`BookProof.ChapterA3.pauliCoeff_null` (μ : Fin 4) : pauliCoeff (pauliσ 0 + pauliσ 3) μ = (if μ = 0 then 1 else 0) + (if μ = 3 then 1 else 0)

Proved

BookProof.ChapterA3.pauliCoeff_null

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4d.

BookProof.ChapterA3.pauliCoeff_null (μ : Fin 4) : pauliCoeff (pauliσ 0 + pauliσ 3) μ = (if μ = 0 then 1 else 0) + (if μ = 3 then 1 else 0)

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

Preamble

-- Generated from ChapterA4d.lean — theorem BookProof.ChapterA3.pauliCoeff_null
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_null (μ : Fin 4) :
    pauliCoeff (pauliσ 0 + pauliσ 3) μ =
      (if μ = 0 then 1 else 0) + (if μ = 3 then 1 else 0) := by sorry

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