`BookProof.TensorCore.isGraphCore_sectorCore` (hcore : IsGraphCore D A) (n : ℕ) : IsGraphCore (sectorCore Hs D₂ D n) (sectorOp Hs D₂ A n)

Proved

BookProof.TensorCore.isGraphCore_sectorCore

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTensorGraphCore.

BookProof.TensorCore.isGraphCore_sectorCore (hcore : IsGraphCore D A) (n : ℕ) : IsGraphCore (sectorCore Hs D₂ D n) (sectorOp Hs D₂ A n)

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

Preamble

-- Generated from ChapterTensorGraphCore.lean — theorem BookProof.TensorCore.isGraphCore_sectorCore
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterTensorGraphCore
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterGraphCoreTransfer
open BookProof.DirectSumEsa
open BookProof.GraphCore
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.isGraphCore_sectorCore (hcore : IsGraphCore D A) (n : ℕ) :
    IsGraphCore (sectorCore Hs D₂ D n) (sectorOp Hs D₂ A n) := by sorry

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