Prove2Me

Lean-Workbook Plus 20139: Logarithmic inequality

Proved
WorkbookRestored.plus_20139

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

lean-workbookrestored-importssource-checked

For positive real x,yx,y, log⁡x+log⁡y=log⁡(xy)\log x+\log y=\log(xy).

Source: Lean-Workbook row lean_workbook_plus_20139 (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_20139 : ∀ x y : ℝ, x > 0 ∧ y > 0 → Real.log x + Real.log y = Real.log (x*y)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_20139; immutable original Prove2Me node bd9117b0-cfcf-47e4-8899-59eeae1c9a32

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