A fourth-power bound for a cyclic cubic product sum

Proved

WorkbookSource.base_12168

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

lean-workbooksource-checked

Prove that, for all positive real numbers $x, y$ and $z$ , $(x+y+z)^4\geq \frac{256}{27}(x^3y+y^3z+z^3x)+\frac{473}{27}(x+y+z)xyz$

Source: InternLM Lean-Workbook, record lean_workbook_12168 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_12168 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) : (x + y + z) ^ 4 ≥ (256 / 27) * (x ^ 3 * y + y ^ 3 * z + z ^ 3 * x) + (473 / 27) * (x + y + z) * x * y * z  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_12168; Apache-2.0

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