`BookProof.DirectSumEsa.hasZeroDeficiencyOn_of_essentiallySelfAdjointOn` {Dom : Submodule ℂ F} (A : Dom →ₗ[ℂ] Dom) (h : EssentiallySelfAdjointOn Dom (Dom.subtype.comp A)) : HasZero

Proved

BookProof.DirectSumEsa.hasZeroDeficiencyOn_of_essentiallySelfAdjointOn

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterDirectSumEsa.

BookProof.DirectSumEsa.hasZeroDeficiencyOn_of_essentiallySelfAdjointOn {Dom : Submodule ℂ F} (A : Dom →ₗ[ℂ] Dom) (h : EssentiallySelfAdjointOn Dom (Dom.subtype.comp A)) : HasZeroDeficiencyOn Dom A

Formalization note: Lean 4 identifier BookProof.DirectSumEsa.hasZeroDeficiencyOn_of_essentiallySelfAdjointOn.

Preamble

-- Generated from ChapterDirectSumEsa.lean — theorem BookProof.DirectSumEsa.hasZeroDeficiencyOn_of_essentiallySelfAdjointOn
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Mathlib
import Definitions.Def_ChapterDirectSumEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesFlow
open BookProof.DirectSumEsa


open scoped ENNReal


open BookProof.FarisLavine

noncomputable section

variable {ι : Type*} {G : ι → Type*} [∀ i, NormedAddCommGroup (G i)]
  [∀ i, InnerProductSpace ℂ (G i)]

variable {D : ∀ i, Submodule ℂ (G i)}
variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
open BookProof.NavierStokesFlow

Formal statement

theorem BookProof.DirectSumEsa.hasZeroDeficiencyOn_of_essentiallySelfAdjointOn {Dom : Submodule ℂ F}
    (A : Dom →ₗ[ℂ] Dom) (h : EssentiallySelfAdjointOn Dom (Dom.subtype.comp A)) :
    HasZeroDeficiencyOn Dom A := by sorry

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