`BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_essentiallySelfAdjointOn_core` (hκ : 0 ≤ κ) : EssentiallySelfAdjointOn (lpFiniteModes ℕ) ((nsH κ hκ).comp (Submodule.inclusion (f

Proved

BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_essentiallySelfAdjointOn_core

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesHermiteFarisLavine.

BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_essentiallySelfAdjointOn_core (hκ : 0 ≤ κ) : EssentiallySelfAdjointOn (lpFiniteModes ℕ) ((nsH κ hκ).comp (Submodule.inclusion (finiteModes_le_maxDom (oscSymbol κ))))

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_essentiallySelfAdjointOn_core.

Preamble

-- Generated from ChapterNavierStokesHermiteFarisLavine.lean — theorem BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_essentiallySelfAdjointOn_core
import Mathlib
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
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.HermiteFarisLavine


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato

variable {κ : ℝ}
variable {x : maxDom (oscSymbol κ)}

Formal statement

theorem BookProof.NavierStokesFlow.HermiteFarisLavine.nsH_essentiallySelfAdjointOn_core (hκ : 0 ≤ κ) :
    EssentiallySelfAdjointOn (lpFiniteModes ℕ)
      ((nsH κ hκ).comp (Submodule.inclusion (finiteModes_le_maxDom (oscSymbol κ)))) := by sorry

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