`BookProof.TensorCore.exists_ne_zero_mem_sectorCore_one` (hD : D ≤ D₂) {a : Hs.carrier} (haD : a ∈ D) (ha0 : a ≠ 0) : ∃ x ∈ sectorCore Hs D₂ D 1, x ≠ 0

Proved

BookProof.TensorCore.exists_ne_zero_mem_sectorCore_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterTensorGraphCore.

BookProof.TensorCore.exists_ne_zero_mem_sectorCore_one (hD : D ≤ D₂) {a : Hs.carrier} (haD : a ∈ D) (ha0 : a ≠ 0) : ∃ x ∈ sectorCore Hs D₂ D 1, x ≠ 0

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

Preamble

-- Generated from ChapterTensorGraphCore.lean — theorem BookProof.TensorCore.exists_ne_zero_mem_sectorCore_one
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.exists_ne_zero_mem_sectorCore_one (hD : D ≤ D₂) {a : Hs.carrier} (haD : a ∈ D)
    (ha0 : a ≠ 0) : ∃ x ∈ sectorCore Hs D₂ D 1, x ≠ 0 := by sorry

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