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Lean-Workbook Plus 20955: Logarithmic inequality

Proved
WorkbookRestored.plus_20955

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

lean-workbookrestored-importssource-checked

For 0<u<1,0<u<1, prove that ln⁡(1−u)<−u\ln(1-u)<-u.

Source: Lean-Workbook row lean_workbook_plus_20955 (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_20955 (u : ℝ) (h : 0 < u) (h' : u < 1) : Real.log (1 - u) < -u   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_20955; immutable original Prove2Me node b64bcfc8-0082-43bb-8261-b485ea80988b

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