`BookProof.ChapterPauliFundamental.pauli_unique` {B : Fin 4 → M4} (hA : IsCliffordC A) (S T : M4) (hS : IsUnit S.det) (hT : IsUnit T.det) (hSeq : ∀ μ, B μ = S * A μ * S⁻¹) (hTeq :

Proved

BookProof.ChapterPauliFundamental.pauli_unique

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliFundamental.

BookProof.ChapterPauliFundamental.pauli_unique {B : Fin 4 → M4} (hA : IsCliffordC A) (S T : M4) (hS : IsUnit S.det) (hT : IsUnit T.det) (hSeq : ∀ μ, B μ = S * A μ * S⁻¹) (hTeq : ∀ μ, B μ = T * A μ * T⁻¹) : ∃ c : ℂ, c ≠ 0 ∧ T = c • S

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

Preamble

-- Generated from ChapterPauliFundamental.lean — theorem BookProof.ChapterPauliFundamental.pauli_unique
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_unique {B : Fin 4 → M4} (hA : IsCliffordC A)
    (S T : M4) (hS : IsUnit S.det) (hT : IsUnit T.det)
    (hSeq : ∀ μ, B μ = S * A μ * S⁻¹) (hTeq : ∀ μ, B μ = T * A μ * T⁻¹) :
    ∃ c : ℂ, c ≠ 0 ∧ T = c • S := by sorry

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