A sixth-power bound for three quadratic factors

Proved

WorkbookSource.base_23054

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

lean-workbooksource-checked

Let $x,y,z \ge 0$ . Prove that : $\left (x+y+z \right )^6 \ge \left (8x^2+yz \right )\left (8y^2+xz \right )\left (8z^2+xy \right )$

Source: InternLM Lean-Workbook, record lean_workbook_23054 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_23054 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : (x + y + z) ^ 6 ≥ (8 * x ^ 2 + y * z) * (8 * y ^ 2 + x * z) * (8 * z ^ 2 + x * y)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_23054; Apache-2.0

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