lean_workbook_plus_32419

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

If $x,\,y$ are non-negattive numbers, then \n $xy(x^2+y^2) \leqslant 2+2xy(x+y)(x+y-2).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_32419 (x y : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) : x * y * (x ^ 2 + y ^ 2) ≤ 2 + 2 * x * y * (x + y) * (x + y - 2)   :=  by sorry

Source