`BookProof.ChapterA3.cliffordR_lorentz_comb` (Λ : Matrix (Fin 4) (Fin 4) ℝ) (hΛ : Λ ∈ LorentzO) : IsCliffordR (fun μ => ∑ ν, Λ μ ν • mgammaR ν)

Proved

BookProof.ChapterA3.cliffordR_lorentz_comb

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3c.

BookProof.ChapterA3.cliffordR_lorentz_comb (Λ : Matrix (Fin 4) (Fin 4) ℝ) (hΛ : Λ ∈ LorentzO) : IsCliffordR (fun μ => ∑ ν, Λ μ ν • mgammaR ν)

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

Preamble

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


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.cliffordR_lorentz_comb (Λ : Matrix (Fin 4) (Fin 4) ℝ) (hΛ : Λ ∈ LorentzO) :
    IsCliffordR (fun μ => ∑ ν, Λ μ ν • mgammaR ν) := by sorry

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