`BookProof.ChapterA4f.infinite_spin_excluded` {T : Matrix (Fin 2) (Fin 2) ℂ} (hT : T ∈ SEtwo) (hc : T 1 0 ≠ 0) : ∀ c : ℂ, c ≠ 0 → ∃ l : ℂ, l ≠ 0 ∧ boostZ l * T * boostZ...

Proved

BookProof.ChapterA4f.infinite_spin_excluded

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4f.

BookProof.ChapterA4f.infinite_spin_excluded {T : Matrix (Fin 2) (Fin 2) ℂ} (hT : T ∈ SEtwo) (hc : T 1 0 ≠ 0) : ∀ c : ℂ, c ≠ 0 → ∃ l : ℂ, l ≠ 0 ∧ boostZ l * T * boostZ l⁻¹ ∈ SEtwo ∧ (boostZ l * T * boostZ l⁻¹) 1 0 = c

Formalization note: Lean 4 identifier BookProof.ChapterA4f.infinite_spin_excluded.

Preamble

-- Generated from ChapterA4f.lean — theorem BookProof.ChapterA4f.infinite_spin_excluded
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA5
import Mathlib
import Definitions.Def_ChapterA4f
import Definitions.Def_ChapterA4d
open BookProof.ChapterA4f


open Matrix
open scoped ComplexConjugate


open BookProof.ChapterA3 BookProof.ChapterA5

Formal statement

theorem BookProof.ChapterA4f.infinite_spin_excluded {T : Matrix (Fin 2) (Fin 2) ℂ} (hT : T ∈ SEtwo)
    (hc : T 1 0 ≠ 0) :
    ∀ c : ℂ, c ≠ 0 → ∃ l : ℂ, l ≠ 0 ∧ boostZ l * T * boostZ l⁻¹ ∈ SEtwo ∧
      (boostZ l * T * boostZ l⁻¹) 1 0 = c := by sorry

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