`BookProof.ChapterPinDoubleCover.LamZ_spec` : ∀ S ∈ Omega, ∀ μ : Fin 4, mgammaZ μ * S = S * (∑ ν : Fin 4, (LamZ S) μ ν • mgammaZ ν)

Proved

BookProof.ChapterPinDoubleCover.LamZ_spec

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPinDoubleCover.

BookProof.ChapterPinDoubleCover.LamZ_spec : ∀ S ∈ Omega, ∀ μ : Fin 4, mgammaZ μ * S = S * (∑ ν : Fin 4, (LamZ S) μ ν • mgammaZ ν)

Formalization note: Lean 4 identifier BookProof.ChapterPinDoubleCover.LamZ_spec.

Preamble

-- Generated from ChapterPinDoubleCover.lean — theorem BookProof.ChapterPinDoubleCover.LamZ_spec
import Mathlib
import Definitions.Def_ChapterPinDoubleCover
import Definitions.Def_ChapterA3
open BookProof.ChapterA3
open BookProof.ChapterPinDoubleCover


open Matrix


open BookProof.ChapterA3
open Classical

Formal statement

theorem BookProof.ChapterPinDoubleCover.LamZ_spec :
    ∀ S ∈ Omega, ∀ μ : Fin 4,
      mgammaZ μ * S = S * (∑ ν : Fin 4, (LamZ S) μ ν • mgammaZ ν) := by sorry

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