A sixth-power bound for three mixed quadratic factors

Proved

WorkbookSource.base_22823

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

lean-workbooksource-checked

Let $x;y;z\ge 0$ Prove that $(x+y+z)^6\ge 64(x^2+yz)(y^2+xz)(z^2+xy)$

Source: InternLM Lean-Workbook, record lean_workbook_22823 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_22823 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : (x + y + z) ^ 6 ≥ 64 * (x ^ 2 + y * z) * (y ^ 2 + z * x) * (z ^ 2 + x * y)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_22823; Apache-2.0

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