A fifteenth-degree symmetric inequality with a triple-product correction

Proved

WorkbookSource.base_56382

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

lean-workbooksource-checked

Prove that for positive variables $x$ , $y$ , and $z$ , the inequality $x^{15} + y^{15} + z^{15} + 3x^5y^5z^5 \geq x^6y^5z^4 + x^6y^4z^5 + x^5y^6z^4 + x^4y^6z^5 + x^5y^4z^6 + x^4y^5z^6$ holds.

Source: InternLM Lean-Workbook, record lean_workbook_56382 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_56382 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : x ^ 15 + y ^ 15 + z ^ 15 + 3 * x ^ 5 * y ^ 5 * z ^ 5 ≥ x ^ 6 * y ^ 5 * z ^ 4 + x ^ 6 * y ^ 4 * z ^ 5 + x ^ 5 * y ^ 6 * z ^ 4 + x ^ 4 * y ^ 6 * z ^ 5 + x ^ 5 * y ^ 4 * z ^ 6 + x ^ 4 * y ^ 5 * z ^ 6  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_56382; Apache-2.0

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