A cyclic ratio sum with a triple-product correction

Proved

WorkbookSource.plus_48343

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

lean-workbooksource-checked

Let $a,b,c>0$ and $a+b+c=3$ . Prove that :

\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+2abc\ge 5

Source: InternLM Lean-Workbook, record lean_workbook_plus_48343 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_48343 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a / b + b / c + c / a + 2 * a * b * c ≥ 5   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_48343; Apache-2.0

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