`BookProof.ChapterLorentzRealRep.linIndep_of_gram` {n : ℕ} (v : Fin n → Matrix (Fin 4) (Fin 4) ℝ) (h : ∀ i j, ((v i)ᵀ * v j).trace = if i = j then (4 : ℝ) else 0) : LinearIndepende

Proved

BookProof.ChapterLorentzRealRep.linIndep_of_gram

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRep.

BookProof.ChapterLorentzRealRep.linIndep_of_gram {n : ℕ} (v : Fin n → Matrix (Fin 4) (Fin 4) ℝ) (h : ∀ i j, ((v i)ᵀ * v j).trace = if i = j then (4 : ℝ) else 0) : LinearIndependent ℝ v

Formalization note: Lean 4 identifier BookProof.ChapterLorentzRealRep.linIndep_of_gram.

Preamble

-- Generated from ChapterLorentzRealRep.lean — theorem BookProof.ChapterLorentzRealRep.linIndep_of_gram
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterPinOmega
import Mathlib
import Definitions.Def_ChapterLorentzRealRep
open BookProof.ChapterLorentzRealRep


open Matrix


open BookProof.ChapterA3 BookProof.ChapterPinOmega

Formal statement

theorem BookProof.ChapterLorentzRealRep.linIndep_of_gram {n : ℕ} (v : Fin n → Matrix (Fin 4) (Fin 4) ℝ)
    (h : ∀ i j, ((v i)ᵀ * v j).trace = if i = j then (4 : ℝ) else 0) :
    LinearIndependent ℝ v := by sorry

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