A product of mixed cyclic ratios is at least 343 over eight

Proved

WorkbookSource.base_33335

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

lean-workbooksource-checked

Let $a,b,c>0.$ Prove that

\left(\frac{c+2a}{b}+\frac{c}{a+b}\right)\left(\frac{a+2b}{c}+\frac{a}{b+c}\right)\left(\frac{b+2c}{a}+\frac{b}{c+a}\right)\geq \frac{343}{8}

Source: InternLM Lean-Workbook, record lean_workbook_33335 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_33335 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : ((c + 2 * a) / b + c / (a + b)) * ((a + 2 * b) / c + a / (b + c)) * ((b + 2 * c) / a + b / (c + a)) ≥ 343 / 8  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33335; Apache-2.0

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