`BookProof.ChapterLorentzRealRep.gram_half` : ∀ i j : Fin 4, ((bHalf i)ᵀ * bHalf j).trace = if i = j then 4 else 0

Proved

BookProof.ChapterLorentzRealRep.gram_half

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRep.

BookProof.ChapterLorentzRealRep.gram_half : ∀ i j : Fin 4, ((bHalf i)ᵀ * bHalf j).trace = if i = j then 4 else 0

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

Preamble

-- Generated from ChapterLorentzRealRep.lean — theorem BookProof.ChapterLorentzRealRep.gram_half
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.gram_half : ∀ i j : Fin 4, ((bHalf i)ᵀ * bHalf j).trace = if i = j then 4 else 0 := by sorry

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