A fourth-power ratio bounds a weighted pairwise product

Proved

WorkbookSource.plus_7046

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

lean-workbooksource-checked

Let $x,y,z>0$ ,prove that:

$\frac{(2y+z+x)^4(2z+x+y)^4}{(z+2x+y)^4}\geq 64yz(y+z)^2$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_7046 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_7046 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (2 * y + z + x) ^ 4 * (2 * z + x + y) ^ 4 / (z + 2 * x + y) ^ 4 ≥ 64 * y * z * (y + z) ^ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_7046; Apache-2.0

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