A product comparison for shifted quadratic factors

Proved

WorkbookSource.base_30380

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

lean-workbooksource-checked

Let $x,y,z \in \mathbb{R}$ and greater than or equal to $1$ . Prove, $\prod (x^2-2x+2) \le (xyz)^2-2xyz+2$

Source: InternLM Lean-Workbook, record lean_workbook_30380 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_30380 (x y z : ℝ) (hx : 1 ≤ x) (hy : 1 ≤ y) (hz : 1 ≤ z) : (x^2 - 2 * x + 2) * (y^2 - 2 * y + 2) * (z^2 - 2 * z + 2) ≤ (x * y * z)^2 - 2 * x * y * z + 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_30380; Apache-2.0

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