Prove2Me

`BookProof.ChapterA3.mgammaLin_orthogonal_invariant` {W : Submodule ℂ MajoranaSpace} (hW : ∀ μ, ∀ x ∈ W, mgammaLin μ x ∈ W) (μ : Fin 4) {y : MajoranaSpace} (hy : y ∈ Wᗮ) : mgammaLi

Proved
BookProof.ChapterA3.mgammaLin_orthogonal_invariant

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliCommutant.

BookProof.ChapterA3.mgammaLin_orthogonal_invariant {W : Submodule ℂ MajoranaSpace} (hW : ∀ μ, ∀ x ∈ W, mgammaLin μ x ∈ W) (μ : Fin 4) {y : MajoranaSpace} (hy : y ∈ Wᗮ) : mgammaLin μ y ∈ Wᗮ

Formalization note: Lean 4 identifier BookProof.ChapterA3.mgammaLin_orthogonal_invariant.

Preamble
-- Generated from ChapterPauliCommutant.lean — theorem BookProof.ChapterA3.mgammaLin_orthogonal_invariant
import Mathlib
import Definitions.Def_ChapterPauliCommutant
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
Formal statement
theorem BookProof.ChapterA3.mgammaLin_orthogonal_invariant {W : Submodule ℂ MajoranaSpace}
    (hW : ∀ μ, ∀ x ∈ W, mgammaLin μ x ∈ W) (μ : Fin 4) {y : MajoranaSpace} (hy : y ∈ Wᗮ) :
    mgammaLin μ y ∈ Wᗮ := by sorry

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