`BookProof.ChapterEulerComplexQuat.quat_born_split` (v : Fin n → ℍ[ℝ]) (k : Fin n) : qbornProb v k = (v k).re ^ 2 + (v k).imI ^ 2 + (v k).imJ ^ 2 + (v k).imK ^ 2

Proved

BookProof.ChapterEulerComplexQuat.quat_born_split

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerComplexQuat.

BookProof.ChapterEulerComplexQuat.quat_born_split (v : Fin n → ℍ[ℝ]) (k : Fin n) : qbornProb v k = (v k).re ^ 2 + (v k).imI ^ 2 + (v k).imJ ^ 2 + (v k).imK ^ 2

Formalization note: Lean 4 identifier BookProof.ChapterEulerComplexQuat.quat_born_split.

Preamble

-- Generated from ChapterEulerComplexQuat.lean — theorem BookProof.ChapterEulerComplexQuat.quat_born_split
import Mathlib
import Definitions.Def_ChapterEulerComplexQuat
open BookProof.ChapterEulerComplexQuat


open scoped Quaternion BigOperators


variable {n : ℕ}

Formal statement

theorem BookProof.ChapterEulerComplexQuat.quat_born_split (v : Fin n → ℍ[ℝ]) (k : Fin n) :
    qbornProb v k =
      (v k).re ^ 2 + (v k).imI ^ 2 + (v k).imJ ^ 2 + (v k).imK ^ 2 := by sorry

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