`BookProof.TensorCore.essentiallySelfAdjointOn_sectorCore` (hcore : IsGraphCore D A) (n : ℕ) (hesa : EssentiallySelfAdjointOn (sectorDom Hs D₂ n) (sectorOp Hs D₂ A n)) : Essentiall

Proved

BookProof.TensorCore.essentiallySelfAdjointOn_sectorCore

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTensorGraphCore.

BookProof.TensorCore.essentiallySelfAdjointOn_sectorCore (hcore : IsGraphCore D A) (n : ℕ) (hesa : EssentiallySelfAdjointOn (sectorDom Hs D₂ n) (sectorOp Hs D₂ A n)) : EssentiallySelfAdjointOn (sectorCore Hs D₂ D n) (restrictOp (sectorOp Hs D₂ A n) (sectorCore_le_sectorDom Hs D₂ D n))

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

Preamble

-- Generated from ChapterTensorGraphCore.lean — theorem BookProof.TensorCore.essentiallySelfAdjointOn_sectorCore
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterTensorGraphCore
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterGraphCoreTransfer
import Theorems.Thm_BookProof_TensorCore_sectorCore_le_sectorDom
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.essentiallySelfAdjointOn_sectorCore (hcore : IsGraphCore D A) (n : ℕ)
    (hesa : EssentiallySelfAdjointOn (sectorDom Hs D₂ n) (sectorOp Hs D₂ A n)) :
    EssentiallySelfAdjointOn (sectorCore Hs D₂ D n)
      (restrictOp (sectorOp Hs D₂ A n) (sectorCore_le_sectorDom Hs D₂ D n)) := by sorry

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