`BookProof.ChapterLorentzRealRepSum.gram_all` : ∀ i j : Fin 14, ((bAll i)ᵀ * bAll j).trace = if i = j then 4 else 0

Proved

BookProof.ChapterLorentzRealRepSum.gram_all

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRepSum.

BookProof.ChapterLorentzRealRepSum.gram_all : ∀ i j : Fin 14, ((bAll i)ᵀ * bAll j).trace = if i = j then 4 else 0

Formalization note: Lean 4 identifier BookProof.ChapterLorentzRealRepSum.gram_all.

Preamble

-- Generated from ChapterLorentzRealRepSum.lean — theorem BookProof.ChapterLorentzRealRepSum.gram_all
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterPinOmega
import Definitions.Def_ChapterLorentzRealRep
import Mathlib
import Definitions.Def_ChapterLorentzRealRepSum
open BookProof.ChapterLorentzRealRepSum


open Matrix


open BookProof.ChapterA3 BookProof.ChapterPinOmega BookProof.ChapterLorentzRealRep
open Module

Formal statement

theorem BookProof.ChapterLorentzRealRepSum.gram_all : ∀ i j : Fin 14, ((bAll i)ᵀ * bAll j).trace = if i = j then 4 else 0 := by sorry

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