Lean-Workbook Plus 26636: Logarithmic inequality

Proved

WorkbookRestored.plus_26636

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

lean-workbookrestored-importssource-checked

For every real $x>0$ , $\log x\le x-1$ .

Source: Lean-Workbook row lean_workbook_plus_26636 (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_26636 (x : ℝ) (hx : 0 < x) : Real.log x ≤ x - 1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_26636; immutable original Prove2Me node 38baa84e-75d4-4a60-b30c-b9808a31e71e

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