A cyclic quartic upper bound on a sphere

Proved

WorkbookSource.base_44986

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

lean-workbooksource-checked

Using Vasile's inequality, prove that for $x, y, z \in \mathbb{R}$ and $x^2 + y^2 + z^2 = 3$ , $x^3y + y^3z + z^3x \leq 3$ .

Source: InternLM Lean-Workbook, record lean_workbook_44986 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_44986 (x y z : ℝ) (h : x ^ 2 + y ^ 2 + z ^ 2 = 3) :
  x ^ 3 * y + y ^ 3 * z + z ^ 3 * x ≤ 3  :=  by sorry

Source