`BookProof.ChapterPauliFundamental.gp_push` (hA : IsCliffordC A) (μ : Fin 4) : ∀ l : List (Fin 4), (∀ ν ∈ l, ν ≠ μ) → A μ * gp A l = ((-1 : ℂ) ^ l.length) • (gp A l * A μ)

Proved

BookProof.ChapterPauliFundamental.gp_push

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliFundamental.

BookProof.ChapterPauliFundamental.gp_push (hA : IsCliffordC A) (μ : Fin 4) : ∀ l : List (Fin 4), (∀ ν ∈ l, ν ≠ μ) → A μ * gp A l = ((-1 : ℂ) ^ l.length) • (gp A l * A μ)

Formalization note: Lean 4 identifier BookProof.ChapterPauliFundamental.gp_push.

Preamble

-- Generated from ChapterPauliFundamental.lean — theorem BookProof.ChapterPauliFundamental.gp_push
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterGammaCommutant
import Mathlib
import Definitions.Def_ChapterPauliFundamental
import Definitions.Def_ChapterA3b
open BookProof.ChapterPauliFundamental


open Matrix Finset


open BookProof.ChapterA3 BookProof.ChapterGammaCommutant

variable {A : Fin 4 → M4}

Formal statement

theorem BookProof.ChapterPauliFundamental.gp_push (hA : IsCliffordC A) (μ : Fin 4) :
    ∀ l : List (Fin 4), (∀ ν ∈ l, ν ≠ μ) →
      A μ * gp A l = ((-1 : ℂ) ^ l.length) • (gp A l * A μ) := by sorry

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