`BookProof.ChapterA3.pauliCoeff_add` (A B : Matrix (Fin 2) (Fin 2) ℂ) (μ : Fin 4) : pauliCoeff (A + B) μ = pauliCoeff A μ + pauliCoeff B μ

Proved

BookProof.ChapterA3.pauliCoeff_add

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4d.

BookProof.ChapterA3.pauliCoeff_add (A B : Matrix (Fin 2) (Fin 2) ℂ) (μ : Fin 4) : pauliCoeff (A + B) μ = pauliCoeff A μ + pauliCoeff B μ

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

Preamble

-- Generated from ChapterA4d.lean — theorem BookProof.ChapterA3.pauliCoeff_add
import Mathlib
import Definitions.Def_ChapterA4d
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3h
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.pauliCoeff_add (A B : Matrix (Fin 2) (Fin 2) ℂ) (μ : Fin 4) :
    pauliCoeff (A + B) μ = pauliCoeff A μ + pauliCoeff B μ := by sorry

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