`BookProof.ChapterLorentzRealRepFull.gram_twoR` : ∀ i j : Fin 2, ((w2R i)ᵀ * w2R j).trace = if i = j then (4 : ℝ) else 0

Proved

BookProof.ChapterLorentzRealRepFull.gram_twoR

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRepFull.

BookProof.ChapterLorentzRealRepFull.gram_twoR : ∀ i j : Fin 2, ((w2R i)ᵀ * w2R j).trace = if i = j then (4 : ℝ) else 0

Formalization note: Lean 4 identifier BookProof.ChapterLorentzRealRepFull.gram_twoR.

Preamble

-- Generated from ChapterLorentzRealRepFull.lean — theorem BookProof.ChapterLorentzRealRepFull.gram_twoR
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterPinOmega
import Definitions.Def_ChapterLorentzRealRepSum
import Mathlib
import Definitions.Def_ChapterLorentzRealRepFull
import Definitions.Def_ChapterLorentzRealRep
open BookProof.ChapterLorentzRealRep
open BookProof.ChapterLorentzRealRepFull


open Matrix


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

Formal statement

theorem BookProof.ChapterLorentzRealRepFull.gram_twoR : ∀ i j : Fin 2, ((w2R i)ᵀ * w2R j).trace = if i = j then (4 : ℝ) else 0 := by sorry

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