A cyclic sixth-degree power-sum comparison

Proved

WorkbookSource.base_50718

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

lean-workbooksource-checked

Prove this: $2x^{6}+2y^{6}+2z^{6}+x^{3}y^{3}+x^{3}z^{3}+y^{3}z^{3}\geq 3x^{4}y^{2}+3y^{4}z^{2}+3z^{4}x^{2},\ \forall x,y,z>0$

Source: InternLM Lean-Workbook, record lean_workbook_50718 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_50718 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : 2 * x ^ 6 + 2 * y ^ 6 + 2 * z ^ 6 + x ^ 3 * y ^ 3 + x ^ 3 * z ^ 3 + y ^ 3 * z ^ 3 ≥ 3 * x ^ 4 * y ^ 2 + 3 * y ^ 4 * z ^ 2 + 3 * z ^ 4 * x ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_50718; Apache-2.0

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