`BookProof.NavierStokesFlow.AffineFiber.affH_essentiallySelfAdjointOn_core` {κ c : ℝ} (hκ : 0 ≤ κ) (hc : 0 ≤ c) : EssentiallySelfAdjointOn (lpFiniteModes ℕ) ((affH hκ hc).comp (Sub

Proved

BookProof.NavierStokesFlow.AffineFiber.affH_essentiallySelfAdjointOn_core

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesAffineFiberEsa.

BookProof.NavierStokesFlow.AffineFiber.affH_essentiallySelfAdjointOn_core {κ c : ℝ} (hκ : 0 ≤ κ) (hc : 0 ≤ c) : EssentiallySelfAdjointOn (lpFiniteModes ℕ) ((affH hκ hc).comp (Submodule.inclusion (finiteModes_le_maxDom (oscSymbol (affMu κ c)))))

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.AffineFiber.affH_essentiallySelfAdjointOn_core.

Preamble

-- Generated from ChapterNavierStokesAffineFiberEsa.lean — theorem BookProof.NavierStokesFlow.AffineFiber.affH_essentiallySelfAdjointOn_core
import Mathlib
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.AffineFiber


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato HermiteFarisLavine ShiftHamiltonian

variable {ι : Type*}

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}
variable (P : PairShift ι)

Formal statement

theorem BookProof.NavierStokesFlow.AffineFiber.affH_essentiallySelfAdjointOn_core {κ c : ℝ} (hκ : 0 ≤ κ) (hc : 0 ≤ c) :
    EssentiallySelfAdjointOn (lpFiniteModes ℕ)
      ((affH hκ hc).comp
        (Submodule.inclusion (finiteModes_le_maxDom (oscSymbol (affMu κ c))))) := by sorry

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