`BookProof.ChapterA3.det_pauli_comb` (x : Fin 4 → ℂ) : (∑ μ, x μ • pauliσ μ).det = Qc x

Proved

BookProof.ChapterA3.det_pauli_comb

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3h.

BookProof.ChapterA3.det_pauli_comb (x : Fin 4 → ℂ) : (∑ μ, x μ • pauliσ μ).det = Qc x

Formalization note: Lean 4 identifier BookProof.ChapterA3.det_pauli_comb.

Preamble

-- Generated from ChapterA3h.lean — theorem BookProof.ChapterA3.det_pauli_comb
import Mathlib
import Definitions.Def_ChapterA3h
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.det_pauli_comb (x : Fin 4 → ℂ) :
    (∑ μ, x μ • pauliσ μ).det = Qc x := by sorry

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