A cubic sum with a pair-product rational correction

Proved

WorkbookSource.base_46202

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

lean-workbooksource-checked

For $a,b,c$ positive reals

$\sum a^3 + 3abc + 2\sum \frac {a^2b^2}{(a + b)} \geq \frac {3}{2}\sum ab(a + b)$

Source: InternLM Lean-Workbook, record lean_workbook_46202 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_46202 {a b c : ℝ} (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : a^3 + b^3 + c^3 + 3 * a * b * c + 2 * (a^2 * b^2 / (a + b) + b^2 * c^2 / (b + c) + c^2 * a^2 / (c + a)) ≥ 3 / 2 * (a * b * (a + b) + b * c * (b + c) + c * a * (c + a))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_46202; Apache-2.0

View graph