A normalized cubic sum with a triple-product correction

Proved

WorkbookSource.base_16937

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

lean-workbooksource-checked

Prove that for $a, b, c > 0$ ,

$\frac{a^3 + b^3 + c^3}{3abc} + \frac{24abc}{(a + b)(b + c)(c + a)} \geq 4$

Source: InternLM Lean-Workbook, record lean_workbook_16937 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_16937 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 + b^3 + c^3) / (3 * a * b * c) + (24 * a * b * c) / ((a + b) * (b + c) * (c + a)) ≥ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_16937; Apache-2.0

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