`BookProof.ChapterA3.lambda_surjective` (hpf : PauliFundamental) (Λ : Matrix (Fin 4) (Fin 4) ℝ) (hΛ : Λ ∈ LorentzO) : ∃ S : Matrix (Fin 4) (Fin 4) ℝ, IsPin S ∧ LambdaOf S = Λ

Proved

BookProof.ChapterA3.lambda_surjective

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3c.

BookProof.ChapterA3.lambda_surjective (hpf : PauliFundamental) (Λ : Matrix (Fin 4) (Fin 4) ℝ) (hΛ : Λ ∈ LorentzO) : ∃ S : Matrix (Fin 4) (Fin 4) ℝ, IsPin S ∧ LambdaOf S = Λ

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

Preamble

-- Generated from ChapterA3c.lean — theorem BookProof.ChapterA3.lambda_surjective
import Mathlib
import Definitions.Def_ChapterA3c
import Definitions.Def_ChapterA3b
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.lambda_surjective (hpf : PauliFundamental)
    (Λ : Matrix (Fin 4) (Fin 4) ℝ) (hΛ : Λ ∈ LorentzO) :
    ∃ S : Matrix (Fin 4) (Fin 4) ℝ, IsPin S ∧ LambdaOf S = Λ := by sorry

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