An elementary bound for a real power of two

Proved

WorkbookRestored.plus_12796

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

lean-workbookrestored-importssource-checked

If $0\le x\le1$ , then $2^x\le x+2$ .

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_12796 (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_12796 (x : ℝ) (hx : 0 ≤ x ∧ x ≤ 1) : x + 2 ≥ 2^x   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_12796; original Prove2Me node e9fb15a2-615c-4159-960b-127189f6521a; Apache-2.0

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