A cubic-quadratic upper bound at total five

Proved

WorkbookSource.base_56621

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

lean-workbooksource-checked

Prove that $x^2y + z^2x + x^2 + (y - 1)^2 + 2xyz \leq 32$ given $x, y, z \geq 0$ and $x + y + z = 5$ .

Source: InternLM Lean-Workbook, record lean_workbook_56621 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_56621 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) (h : x + y + z = 5) : x^2*y + z^2*x + x^2 + (y - 1)^2 + 2*x*y*z ≤ 32  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_56621; Apache-2.0

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