lean_workbook_plus_37004

Proved

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

Prove that $8(x^4+y^4+xy^3+yx^3) \leq 9(x^4+y^4+2x^2y^2)$ for all positive real numbers $x,y$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_37004 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) : 8 * (x^4 + y^4 + x*y^3 + y*x^3) ≤ 9 * (x^4 + y^4 + 2*x^2*y^2)   :=  by sorry

Source