Comparing reciprocal and ordinary exponents above one

Proved

WorkbookRestored.plus_24509

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

lean-workbookrestored-importssource-checked

If $x>1$ , then $x^{1/x}\le x^x$ .

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_24509 (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_24509 (x : ℝ) (hx : 1 < x) : x^(1/x) ≤ x^x   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_24509; original Prove2Me node cc34ef08-2ef9-4859-b15c-992e2fe37c02; Apache-2.0

View graph