Prove2Me

Lean-Workbook Plus 51489: Logarithmic inequality

Proved
WorkbookRestored.plus_51489

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

lean-workbookrestored-importssource-checked

For real a>1a>1, 1−1/a−log⁡a<01-1/a-\log a<0.

Source: Lean-Workbook row lean_workbook_plus_51489 (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_51489 (a : ℝ) (ha : 1 < a) : 1 - (1 / a) - Real.log a < 0   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_51489; immutable original Prove2Me node edabfb75-5508-4ad6-a5fe-a27f3852ca46

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