`BookProof.ChapterLorentzRealRepSum.gram_half10R` : ∀ (i : Fin 4) (j : Fin 6), ((bHalfR i)ᵀ * b10R j).trace = (0 : ℝ)

Proved

BookProof.ChapterLorentzRealRepSum.gram_half10R

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRepSum.

BookProof.ChapterLorentzRealRepSum.gram_half10R : ∀ (i : Fin 4) (j : Fin 6), ((bHalfR i)ᵀ * b10R j).trace = (0 : ℝ)

Formalization note: Lean 4 identifier BookProof.ChapterLorentzRealRepSum.gram_half10R.

Preamble

-- Generated from ChapterLorentzRealRepSum.lean — theorem BookProof.ChapterLorentzRealRepSum.gram_half10R
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_half10R : ∀ (i : Fin 4) (j : Fin 6), ((bHalfR i)ᵀ * b10R j).trace = (0 : ℝ) := by sorry

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