`BookProof.TensorCore.sectorCore_le_sectorDom` (n : ℕ) : sectorCore Hs D₂ D n ≤ sectorDom Hs D₂ n

Proved

BookProof.TensorCore.sectorCore_le_sectorDom

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTensorGraphCore.

BookProof.TensorCore.sectorCore_le_sectorDom (n : ℕ) : sectorCore Hs D₂ D n ≤ sectorDom Hs D₂ n

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

Preamble

-- Generated from ChapterTensorGraphCore.lean — theorem BookProof.TensorCore.sectorCore_le_sectorDom
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterGraphCoreTransfer
import Mathlib
import Definitions.Def_ChapterTensorGraphCore
import Definitions.Def_ChapterDirectSumEsa
open BookProof.DirectSumEsa
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.sectorCore_le_sectorDom (n : ℕ) :
    sectorCore Hs D₂ D n ≤ sectorDom Hs D₂ n := by sorry

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