`BookProof.LorentzOrthochronous.lorentz_time_row` {l : Matrix (Fin 4) (Fin 4) ℝ} (h : IsLorentz l) : (l 0 0) ^ 2 = 1 + (l 0 1) ^ 2 + (l 0 2) ^ 2 + (l 0 3) ^ 2

Proved

BookProof.LorentzOrthochronous.lorentz_time_row

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzOrthochronous.

BookProof.LorentzOrthochronous.lorentz_time_row {l : Matrix (Fin 4) (Fin 4) ℝ} (h : IsLorentz l) : (l 0 0) ^ 2 = 1 + (l 0 1) ^ 2 + (l 0 2) ^ 2 + (l 0 3) ^ 2

Formalization note: Lean 4 identifier BookProof.LorentzOrthochronous.lorentz_time_row.

Preamble

-- Generated from ChapterLorentzOrthochronous.lean — theorem BookProof.LorentzOrthochronous.lorentz_time_row
import Mathlib
import Definitions.Def_ChapterLorentzOrthochronous
import Definitions.Def_ChapterLorentzGroup
open BookProof.LorentzGroup
open BookProof.LorentzOrthochronous



open Matrix
open BookProof.LorentzGroup

Formal statement

theorem BookProof.LorentzOrthochronous.lorentz_time_row {l : Matrix (Fin 4) (Fin 4) ℝ} (h : IsLorentz l) :
    (l 0 0) ^ 2 = 1 + (l 0 1) ^ 2 + (l 0 2) ^ 2 + (l 0 3) ^ 2 := by sorry

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