A cyclic quartic inequality at unit product

Proved

WorkbookSource.base_19519

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

lean-workbooksource-checked

Given $x, y, z > 0$ and $xyz = 1$ , prove that ${x}^{3}y+{y}^{3}z+{z}^{3}x\geq xy+zx+yz$ .

Source: InternLM Lean-Workbook, record lean_workbook_19519 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_19519 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) (habc : x * y * z = 1) : 
  x^3 * y + y^3 * z + z^3 * x ≥ x * y + z * x + y * z  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_19519; Apache-2.0

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