`BookProof.ChapterA3.hasLambda_of_intModel` (Sz Λz : Matrix (Fin 4) (Fin 4) ℤ) (hSS : Sz * Sz = -1) (hconj : ∀ μ, -Sz * mgammaZ μ * Sz = ∑ ν, Λz μ ν • mgammaZ ν) : HasLambda ((Int.

Proved

BookProof.ChapterA3.hasLambda_of_intModel

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3d.

BookProof.ChapterA3.hasLambda_of_intModel (Sz Λz : Matrix (Fin 4) (Fin 4) ℤ) (hSS : Sz * Sz = -1) (hconj : ∀ μ, -Sz * mgammaZ μ * Sz = ∑ ν, Λz μ ν • mgammaZ ν) : HasLambda ((Int.castRingHom ℝ).mapMatrix Sz) ((Int.castRingHom ℝ).mapMatrix Λz)

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

Preamble

-- Generated from ChapterA3d.lean — theorem BookProof.ChapterA3.hasLambda_of_intModel
import Mathlib
import Definitions.Def_ChapterA3d
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3c
open BookProof.ChapterA3


open Matrix

Formal statement

theorem BookProof.ChapterA3.hasLambda_of_intModel (Sz Λz : Matrix (Fin 4) (Fin 4) ℤ)
    (hSS : Sz * Sz = -1)
    (hconj : ∀ μ, -Sz * mgammaZ μ * Sz = ∑ ν, Λz μ ν • mgammaZ ν) :
    HasLambda ((Int.castRingHom ℝ).mapMatrix Sz)
      ((Int.castRingHom ℝ).mapMatrix Λz) := by sorry

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