A quartic and sextic cyclic product inequality

Proved

WorkbookSource.base_26618

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

lean-workbooksource-checked

Let $x,y,z \in R$ ,prove that: $C.(x^4+y^4+z^4)(x^2y^4+y^2z^4+z^2x^4)\geq (xy^4+yz^4+zx^4)^2.$

Source: InternLM Lean-Workbook, record lean_workbook_26618 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_26618 (x y z : ℝ) : (x^4 + y^4 + z^4) * (x^2 * y^4 + y^2 * z^4 + z^2 * x^4) ≥ (x * y^4 + y * z^4 + z * x^4)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_26618; Apache-2.0

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