`BookProof.NavierStokesFlow.FockOfFock.hTwoLevel_not_bounded` (ext : J → ℝ) (eps : K → ℝ) (hext : ∀ C : ℝ, ∃ j, C < |ext j|) : ¬ ∃ C : ℝ, ∀ f : FockOfFockDom J K,...

Proved

BookProof.NavierStokesFlow.FockOfFock.hTwoLevel_not_bounded

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesFockEsa.

BookProof.NavierStokesFlow.FockOfFock.hTwoLevel_not_bounded (ext : J → ℝ) (eps : K → ℝ) (hext : ∀ C : ℝ, ∃ j, C < |ext j|) : ¬ ∃ C : ℝ, ∀ f : FockOfFockDom J K, ‖hTwoLevel ext eps f‖ ≤ C * ‖f‖

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.FockOfFock.hTwoLevel_not_bounded.

Preamble

-- Generated from ChapterNavierStokesFockEsa.lean — theorem BookProof.NavierStokesFlow.FockOfFock.hTwoLevel_not_bounded
import Mathlib
import Definitions.Def_ChapterNavierStokesFockEsa
import Definitions.Def_ChapterFockOneParticleGap
import Definitions.Def_ChapterFockSecondQuantization
import Definitions.Def_ChapterNavierStokesFockSpace
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.FockOneParticleGap
open BookProof.FockSecondQuantization
open BookProof.NavierStokesFlow.FockOfFock
open BookProof.NavierStokesFlow


open MeasureTheory



open FullEsa LagrangianEsa

variable {M : Type*} [DecidableEq M]
variable {M : Type*} [DecidableEq M] {Ω : Type*} [MeasurableSpace Ω]
variable {J K : Type*} [DecidableEq J] [DecidableEq K]

Formal statement

theorem BookProof.NavierStokesFlow.FockOfFock.hTwoLevel_not_bounded (ext : J → ℝ) (eps : K → ℝ) (hext : ∀ C : ℝ, ∃ j, C < |ext j|) :
    ¬ ∃ C : ℝ, ∀ f : FockOfFockDom J K, ‖hTwoLevel ext eps f‖ ≤ C * ‖f‖ := by sorry

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