A symmetric quartic inequality for positive variables

Proved

WorkbookSource.base_2405

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

If $x,y,z>0$ , prove that $\sum x^4+xyz(x+y+z)\ge 2\sum x^2y^2$ .

Source: InternLM Lean-Workbook, record lean_workbook_2405 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2405 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) : x ^ 4 + y ^ 4 + z ^ 4 + x * y * z * (x + y + z) ≥ 2 * (x ^ 2 * y ^ 2 + y ^ 2 * z ^ 2 + z ^ 2 * x ^ 2)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2405; Apache-2.0

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