A weighted linear product ratio is at least one hundred twenty-eight thirds

Proved

WorkbookSource.base_44837

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers . Prove that

\frac {(2a+b)(b+2c)(a+3b+c)}{abc} \geq \frac {128} {3}

Source: InternLM Lean-Workbook, record lean_workbook_44837 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_44837 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (2 * a + b) * (b + 2 * c) * (a + 3 * b + c) / (a * b * c) ≥ 128 / 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_44837; Apache-2.0

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