Prove2Me

Real logarithm identity #51735

Proved
WorkbookCorrected.plus_51735

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

arithmeticcorrectedelementaryworkbook

The elementary natural-number / rational identity

(Real.sqrt3(Real.sqrt2))(Real.sqrt2)=Real.sqrt9(Real.sqrt 3 ^ (Real.sqrt 2)) ^ (Real.sqrt 2) = Real.sqrt 9

holds by direct arithmetic evaluation.

Formalization Note: This corrects Lean-Workbook record lean_workbook_plus_51735, 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_51735 (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_51735 : (Real.sqrt 3 ^ (Real.sqrt 2)) ^ (Real.sqrt 2) = Real.sqrt 9 := by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook; record lean_workbook_plus_51735; Apache-2.0; corrects Open node 1a64f6db-dc89-4ca4-8369-c588827165f6

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