`BookProof.NavierStokesFlow.MomentumEsa.navierStokes_fock_hamiltonian_essentiallySelfAdjointOn_core` (d : ℕ) (p q : Fin d → ℕ → ℝ) (H : maxDom (nsFockSymbol d p q) →ₗ[ℂ] L2I Config

Proved

BookProof.NavierStokesFlow.MomentumEsa.navierStokes_fock_hamiltonian_essentiallySelfAdjointOn_core

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesMomentumEsa.

BookProof.NavierStokesFlow.MomentumEsa.navierStokes_fock_hamiltonian_essentiallySelfAdjointOn_core (d : ℕ) (p q : Fin d → ℕ → ℝ) (H : maxDom (nsFockSymbol d p q) →ₗ[ℂ] L2I Config) (a b cst : ℝ) (hH : SymmetricOn (maxDom (nsFockSymbol d p q)) H) (hcst : 0 ≤ cst) (hrel : ∀ x : maxDom (nsFockSymbol d p q), ‖H x‖ ^ 2 ≤ a * ‖diagMax (nsFockSymbol d p q) x‖ ^ 2 + b * ‖(x : L2I Config)‖ ^ 2) (hcomm : ∀ x : maxDom (nsFockSymbol d p q), |commForm H (diagMax (nsFockSymbol d p q)) x| ≤ cst * quadForm (diagMax (nsFockSymbol d p q)) x) : EssentiallySelfAdjointOn (lpFiniteModes Config) (H.comp (Submodule.inclusion (finiteModes_le_maxDom (nsFockSymbol d p q))))

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

Preamble

-- Generated from ChapterNavierStokesMomentumEsa.lean — theorem BookProof.NavierStokesFlow.MomentumEsa.navierStokes_fock_hamiltonian_essentiallySelfAdjointOn_core
import Mathlib
import Definitions.Def_ChapterNavierStokesMomentumEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesGaugeY
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesGaugeY
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.navierStokes_fock_hamiltonian_essentiallySelfAdjointOn_core (d : ℕ)
    (p q : Fin d → ℕ → ℝ)
    (H : maxDom (nsFockSymbol d p q) →ₗ[ℂ] L2I Config) (a b cst : ℝ)
    (hH : SymmetricOn (maxDom (nsFockSymbol d p q)) H) (hcst : 0 ≤ cst)
    (hrel : ∀ x : maxDom (nsFockSymbol d p q),
      ‖H x‖ ^ 2 ≤ a * ‖diagMax (nsFockSymbol d p q) x‖ ^ 2 + b * ‖(x : L2I Config)‖ ^ 2)
    (hcomm : ∀ x : maxDom (nsFockSymbol d p q),
      |commForm H (diagMax (nsFockSymbol d p q)) x|
        ≤ cst * quadForm (diagMax (nsFockSymbol d p q)) x) :
    EssentiallySelfAdjointOn (lpFiniteModes Config)
      (H.comp (Submodule.inclusion (finiteModes_le_maxDom (nsFockSymbol d p q)))) := by sorry

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