`BookProof.ChapterA3.lorentz_of_conjR` (S : Matrix (Fin 4) (Fin 4) ℝ) (hS : IsUnit S.det) (Λ : Matrix (Fin 4) (Fin 4) ℝ) (hΛ : HasLambda S Λ) : Λ * minkowskiMat * Λᵀ = minkowskiMat

Proved

BookProof.ChapterA3.lorentz_of_conjR

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3c.

BookProof.ChapterA3.lorentz_of_conjR (S : Matrix (Fin 4) (Fin 4) ℝ) (hS : IsUnit S.det) (Λ : Matrix (Fin 4) (Fin 4) ℝ) (hΛ : HasLambda S Λ) : Λ * minkowskiMat * Λᵀ = minkowskiMat

Formalization note: Lean 4 identifier BookProof.ChapterA3.lorentz_of_conjR.

Preamble

-- Generated from ChapterA3c.lean — theorem BookProof.ChapterA3.lorentz_of_conjR
import Mathlib
import Definitions.Def_ChapterA3c
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3b
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.lorentz_of_conjR (S : Matrix (Fin 4) (Fin 4) ℝ) (hS : IsUnit S.det)
    (Λ : Matrix (Fin 4) (Fin 4) ℝ) (hΛ : HasLambda S Λ) :
    Λ * minkowskiMat * Λᵀ = minkowskiMat := by sorry

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