`BookProof.ChapterPauliFundamental.pauli_exists` {B : Fin 4 → M4} (hA : IsCliffordC A) (hB : IsCliffordC B) : ∃ S : M4, IsUnit S.det ∧ ∀ μ, B μ = S * A μ * S⁻¹

Proved

BookProof.ChapterPauliFundamental.pauli_exists

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliFundamental.

BookProof.ChapterPauliFundamental.pauli_exists {B : Fin 4 → M4} (hA : IsCliffordC A) (hB : IsCliffordC B) : ∃ S : M4, IsUnit S.det ∧ ∀ μ, B μ = S * A μ * S⁻¹

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

Preamble

-- Generated from ChapterPauliFundamental.lean — theorem BookProof.ChapterPauliFundamental.pauli_exists
import Definitions.Def_ChapterGammaCommutant
import Mathlib
import Definitions.Def_ChapterPauliFundamental
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3b
open BookProof.ChapterA3
open BookProof.ChapterPauliFundamental


open Matrix Finset


open BookProof.ChapterA3 BookProof.ChapterGammaCommutant

variable {A : Fin 4 → M4}

Formal statement

theorem BookProof.ChapterPauliFundamental.pauli_exists {B : Fin 4 → M4} (hA : IsCliffordC A) (hB : IsCliffordC B) :
    ∃ S : M4, IsUnit S.det ∧ ∀ μ, B μ = S * A μ * S⁻¹ := by sorry

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