A cyclic quartic sum times the quadratic sum bounds pairwise products

Proved

WorkbookSource.base_36028

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

lean-workbooksource-checked

Let $x,y,z\geq 0$ ,prove that: $(x^3y+y^3z+z^3x)(x^2+y^2+z^2)\geq (xy+zx+yz)(y^2z^2+z^2x^2+x^2y^2).$

Source: InternLM Lean-Workbook, record lean_workbook_36028 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_36028 (x y z : ℝ) (hx : x ≥ 0) (hy : y ≥ 0) (hz : z ≥ 0) : (x^3 * y + y^3 * z + z^3 * x) * (x^2 + y^2 + z^2) ≥ (x * y + y * z + z * x) * (y^2 * z^2 + z^2 * x^2 + x^2 * y^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_36028; Apache-2.0

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