A symmetric cubic bound under a quadratic norm constraint

Proved

WorkbookSource.base_38274

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

lean-workbooksource-checked

Let three non-negative reals $x,y,z$ satisfy : $x^2+y^2+z^2=2$ . Prove that :

(x+y+z+2)(xy+yz+zx)-9xyz \le 4

Source: InternLM Lean-Workbook, record lean_workbook_38274 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_38274 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) (h : x^2 + y^2 + z^2 = 2) :
  (x + y + z + 2) * (x * y + y * z + z * x) - 9 * x * y * z ≤ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_38274; Apache-2.0

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