`BookProof.TensorPerm.inner_purePow` : ∀ (n : ℕ) (f g : Fin n → E.carrier), (inner ℂ (purePow E n f) (purePow E n g) : ℂ) = ∏ i, inner ℂ (f i) (g i)

Proved

BookProof.TensorPerm.inner_purePow

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTensorPermutation.

BookProof.TensorPerm.inner_purePow : ∀ (n : ℕ) (f g : Fin n → E.carrier), (inner ℂ (purePow E n f) (purePow E n g) : ℂ) = ∏ i, inner ℂ (f i) (g i)

Formalization note: Lean 4 identifier BookProof.TensorPerm.inner_purePow.

Preamble

-- Generated from ChapterTensorPermutation.lean — theorem BookProof.TensorPerm.inner_purePow
import Definitions.Def_ChapterGroupAverageEsa
import Mathlib
import Definitions.Def_ChapterTensorPermutation
import Definitions.Def_ChapterTensorGraphCore
open BookProof.TensorCore
open BookProof.TensorPerm



open scoped TensorProduct
open BookProof.TensorCore BookProof.GroupAverage

noncomputable section

variable (E : BookProof.TensorCore.IPSpace)

Formal statement

theorem BookProof.TensorPerm.inner_purePow : ∀ (n : ℕ) (f g : Fin n → E.carrier),
    (inner ℂ (purePow E n f) (purePow E n g) : ℂ) = ∏ i, inner ℂ (f i) (g i) := by sorry

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