Prove2Me

A weighted cyclic ratio lower bound with a triple-product correction

Proved
WorkbookSource.base_14206

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

lean-workbooksource-checked

Let a,b,c>0a,b,c >0 such that a+b+c=3.a+b+c=3. Prove that

a+2bc+b+2ca+c+2ab≥3(5−2abc)\frac{a+2b}{c} + \frac{b+2c}{a} + \frac{c+2a}{b} \ge 3(5-2abc)

Source: InternLM Lean-Workbook, record lean_workbook_14206 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_14206 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : (a + 2 * b) / c + (b + 2 * c) / a + (c + 2 * a) / b ≥ 3 * (5 - 2 * a * b * c)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_14206; Apache-2.0

View graph