A cyclic ratio sum with a cubic reciprocal correction

Proved

WorkbookSource.base_31981

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

lean-workbooksource-checked

For $a,b,c > 0$ Show that $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3abc}{a^{2}b+b^{2}c+c^{2}a}\geq 4$

Source: InternLM Lean-Workbook, record lean_workbook_31981 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_31981 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / b + b / c + c / a + 3 * a * b * c / (a ^ 2 * b + b ^ 2 * c + c ^ 2 * a)) ≥ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_31981; Apache-2.0

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