A symmetric sixth-degree comparison with triple-product terms

Proved

WorkbookSource.plus_58495

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

lean-workbooksource-checked

Let: $x,y,z \geq 0$ . Prove that: $5(x^{6}+y^{6}+z^{6})+13(x^{3}y^{3}+y^{3}z^{3}+z^{3}x^{3})\geq 27x^{2}y^{2}z^{2}+9xyz(x^{3}+y^{3}+z^{3})$

Source: InternLM Lean-Workbook, record lean_workbook_plus_58495 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_58495 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) : 5 * (x ^ 6 + y ^ 6 + z ^ 6) + 13 * (x ^ 3 * y ^ 3 + y ^ 3 * z ^ 3 + z ^ 3 * x ^ 3) ≥ 27 * x ^ 2 * y ^ 2 * z ^ 2 + 9 * x * y * z * (x ^ 3 + y ^ 3 + z ^ 3)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_58495; Apache-2.0

View graph