Prove2Me

`BookProof.NavierStokesFlow.MomentumEsa.hasZeroDeficiencyOn_of_esa_core` {c : ι → ℝ} (H : maxDom c →ₗ[ℂ] L2I ι) (Hc : lpFiniteModes ι →ₗ[ℂ] lpFiniteModes ι) (hHc : ∀ x :...

Proved
BookProof.NavierStokesFlow.MomentumEsa.hasZeroDeficiencyOn_of_esa_core

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesMomentumEsa.

BookProof.NavierStokesFlow.MomentumEsa.hasZeroDeficiencyOn_of_esa_core {c : ι → ℝ} (H : maxDom c →ₗ[ℂ] L2I ι) (Hc : lpFiniteModes ι →ₗ[ℂ] lpFiniteModes ι) (hHc : ∀ x : lpFiniteModes ι, ((Hc x : lpFiniteModes ι) : L2I ι) = H (Submodule.inclusion (finiteModes_le_maxDom c) x)) (hesa : EssentiallySelfAdjointOn (lpFiniteModes ι) (H.comp (Submodule.inclusion (finiteModes_le_maxDom c)))) : HasZeroDeficiencyOn (lpFiniteModes ι) Hc

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.MomentumEsa.hasZeroDeficiencyOn_of_esa_core.

Preamble
-- Generated from ChapterNavierStokesMomentumEsa.lean — theorem BookProof.NavierStokesFlow.MomentumEsa.hasZeroDeficiencyOn_of_esa_core
import Mathlib
import Definitions.Def_ChapterNavierStokesMomentumEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesFlow
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.MomentumEsa




open LpNat BookProof.FarisLavine IkebeKato FarisLavineLift DiagonalEsa

variable {ι : Type*}
Formal statement
theorem BookProof.NavierStokesFlow.MomentumEsa.hasZeroDeficiencyOn_of_esa_core {c : ι → ℝ} (H : maxDom c →ₗ[ℂ] L2I ι)
    (Hc : lpFiniteModes ι →ₗ[ℂ] lpFiniteModes ι)
    (hHc : ∀ x : lpFiniteModes ι, ((Hc x : lpFiniteModes ι) : L2I ι)
      = H (Submodule.inclusion (finiteModes_le_maxDom c) x))
    (hesa : EssentiallySelfAdjointOn (lpFiniteModes ι)
      (H.comp (Submodule.inclusion (finiteModes_le_maxDom c)))) :
    HasZeroDeficiencyOn (lpFiniteModes ι) Hc := by sorry

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