`BookProof.ChapterPinDoubleCover.LamZ_spec_C` : ∀ S ∈ Omega, ∀ μ : Fin 4, mgamma μ * (Int.castRingHom ℂ).mapMatrix S = (Int.castRingHom ℂ).mapMatrix S * (∑ ν : Fin 4, (LamZ S) μ ν

Proved

BookProof.ChapterPinDoubleCover.LamZ_spec_C

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPinDoubleCover.

BookProof.ChapterPinDoubleCover.LamZ_spec_C : ∀ S ∈ Omega, ∀ μ : Fin 4, mgamma μ * (Int.castRingHom ℂ).mapMatrix S = (Int.castRingHom ℂ).mapMatrix S * (∑ ν : Fin 4, (LamZ S) μ ν • mgamma ν)

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

Preamble

-- Generated from ChapterPinDoubleCover.lean — theorem BookProof.ChapterPinDoubleCover.LamZ_spec_C
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_C :
    ∀ S ∈ Omega, ∀ μ : Fin 4,
      mgamma μ * (Int.castRingHom ℂ).mapMatrix S
        = (Int.castRingHom ℂ).mapMatrix S * (∑ ν : Fin 4, (LamZ S) μ ν • mgamma ν) := by sorry

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