`BookProof.GraphCore.deficiencyTrivialAt_of_graphCore` {D₁ D₂ : Submodule ℂ F} (T : D₂ →ₗ[ℂ] F) (h : D₁ ≤ D₂) (hcore : IsGraphCore D₁ T) {z : ℂ} (h₂ :...

Proved

BookProof.GraphCore.deficiencyTrivialAt_of_graphCore

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGraphCoreTransfer.

BookProof.GraphCore.deficiencyTrivialAt_of_graphCore {D₁ D₂ : Submodule ℂ F} (T : D₂ →ₗ[ℂ] F) (h : D₁ ≤ D₂) (hcore : IsGraphCore D₁ T) {z : ℂ} (h₂ : DeficiencyTrivialAt D₂ T z) : DeficiencyTrivialAt D₁ (restrictOp T h) z

Formalization note: Lean 4 identifier BookProof.GraphCore.deficiencyTrivialAt_of_graphCore.

Preamble

-- Generated from ChapterGraphCoreTransfer.lean — theorem BookProof.GraphCore.deficiencyTrivialAt_of_graphCore
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterGraphCoreTransfer
import Definitions.Def_ChapterFarisLavineCore
open BookProof.GraphCore



open BookProof.FarisLavine

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]

Formal statement

theorem BookProof.GraphCore.deficiencyTrivialAt_of_graphCore {D₁ D₂ : Submodule ℂ F} (T : D₂ →ₗ[ℂ] F)
    (h : D₁ ≤ D₂) (hcore : IsGraphCore D₁ T) {z : ℂ}
    (h₂ : DeficiencyTrivialAt D₂ T z) :
    DeficiencyTrivialAt D₁ (restrictOp T h) z := by sorry

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