A power identity at exponents zero and one

Proved

WorkbookRestored.plus_24031

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

lean-workbookrestored-importssource-checked

For real $a$ and $x\in\{0,1\}$ , $(1+a)^x=1+ax$ .

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_24031 (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_24031 (x : ℝ) (a : ℝ) (h : x = 0 ∨ x = 1) : (1 + a) ^ x = 1 + a * x   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_24031; original Prove2Me node 4c910ee4-ad42-4d9a-923f-4163dcee487a; Apache-2.0

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