Lean-Workbook Plus 16219: Logarithmic identity

Proved

WorkbookRestored.plus_16219

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

lean-workbookrestored-importssource-checked

If $f(x)=\log(1+x)-\log(1-x)$ for every real $x$ , then $f(0)=0$ .

Source: Lean-Workbook row lean_workbook_plus_16219 (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_16219 (f : ℝ → ℝ) (f_def : ∀ x, f x = Real.log (1 + x) - Real.log (1 - x)) : f 0 = 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_16219; immutable original Prove2Me node 7fc15889-3521-4dbf-9880-e1a2ea72e3b9

View graph