`BookProof.ChapterLorentzRealRep.WHalf_invariant_apply` (S : Matrix (Fin 4) (Fin 4) ℤ) (hS : S ∈ Omega) (A : Matrix (Fin 4) (Fin 4) ℝ) (hA : A ∈ WHalf) : castR S * A * castR (cinv

Proved

BookProof.ChapterLorentzRealRep.WHalf_invariant_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLorentzRealRep.

BookProof.ChapterLorentzRealRep.WHalf_invariant_apply (S : Matrix (Fin 4) (Fin 4) ℤ) (hS : S ∈ Omega) (A : Matrix (Fin 4) (Fin 4) ℝ) (hA : A ∈ WHalf) : castR S * A * castR (cinv S) ∈ WHalf

Formalization note: Lean 4 identifier BookProof.ChapterLorentzRealRep.WHalf_invariant_apply.

Preamble

-- Generated from ChapterLorentzRealRep.lean — theorem BookProof.ChapterLorentzRealRep.WHalf_invariant_apply
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterPinOmega
import Mathlib
import Definitions.Def_ChapterLorentzRealRep
import Definitions.Def_ChapterPinDoubleCover
open BookProof.ChapterLorentzRealRep


open Matrix


open BookProof.ChapterA3 BookProof.ChapterPinOmega

Formal statement

theorem BookProof.ChapterLorentzRealRep.WHalf_invariant_apply (S : Matrix (Fin 4) (Fin 4) ℤ) (hS : S ∈ Omega)
    (A : Matrix (Fin 4) (Fin 4) ℝ) (hA : A ∈ WHalf) :
    castR S * A * castR (cinv S) ∈ WHalf := by sorry

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