A squared cyclic ratio sum bounds an asymmetric product

Proved

WorkbookSource.base_21608

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

lean-workbooksource-checked

Let be given positive real numbers $a,b,c$ ,prove that $(\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+1)^2\ge(2a+b+c)(\frac{2}{a}+\frac{1}{b}+\frac{1}{c}) .$

Source: InternLM Lean-Workbook, record lean_workbook_21608 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_21608 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a / b + b / c + c / a + 1) ^ 2 ≥ (2 * a + b + c) * (2 / a + 1 / b + 1 / c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21608; Apache-2.0

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