`BookProof.ChapterLorentzRealRepDirect.sum_finrank_WFam` : (∑ i, finrank ℝ (WFam i)) = finrank ℝ (Matrix (Fin 4) (Fin 4) ℝ)

Proved

BookProof.ChapterLorentzRealRepDirect.sum_finrank_WFam

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRepDirect.

BookProof.ChapterLorentzRealRepDirect.sum_finrank_WFam : (∑ i, finrank ℝ (WFam i)) = finrank ℝ (Matrix (Fin 4) (Fin 4) ℝ)

Formalization note: Lean 4 identifier BookProof.ChapterLorentzRealRepDirect.sum_finrank_WFam.

Preamble

-- Generated from ChapterLorentzRealRepDirect.lean — theorem BookProof.ChapterLorentzRealRepDirect.sum_finrank_WFam
import Definitions.Def_ChapterLorentzRealRepSum
import Mathlib
import Definitions.Def_ChapterLorentzRealRepDirect
import Definitions.Def_ChapterLorentzRealRep
import Definitions.Def_ChapterLorentzRealRepFull
open BookProof.ChapterLorentzRealRep
open BookProof.ChapterLorentzRealRepFull
open BookProof.ChapterLorentzRealRepDirect


open Matrix Module


open BookProof.ChapterLorentzRealRep BookProof.ChapterLorentzRealRepSum
open BookProof.ChapterLorentzRealRepFull

Formal statement

theorem BookProof.ChapterLorentzRealRepDirect.sum_finrank_WFam :
    (∑ i, finrank ℝ (WFam i)) = finrank ℝ (Matrix (Fin 4) (Fin 4) ℝ) := by sorry

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