A polynomial sum of squares inequality

Proved

WorkbookSource.problem_22076

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that for any $x$ , $y$ and $z$

$x^4+1+y^4+z^2+2x^2\ge 2x^2y^2+2xz+2x$

Source: InternLM Lean-Workbook, record lean_workbook_22076 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_22076 (x y z : ℝ) : x^4 + 1 + y^4 + z^2 + 2 * x^2 ≥ 2 * x^2 * y^2 + 2 * x * z + 2 * x  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_22076; Apache-2.0

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