Prove2Me

`BookProof.ChapterA3.lorentzLie_of_intModel` (Az : Matrix (Fin 4) (Fin 4) ℤ) (h : Az * minkowskiMatZ + minkowskiMatZ * Azᵀ = 0) : (Int.castRingHom ℝ).mapMatrix Az ∈ LorentzLie

Proved
BookProof.ChapterA3.lorentzLie_of_intModel

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3e.

BookProof.ChapterA3.lorentzLie_of_intModel (Az : Matrix (Fin 4) (Fin 4) ℤ) (h : Az * minkowskiMatZ + minkowskiMatZ * Azᵀ = 0) : (Int.castRingHom ℝ).mapMatrix Az ∈ LorentzLie

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

Preamble
-- Generated from ChapterA3e.lean — theorem BookProof.ChapterA3.lorentzLie_of_intModel
import Mathlib
import Definitions.Def_ChapterA3e
import Definitions.Def_ChapterA3b
import Definitions.Def_ChapterA3d
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
Formal statement
theorem BookProof.ChapterA3.lorentzLie_of_intModel (Az : Matrix (Fin 4) (Fin 4) ℤ)
    (h : Az * minkowskiMatZ + minkowskiMatZ * Azᵀ = 0) :
    (Int.castRingHom ℝ).mapMatrix Az ∈ LorentzLie := by sorry

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