`BookProof.ChapterLorentzRealRepFull.finrank_full_eq_add` : finrank ℝ (Matrix (Fin 4) (Fin 4) ℝ) = finrank ℝ WHalf + finrank ℝ W10 + finrank ℝ WPs + finrank ℝ WTwo

Proved

BookProof.ChapterLorentzRealRepFull.finrank_full_eq_add

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRepFull.

BookProof.ChapterLorentzRealRepFull.finrank_full_eq_add : finrank ℝ (Matrix (Fin 4) (Fin 4) ℝ) = finrank ℝ WHalf + finrank ℝ W10 + finrank ℝ WPs + finrank ℝ WTwo

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

Preamble

-- Generated from ChapterLorentzRealRepFull.lean — theorem BookProof.ChapterLorentzRealRepFull.finrank_full_eq_add
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.finrank_full_eq_add :
    finrank ℝ (Matrix (Fin 4) (Fin 4) ℝ)
      = finrank ℝ WHalf + finrank ℝ W10 + finrank ℝ WPs + finrank ℝ WTwo := by sorry

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