A squared fourth-power sum bounds a fifth-power triple product

Proved

WorkbookSource.base_49309

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

lean-workbooksource-checked

Prove that $(x^{4}+y^{4}+z^{4})^{2}\geq 3xyz(x^{5}+y^{5}+z^{5})$ given $x,y,z\geq 0$ .

Source: InternLM Lean-Workbook, record lean_workbook_49309 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_49309 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : (x^4 + y^4 + z^4)^2 ≥ 3 * x * y * z * (x^5 + y^5 + z^5)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_49309; Apache-2.0

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