Prove2Me

Lean-Workbook Plus 34146: Logarithmic inequality

Proved
WorkbookRestored.plus_34146

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

lean-workbookrestored-importssource-checked

If 1<x<y1<x<y, then (x−1)log⁡x<(y−1)log⁡y(x-1)\log x<(y-1)\log y.

Source: Lean-Workbook row lean_workbook_plus_34146 (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_34146 (x y : ℝ) (h₁ : 1 < x) (h₂ : 1 < y) (h₃ : x < y) : (x - 1) * Real.log x < (y - 1) * Real.log y   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_34146; immutable original Prove2Me node 6556d155-1988-48cc-8032-b46deb58d964

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