Prove2Me

Lean-Workbook Plus 76658: Exponential inequality

Proved
WorkbookRestored.plus_76658

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

lean-workbookrestored-importssource-checked

(1−u)1/u<e−1(1-u)^{1/u}<e^{-1} for 0<u<10<u<1.

Source: Lean-Workbook row lean_workbook_plus_76658 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble
import Mathlib.Analysis.SpecialFunctions.Log.Base
open Real
Formal statement
theorem WorkbookRestored.plus_76658 : ∀ u : ℝ, 0 < u ∧ u < 1 → (1 - u) ^ (1 / u) < exp (-1)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_76658; immutable original Prove2Me node 1136b1a7-cb68-484c-b34d-95ccff141502

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