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

Proved

BookProof.ChapterEulerComplexQuat.quat_realification_norm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterEulerComplexQuat.

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

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

Preamble

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


open scoped Quaternion BigOperators


variable {n : ℕ}

Formal statement

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

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