A sixth-degree product bound at fixed positive sum

Proved

WorkbookSource.plus_15891

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

lean-workbooksource-checked

Prove that: $a^2b^2(a^2 + b^2) < = 128$ , $a + b = 4$ and $a,b > 0$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_15891 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_15891 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a + b = 4) : a^2 * b^2 * (a^2 + b^2) ≤ 128   :=  by sorry

Source