Lean-Workbook Plus 26548: Logarithmic inequality

Proved

WorkbookRestored.plus_26548

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

lean-workbookrestored-importssource-checked

For every natural number $n\ge1$ , $\log(n+1)<n$ .

Source: Lean-Workbook row lean_workbook_plus_26548 (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_26548 (n : ℕ) (hn : 1 ≤ n) : Real.log (n + 1) < n   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_26548; immutable original Prove2Me node 69d57df0-8259-4ab5-9389-84a16bb4c572

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