`BookProof.ChapterA3.lorentz_of_conj` (S : Matrix (Fin 4) (Fin 4) ℂ) (hS : IsUnit S.det) (Lam : Matrix (Fin 4) (Fin 4) ℝ) (hLam : ∀ μ, S⁻¹ * mgamma μ * S = ∑ ν, (Lam μ ν : ℂ) • mga

Proved

BookProof.ChapterA3.lorentz_of_conj

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3b.

BookProof.ChapterA3.lorentz_of_conj (S : Matrix (Fin 4) (Fin 4) ℂ) (hS : IsUnit S.det) (Lam : Matrix (Fin 4) (Fin 4) ℝ) (hLam : ∀ μ, S⁻¹ * mgamma μ * S = ∑ ν, (Lam μ ν : ℂ) • mgamma ν) : Lam * minkowskiMat * Lamᵀ = minkowskiMat

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

Preamble

-- Generated from ChapterA3b.lean — theorem BookProof.ChapterA3.lorentz_of_conj
import Mathlib
import Definitions.Def_ChapterA3b
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.lorentz_of_conj (S : Matrix (Fin 4) (Fin 4) ℂ) (hS : IsUnit S.det)
    (Lam : Matrix (Fin 4) (Fin 4) ℝ)
    (hLam : ∀ μ, S⁻¹ * mgamma μ * S = ∑ ν, (Lam μ ν : ℂ) • mgamma ν) :
    Lam * minkowskiMat * Lamᵀ = minkowskiMat := by sorry

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