A fourth-power inequality involving two symmetric sums

Proved

WorkbookSource.base_39721

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

lean-workbooksource-checked

Prove that $2(x+y+z)^4 \geq 9(xy+yz+zx)(x^2+y^2+z^2+xy+yz+zx)$ .

Source: InternLM Lean-Workbook, record lean_workbook_39721 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_39721 (x y z : ℝ) :
  2 * (x + y + z) ^ 4 ≥ 9 * (x * y + y * z + z * x) * (x ^ 2 + y ^ 2 + z ^ 2 + x * y + y * z + z * x)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_39721; Apache-2.0

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