`BookProof.LorentzOrthochronous.isPO_mul` {a b : Matrix (Fin 4) (Fin 4) ℝ} (ha : IsProperOrthochronous a) (hb : IsProperOrthochronous b) : IsProperOrthochronous (a * b)

Proved

BookProof.LorentzOrthochronous.isPO_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzOrthochronous.

BookProof.LorentzOrthochronous.isPO_mul {a b : Matrix (Fin 4) (Fin 4) ℝ} (ha : IsProperOrthochronous a) (hb : IsProperOrthochronous b) : IsProperOrthochronous (a * b)

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

Preamble

-- Generated from ChapterLorentzOrthochronous.lean — theorem BookProof.LorentzOrthochronous.isPO_mul
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.isPO_mul {a b : Matrix (Fin 4) (Fin 4) ℝ}
    (ha : IsProperOrthochronous a) (hb : IsProperOrthochronous b) :
    IsProperOrthochronous (a * b) := by sorry

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