Lean-Workbook Plus 56952: Logarithmic inequality

Proved

WorkbookRestored.plus_56952

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

lean-workbookrestored-importssource-checked

For real $x\ge1$ , $(\log_2x)(\log_2(x+1))+1\ge1$ and $1>0$ .

Source: Lean-Workbook row lean_workbook_plus_56952 (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.Base
open Real

Formal statement

theorem WorkbookRestored.plus_56952 (x : ℝ) (hx : 1 ≤ x) : Real.logb 2 x * Real.logb 2 (x + 1) + 1 ≥ 1 ∧ 1 > 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_56952; immutable original Prove2Me node 4647264e-3a34-4b43-9222-488c0ecf10dc

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