Lean-Workbook Plus 57992: Exponential inequality

Proved

WorkbookRestored.plus_57992

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

lean-workbookrestored-importssource-checked

For every natural number $n$ and real $0<p\le1$ , $1-p^n<e^{-p^n}$ .

Source: Lean-Workbook row lean_workbook_plus_57992 (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.Basic
open Real

Formal statement

theorem WorkbookRestored.plus_57992 (n : ℕ) (p : ℝ) (hp0 : 0 < p) (hp1 : p ≤ 1) :
  (1 - p ^ n) < exp (-p ^ n)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_57992; immutable original Prove2Me node 5ea9bc3b-a0e4-4d6f-9612-49d7d5b8e36e

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