A two-variable quartic product is at most eight at fixed total two

Proved

WorkbookSource.base_27406

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

lean-workbooksource-checked

Let $x,y\geq 0$ and $x+y= 2.$ Show that $(x+1)y(x^2+y^2)\le 8$

Source: InternLM Lean-Workbook, record lean_workbook_27406 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_27406 (x y : ℝ) (h : x + y = 2) (hx : x ≥ 0) (hy : y ≥ 0) : (x + 1) * y * (x ^ 2 + y ^ 2) ≤ 8  :=  by sorry

Source