`BookProof.NavierStokesFlow.MomentumPerturbation.pertHam_essentiallySelfAdjointOn_core` (c : ι → ℝ) (hc : ∀ k, 1 ≤ c k) (u w : maxDom c) : EssentiallySelfAdjointOn (lpFiniteModes ι

Proved

BookProof.NavierStokesFlow.MomentumPerturbation.pertHam_essentiallySelfAdjointOn_core

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesMomentumPerturbation.

BookProof.NavierStokesFlow.MomentumPerturbation.pertHam_essentiallySelfAdjointOn_core (c : ι → ℝ) (hc : ∀ k, 1 ≤ c k) (u w : maxDom c) : EssentiallySelfAdjointOn (lpFiniteModes ι) ((pertHam c (u : L2I ι) (w : L2I ι)).comp (Submodule.inclusion (finiteModes_le_maxDom c)))

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.MomentumPerturbation.pertHam_essentiallySelfAdjointOn_core.

Preamble

-- Generated from ChapterNavierStokesMomentumPerturbation.lean — theorem BookProof.NavierStokesFlow.MomentumPerturbation.pertHam_essentiallySelfAdjointOn_core
import Mathlib
import Definitions.Def_ChapterNavierStokesMomentumPerturbation
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.MomentumPerturbation




open LpNat BookProof.FarisLavine IkebeKato

variable {ι : Type*}

Formal statement

theorem BookProof.NavierStokesFlow.MomentumPerturbation.pertHam_essentiallySelfAdjointOn_core (c : ι → ℝ) (hc : ∀ k, 1 ≤ c k)
    (u w : maxDom c) :
    EssentiallySelfAdjointOn (lpFiniteModes ι)
      ((pertHam c (u : L2I ι) (w : L2I ι)).comp
        (Submodule.inclusion (finiteModes_le_maxDom c))) := by sorry

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