`BookProof.TensorCore.sectorOp_apply` (n : ℕ) (x : sectorDom Hs D₂ n) (x₀ : ((domSpace Hs D₂).pow n)) (hx : (x : Hs.pow n) = inclPow Hs D₂ n x₀) : sectorOp Hs D₂ A n x = derPow Hs

Proved

BookProof.TensorCore.sectorOp_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTensorGraphCore.

BookProof.TensorCore.sectorOp_apply (n : ℕ) (x : sectorDom Hs D₂ n) (x₀ : ((domSpace Hs D₂).pow n)) (hx : (x : Hs.pow n) = inclPow Hs D₂ n x₀) : sectorOp Hs D₂ A n x = derPow Hs D₂ A n x₀

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

Preamble

-- Generated from ChapterTensorGraphCore.lean — theorem BookProof.TensorCore.sectorOp_apply
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.sectorOp_apply (n : ℕ) (x : sectorDom Hs D₂ n) (x₀ : ((domSpace Hs D₂).pow n))
    (hx : (x : Hs.pow n) = inclPow Hs D₂ n x₀) :
    sectorOp Hs D₂ A n x = derPow Hs D₂ A n x₀ := by sorry

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