`BookProof.LorentzOrthochronous.isLorentz_mul_eta_transpose` {l : Matrix (Fin 4) (Fin 4) ℝ} (h : IsLorentz l) : l * eta * lᵀ = eta

Proved

BookProof.LorentzOrthochronous.isLorentz_mul_eta_transpose

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzOrthochronous.

BookProof.LorentzOrthochronous.isLorentz_mul_eta_transpose {l : Matrix (Fin 4) (Fin 4) ℝ} (h : IsLorentz l) : l * eta * lᵀ = eta

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

Preamble

-- Generated from ChapterLorentzOrthochronous.lean — theorem BookProof.LorentzOrthochronous.isLorentz_mul_eta_transpose
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.isLorentz_mul_eta_transpose {l : Matrix (Fin 4) (Fin 4) ℝ} (h : IsLorentz l) :
    l * eta * lᵀ = eta := by sorry

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