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`BookProof.ChapterE.exp_J` (t : ℝ) : NormedSpace.exp (t • J) = !![Real.cos t, -Real.sin t; Real.sin t, Real.cos t]

Proved
BookProof.ChapterE.exp_J

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterE.

BookProof.ChapterE.exp_J (t : ℝ) : NormedSpace.exp (t • J) = !![Real.cos t, -Real.sin t; Real.sin t, Real.cos t]

Formalization note: Lean 4 identifier BookProof.ChapterE.exp_J.

Preamble
-- Generated from ChapterE.lean — theorem BookProof.ChapterE.exp_J
import Mathlib
import Definitions.Def_ChapterE
open BookProof.ChapterE


open scoped Matrix BigOperators
open Filter
open scoped Topology
Formal statement
theorem BookProof.ChapterE.exp_J (t : ℝ) :
    NormedSpace.exp (t • J) = !![Real.cos t, -Real.sin t; Real.sin t, Real.cos t] := by sorry

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