A cubic ratio sum with a triple-product correction

Proved

WorkbookSource.base_33608

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

lean-workbooksource-checked

For any three positive reals a, b, c, we have $\frac{a^3+3abc}{b+c}+\frac{b^3+3abc}{c+a}+\frac{c^3+3abc}{a+b} \ge 2(ab+bc+ca)$ .

Source: InternLM Lean-Workbook, record lean_workbook_33608 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_33608 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^3 + 3 * a * b * c) / (b + c) + (b^3 + 3 * a * b * c) / (c + a) + (c^3 + 3 * a * b * c) / (a + b) ≥ 2 * (a * b + b * c + c * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33608; Apache-2.0

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