A cyclic ratio sum with an asymmetric quadratic correction

Proved

WorkbookSource.base_14266

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

lean-workbooksource-checked

Let $a,b,c>0$ . Prove that $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{2ab}{a^2+b^2} \geq 4$

Source: InternLM Lean-Workbook, record lean_workbook_14266 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_14266 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a / b + b / c + c / a + 2 * a * b / (a ^ 2 + b ^ 2) ≥ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_14266; Apache-2.0

View graph