A cyclic fifth-degree sum bounds a symmetric product

Proved

WorkbookSource.base_18620

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

lean-workbooksource-checked

If x,y,z>0,then $x^4y+y^4z+z^4x\geq \frac{1}{3}(x+y+z)^2xyz$

Source: InternLM Lean-Workbook, record lean_workbook_18620 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_18620 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : x ^ 4 * y + y ^ 4 * z + z ^ 4 * x ≥ (1 / 3) * (x + y + z) ^ 2 * x * y * z  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18620; Apache-2.0

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