lean_workbook_plus_8313

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that for positive real numbers $x, y, z$ satisfying $xyz = 1$ , the following inequality holds:\n $(\sum_{sym}x^{5}y+\sum_{cyc}x^{4}yz)\leq 3\sum_{cyc}x^{6}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_8313 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (habc : x * y * z = 1) : (x ^ 5 * y + y ^ 5 * z + z ^ 5 * x + (x ^ 4 * y * z + y ^ 4 * z * x + z ^ 4 * x * y)) ≤ 3 * (x ^ 6 + y ^ 6 + z ^ 6)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph