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Nested irrational powers

Proved
WorkbookRestored.plus_51735

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

lean-workbookrestored-importssource-checked

((3)2)2=9=3((\sqrt3)^{\sqrt2})^{\sqrt2}=\sqrt9=3((3​)2​)2​=9​=3, with real exponentiation. The formal statement asserts the equality to 9\sqrt99​.

Source: Lean-Workbook row lean_workbook_plus_51735 (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.Pow.Real
Formal statement
theorem WorkbookRestored.plus_51735 : (Real.sqrt 3 ^ (Real.sqrt 2)) ^ (Real.sqrt 2) = Real.sqrt 9   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_51735; immutable original Prove2Me node 1a64f6db-dc89-4ca4-8369-c588827165f6

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