Prove2Me

Real logarithm identity #11295

Disproved
WorkbookCorrected.plus_11295

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

2(−Real.sqrt2)=(4(1/2))(−Real.sqrt2)2^(-Real.sqrt 2) = (4^(1 / 2))^(-Real.sqrt 2)

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_11295, 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_11295 (Apache-2.0).

Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real
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_11295 : (2:ℝ) ^ (-Real.sqrt 2) = ((4:ℝ) ^ (1 / 2)) ^ (-Real.sqrt 2) := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_11295; Apache-2.0; corrects Open node 3e9b173c-b796-41a7-8d85-b0ca0172fb59

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