2.0

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