`BookProof.ChapterA3.lorentzLie_add` {A₁ A₂ : Matrix (Fin 4) (Fin 4) ℝ} (h1 : A₁ ∈ LorentzLie) (h2 : A₂ ∈ LorentzLie) : A₁ + A₂ ∈ LorentzLie

Proved

BookProof.ChapterA3.lorentzLie_add

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3e.

BookProof.ChapterA3.lorentzLie_add {A₁ A₂ : Matrix (Fin 4) (Fin 4) ℝ} (h1 : A₁ ∈ LorentzLie) (h2 : A₂ ∈ LorentzLie) : A₁ + A₂ ∈ LorentzLie

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

Preamble

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


open Matrix

Formal statement

theorem BookProof.ChapterA3.lorentzLie_add {A₁ A₂ : Matrix (Fin 4) (Fin 4) ℝ}
    (h1 : A₁ ∈ LorentzLie) (h2 : A₂ ∈ LorentzLie) : A₁ + A₂ ∈ LorentzLie := by sorry

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