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

Proved

BookProof.ChapterLorentzRealRepSum.gram_allR

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRepSum.

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

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

Preamble

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


open Matrix


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

Formal statement

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

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