A cyclic fifth-power sum dominates a mixed sum

Proved

WorkbookSource.plus_78115

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

lean-workbooksource-checked

x, y, z - positive. $x^5 + y^5 + z^5 - x^3z^2 - y^3x^2 - z^3y^2 \ge 0$

Source: InternLM Lean-Workbook, record lean_workbook_plus_78115 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_78115 (x y z : ℝ) (hx : 0 < x) (hy : 0 < y) (hz : 0 < z) : x ^ 5 + y ^ 5 + z ^ 5 - x ^ 3 * z ^ 2 - y ^ 3 * x ^ 2 - z ^ 3 * y ^ 2 ≥ 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_78115; Apache-2.0

View graph