`BookProof.PermSector.purePow_mem_corePow` : ∀ (n : ℕ) (f : Fin n → D₂), (∀ i, ((f i : Hs.carrier)) ∈ D) → purePow (domSpace Hs D₂) n f ∈ corePow Hs D₂ D n

Proved

BookProof.PermSector.purePow_mem_corePow

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPermutationSectorEsa.

BookProof.PermSector.purePow_mem_corePow : ∀ (n : ℕ) (f : Fin n → D₂), (∀ i, ((f i : Hs.carrier)) ∈ D) → purePow (domSpace Hs D₂) n f ∈ corePow Hs D₂ D n

Formalization note: Lean 4 identifier BookProof.PermSector.purePow_mem_corePow.

Preamble

-- Generated from ChapterPermutationSectorEsa.lean — theorem BookProof.PermSector.purePow_mem_corePow
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterGraphCoreTransfer
import Definitions.Def_ChapterReducingSubspaceEsa
import Definitions.Def_ChapterGroupAverageEsa
import Definitions.Def_ChapterTensorPermutation
import Mathlib
import Definitions.Def_ChapterPermutationSectorEsa
import Definitions.Def_ChapterTensorGraphCore
open BookProof.TensorCore
open BookProof.PermSector



open scoped TensorProduct
open BookProof.FarisLavine BookProof.GraphCore BookProof.ReducedEsa BookProof.TensorCore
open BookProof.GroupAverage BookProof.TensorPerm

noncomputable section

variable (Hs : IPSpace) (D₂ : Submodule ℂ Hs.carrier) (A : D₂ →ₗ[ℂ] Hs.carrier)
  (D : Submodule ℂ Hs.carrier)

Formal statement

theorem BookProof.PermSector.purePow_mem_corePow : ∀ (n : ℕ) (f : Fin n → D₂),
    (∀ i, ((f i : Hs.carrier)) ∈ D) →
      purePow (domSpace Hs D₂) n f ∈ corePow Hs D₂ D n := by sorry

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