`BookProof.ChapterLorentzRealRepDirect.WFam_conj_invariant` (S : Matrix (Fin 4) (Fin 4) ℤ) (hS : S ∈ Omega) (i : Fin 4) : (WFam i).map (conjL (castR S) (castR (cinv S))) ≤ WFam i

Proved

BookProof.ChapterLorentzRealRepDirect.WFam_conj_invariant

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRepDirect.

BookProof.ChapterLorentzRealRepDirect.WFam_conj_invariant (S : Matrix (Fin 4) (Fin 4) ℤ) (hS : S ∈ Omega) (i : Fin 4) : (WFam i).map (conjL (castR S) (castR (cinv S))) ≤ WFam i

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

Preamble

-- Generated from ChapterLorentzRealRepDirect.lean — theorem BookProof.ChapterLorentzRealRepDirect.WFam_conj_invariant
import Definitions.Def_ChapterLorentzRealRepSum
import Definitions.Def_ChapterLorentzRealRepFull
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterPinOmega
import Mathlib
import Definitions.Def_ChapterLorentzRealRepDirect
import Definitions.Def_ChapterLorentzRealRep
import Definitions.Def_ChapterPinDoubleCover
open BookProof.ChapterLorentzRealRep
open BookProof.ChapterLorentzRealRepDirect


open Matrix Module


open BookProof.ChapterLorentzRealRep BookProof.ChapterLorentzRealRepSum
open BookProof.ChapterLorentzRealRepFull
open BookProof.ChapterA3 BookProof.ChapterPinOmega

Formal statement

theorem BookProof.ChapterLorentzRealRepDirect.WFam_conj_invariant (S : Matrix (Fin 4) (Fin 4) ℤ) (hS : S ∈ Omega) (i : Fin 4) :
    (WFam i).map (conjL (castR S) (castR (cinv S))) ≤ WFam i := by sorry

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