Prove2Me

Lean-Workbook Plus 2762: Logarithmic inequality

Proved
WorkbookRestored.plus_2762

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

lean-workbookrestored-importssource-checked

Show that x−ln⁡(1+x)x- \ln (1+x) is positive for all positive xx.

Source: Lean-Workbook row lean_workbook_plus_2762 (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_2762 : ∀ x > 0, x - Real.log (1 + x) > 0   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_2762; immutable original Prove2Me node 9312d153-9acb-435d-8591-40e40105958b

View graph