`BookProof.ChapterLorentzRealRepFull.gram_two_10R` : ∀ (i : Fin 2) (j : Fin 6), ((w2R i)ᵀ * b10R j).trace = (0 : ℝ)

Proved

BookProof.ChapterLorentzRealRepFull.gram_two_10R

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRepFull.

BookProof.ChapterLorentzRealRepFull.gram_two_10R : ∀ (i : Fin 2) (j : Fin 6), ((w2R i)ᵀ * b10R j).trace = (0 : ℝ)

Formalization note: Lean 4 identifier BookProof.ChapterLorentzRealRepFull.gram_two_10R.

Preamble

-- Generated from ChapterLorentzRealRepFull.lean — theorem BookProof.ChapterLorentzRealRepFull.gram_two_10R
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_two_10R : ∀ (i : Fin 2) (j : Fin 6), ((w2R i)ᵀ * b10R j).trace = (0 : ℝ) := by sorry

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