A product and cubic-sum bound at sum two

Proved

WorkbookSource.base_9070

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

lean-workbooksource-checked

Let $x,y \geq 0$ with $x + y = 2$ . Prove that $xy(x^3+y^3)\le \frac{8}{3}.$

Source: InternLM Lean-Workbook, record lean_workbook_9070 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9070 (x y : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hxy : x + y = 2) : x * y * (x ^ 3 + y ^ 3) ≤ 8 / 3  :=  by sorry

Source