A symmetric quartic inequality with a triple-product term

Proved

WorkbookSource.base_44753

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

lean-workbooksource-checked

If $x,y,z$ are real numbers, then

$2(xy+yz+zx)(x^2+y^2+z^2)\le 3xyz(x+y+z)+4(x^4+y^4+z^4).$

Source: InternLM Lean-Workbook, record lean_workbook_44753 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_44753 (x y z : ℝ) : 2 * (x * y + y * z + z * x) * (x ^ 2 + y ^ 2 + z ^ 2) ≤ 3 * x * y * z * (x + y + z) + 4 * (x ^ 4 + y ^ 4 + z ^ 4)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_44753; Apache-2.0

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