`BookProof.LorentzOrthochronous.orthochronous_mul` {a b : Matrix (Fin 4) (Fin 4) ℝ} (ha : IsLorentz a) (hb : IsLorentz b) (h0a : 0 < a 0 0) (h0b : 0 < b 0 0) : 0 < (a * b) 0 0

Proved

BookProof.LorentzOrthochronous.orthochronous_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzOrthochronous.

BookProof.LorentzOrthochronous.orthochronous_mul {a b : Matrix (Fin 4) (Fin 4) ℝ} (ha : IsLorentz a) (hb : IsLorentz b) (h0a : 0 < a 0 0) (h0b : 0 < b 0 0) : 0 < (a * b) 0 0

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

Preamble

-- Generated from ChapterLorentzOrthochronous.lean — theorem BookProof.LorentzOrthochronous.orthochronous_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.orthochronous_mul {a b : Matrix (Fin 4) (Fin 4) ℝ}
    (ha : IsLorentz a) (hb : IsLorentz b) (h0a : 0 < a 0 0) (h0b : 0 < b 0 0) :
    0 < (a * b) 0 0 := by sorry

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