`BookProof.TensorCore.inner_tmul_pow` (n : ℕ) (x x' : Hs.carrier) (y y' : (Hs.pow n).carrier) : (inner ℂ (x ⊗ₜ[ℂ] y : (Hs.pow (n + 1)).carrier) (x' ⊗ₜ[ℂ] y') : ℂ) = inner ℂ x x' *

Proved

BookProof.TensorCore.inner_tmul_pow

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTensorGraphCore.

BookProof.TensorCore.inner_tmul_pow (n : ℕ) (x x' : Hs.carrier) (y y' : (Hs.pow n).carrier) : (inner ℂ (x ⊗ₜ[ℂ] y : (Hs.pow (n + 1)).carrier) (x' ⊗ₜ[ℂ] y') : ℂ) = inner ℂ x x' * inner ℂ y y'

Formalization note: Lean 4 identifier BookProof.TensorCore.inner_tmul_pow.

Preamble

-- Generated from ChapterTensorGraphCore.lean — theorem BookProof.TensorCore.inner_tmul_pow
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterGraphCoreTransfer
import Mathlib
import Definitions.Def_ChapterTensorGraphCore
open BookProof.TensorCore



open scoped TensorProduct
open BookProof.FarisLavine BookProof.GraphCore

noncomputable section

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

Formal statement

theorem BookProof.TensorCore.inner_tmul_pow (n : ℕ) (x x' : Hs.carrier) (y y' : (Hs.pow n).carrier) :
    (inner ℂ (x ⊗ₜ[ℂ] y : (Hs.pow (n + 1)).carrier) (x' ⊗ₜ[ℂ] y') : ℂ)
      = inner ℂ x x' * inner ℂ y y' := by sorry

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