Lean-Workbook Plus 8656: Exponential inequality

Proved

WorkbookRestored.plus_8656

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

lean-workbookrestored-importssource-checked

Prove that $e^x \ge x+1$ if $x \in [0,+\infty)$ .

Source: Lean-Workbook row lean_workbook_plus_8656 (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_8656 (x : ℝ) (hx : 0 ≤ x) : exp x ≥ x + 1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_8656; immutable original Prove2Me node 2cefba4d-fce5-4908-acdf-e41c99540c83

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