`BookProof.LorentzOrthochronous.isPO_conj` {g s : Matrix (Fin 4) (Fin 4) ℝ} (hg : IsLorentz g) (hs : IsProperOrthochronous s) : IsProperOrthochronous (g * s * g⁻¹)

Proved

BookProof.LorentzOrthochronous.isPO_conj

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzOrthochronous.

BookProof.LorentzOrthochronous.isPO_conj {g s : Matrix (Fin 4) (Fin 4) ℝ} (hg : IsLorentz g) (hs : IsProperOrthochronous s) : IsProperOrthochronous (g * s * g⁻¹)

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

Preamble

-- Generated from ChapterLorentzOrthochronous.lean — theorem BookProof.LorentzOrthochronous.isPO_conj
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_conj {g s : Matrix (Fin 4) (Fin 4) ℝ}
    (hg : IsLorentz g) (hs : IsProperOrthochronous s) :
    IsProperOrthochronous (g * s * g⁻¹) := by sorry

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