Prove2Me

Lean-Workbook Plus 23528: Logarithmic inequality

Proved
WorkbookRestored.plus_23528

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

lean-workbookrestored-importssource-checked

For 0<x<10<x<1, log⁡x<x−1<(x−1)/(2−x)\log x<x-1<(x-1)/(2-x).

Source: Lean-Workbook row lean_workbook_plus_23528 (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_23528 (x : ℝ) (hx : 0 < x ∧ x < 1) :
  Real.log x < x - 1 ∧ x - 1 < (x - 1) / (2 - x)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_23528; immutable original Prove2Me node 4ab08d67-1d7d-45db-9d17-98579a107cc2

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