A symmetric comparison of positive real powers

Proved

WorkbookRestored.plus_28770

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For $x\ge y>0$ , $x^x y^y\ge x^y y^x$ .

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_28770 (Apache-2.0).

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Analysis.SpecialFunctions.Log.Basic
open Real

Formal statement

theorem WorkbookRestored.plus_28770 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) (hxy : x ≥ y) : x^x * y^y ≥ x^y * y^x   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_28770; original Prove2Me node 99f6d3cb-e242-478d-9b59-76fe95732fb7; Apache-2.0

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