A quartic bound with a triple-product correction at fixed sum two

Proved

WorkbookSource.base_55925

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

lean-workbooksource-checked

Let $x,y,z\ge0$ such that $x+y+z=2$ . Prove that $x^2y^2+y^2z^2+z^2x^2-2xyz\leq 1$

Source: InternLM Lean-Workbook, record lean_workbook_55925 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_55925 (x y z : ℝ) (h : x + y + z = 2) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) : x^2 * y^2 + y^2 * z^2 + z^2 * x^2 - 2 * x * y * z ≤ 1  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_55925; Apache-2.0

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