A seventh-degree cyclic polynomial inequality

Proved

WorkbookSource.base_8206

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

lean-workbooksource-checked

For $x,y,z > 0$ , prove that $\sum_{cyc} x^3(y^2 + z^2)^2 \ge xyz\sum_{cyc}xy(x + y)^2$

Source: InternLM Lean-Workbook, record lean_workbook_8206 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_8206 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : x^3 * (y^2 + z^2)^2 + y^3 * (z^2 + x^2)^2 + z^3 * (x^2 + y^2)^2 ≥ x * y * z * (x * y * (x + y)^2 + y * z * (y + z)^2 + z * x * (z + x)^2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_8206; Apache-2.0

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