`BookProof.ChapterA3.lorentzLie_sum` {ι : Type*} (s : Finset ι) (A : ι → Matrix (Fin 4) (Fin 4) ℝ) (h : ∀ i ∈ s, A i ∈ LorentzLie) : (∑ i ∈ s, A i) ∈ LorentzLie

Proved

BookProof.ChapterA3.lorentzLie_sum

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3e.

BookProof.ChapterA3.lorentzLie_sum {ι : Type*} (s : Finset ι) (A : ι → Matrix (Fin 4) (Fin 4) ℝ) (h : ∀ i ∈ s, A i ∈ LorentzLie) : (∑ i ∈ s, A i) ∈ LorentzLie

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

Preamble

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


open Matrix

Formal statement

theorem BookProof.ChapterA3.lorentzLie_sum {ι : Type*} (s : Finset ι) (A : ι → Matrix (Fin 4) (Fin 4) ℝ)
    (h : ∀ i ∈ s, A i ∈ LorentzLie) : (∑ i ∈ s, A i) ∈ LorentzLie := by sorry

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