Prove2Me

Real logarithm identity #10289

Disproved
WorkbookCorrected.plus_10289

by carlok · Sep 30, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

Real.log(2(1/2)+1)>(2/3)(1/2)Real.log (2^(1/2) + 1) > (2/3)^(1/2)

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_10289, which omitted a compilable colon/type annotation and/or used a preamble of only Mathlib.Analysis.Complex.Basic.

Source: InternLM Lean-Workbook, record lean_workbook_plus_10289 (Apache-2.0).

Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Analysis.SpecialFunctions.Log.Base
import Mathlib.Analysis.SpecialFunctions.Log.Basic
import Mathlib.Tactic.Ring
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
Formal statement
theorem WorkbookCorrected.plus_10289 : Real.log (2 ^ (1/2) + 1) > (2/3) ^ (1/2) := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_10289; Apache-2.0; corrects Open node 3eaca039-4c19-439e-a259-8da6722a10a6

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