Prove2Me

Lean-Workbook Plus 8018: Logarithmic inequality

Proved
WorkbookRestored.plus_8018

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

lean-workbookrestored-importssource-checked

For every real x>0x>0, log⁡x/(x+1)≤log⁡(x+1)/x\log x/(x+1)\le\log(x+1)/x.

Source: Lean-Workbook row lean_workbook_plus_8018 (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_8018 (x : ℝ) (hx : 0 < x) : (Real.log x) / (x + 1) ≤ (Real.log (x + 1)) / x   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_8018; immutable original Prove2Me node 28c86209-6dbe-40b5-9e1a-04af070184a6

View graph