A squared cubic sum bounds a pairwise sum times a fourth power

Proved

WorkbookSource.plus_40879

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

lean-workbooksource-checked

For $a,b,c\geq 0$ then $(ab+ac+bc)(a+b+c)^4\leq 27(a^3+b^3+c^3)^2$

Source: InternLM Lean-Workbook, record lean_workbook_plus_40879 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_40879 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : (a * b + a * c + b * c) * (a + b + c) ^ 4 ≤ 27 * (a ^ 3 + b ^ 3 + c ^ 3) ^ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_40879; Apache-2.0

View graph