`BookProof.PermSector.inclPow_purePow` : ∀ (n : ℕ) (f : Fin n → D₂), inclPow Hs D₂ n (purePow (domSpace Hs D₂) n f) = purePow Hs n (fun i => ((f i : Hs.carrier)))

Proved

BookProof.PermSector.inclPow_purePow

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPermutationSectorEsa.

BookProof.PermSector.inclPow_purePow : ∀ (n : ℕ) (f : Fin n → D₂), inclPow Hs D₂ n (purePow (domSpace Hs D₂) n f) = purePow Hs n (fun i => ((f i : Hs.carrier)))

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

Preamble

-- Generated from ChapterPermutationSectorEsa.lean — theorem BookProof.PermSector.inclPow_purePow
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.inclPow_purePow : ∀ (n : ℕ) (f : Fin n → D₂),
    inclPow Hs D₂ n (purePow (domSpace Hs D₂) n f)
      = purePow Hs n (fun i => ((f i : Hs.carrier))) := by sorry

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