A sixth-degree inequality with a squared cyclic-difference correction

Proved

WorkbookSource.plus_39181

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

lean-workbooksource-checked

If $x,y,z$ are positive numbers, then $(x^2+y^2+z^2)^3 \geqslant 8(x^3y^3+y^3z^3+z^3x^3)+12(x-y)^2(y-z)^2(z-x)^2.$ (CHNSYWmath)

Source: InternLM Lean-Workbook, record lean_workbook_plus_39181 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_39181 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : (x^2 + y^2 + z^2)^3 ≥ 8 * (x^3 * y^3 + y^3 * z^3 + z^3 * x^3) + 12 * (x - y)^2 * (y - z)^2 * (z - x)^2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_39181; Apache-2.0

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