`BookProof.ChapterA3.pauli_expand` (M : Matrix (Fin 2) (Fin 2) ℂ) : M = ∑ μ, pauliCoeff M μ • pauliσ μ

Proved

BookProof.ChapterA3.pauli_expand

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3h.

BookProof.ChapterA3.pauli_expand (M : Matrix (Fin 2) (Fin 2) ℂ) : M = ∑ μ, pauliCoeff M μ • pauliσ μ

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

Preamble

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


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.pauli_expand (M : Matrix (Fin 2) (Fin 2) ℂ) :
    M = ∑ μ, pauliCoeff M μ • pauliσ μ := by sorry

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