`BookProof.NavierStokesFlow.BilinearEsa.deficiencyTrivialAt_bilH` (κ : J → ℝ) (hκ : ∀ j, 0 ≤ κ j) (z : ℂ) (hblk : ∀ j, DeficiencyTrivialAt (lpFiniteModes ℕ) ((nsH (κ j) (hκ j)).com

Proved

BookProof.NavierStokesFlow.BilinearEsa.deficiencyTrivialAt_bilH

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesBilinearEsa.

BookProof.NavierStokesFlow.BilinearEsa.deficiencyTrivialAt_bilH (κ : J → ℝ) (hκ : ∀ j, 0 ≤ κ j) (z : ℂ) (hblk : ∀ j, DeficiencyTrivialAt (lpFiniteModes ℕ) ((nsH (κ j) (hκ j)).comp (Submodule.inclusion (finiteModes_le_maxDom (oscSymbol (κ j))))) z) : DeficiencyTrivialAt (lpFiniteModes (ℕ × J)) (bilH κ) z

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.BilinearEsa.deficiencyTrivialAt_bilH.

Preamble

-- Generated from ChapterNavierStokesBilinearEsa.lean — theorem BookProof.NavierStokesFlow.BilinearEsa.deficiencyTrivialAt_bilH
import Mathlib
import Definitions.Def_ChapterNavierStokesBilinearEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.BilinearEsa


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato HermiteFarisLavine

variable {J : Type*}

Formal statement

theorem BookProof.NavierStokesFlow.BilinearEsa.deficiencyTrivialAt_bilH (κ : J → ℝ) (hκ : ∀ j, 0 ≤ κ j) (z : ℂ)
    (hblk : ∀ j, DeficiencyTrivialAt (lpFiniteModes ℕ)
      ((nsH (κ j) (hκ j)).comp
        (Submodule.inclusion (finiteModes_le_maxDom (oscSymbol (κ j))))) z) :
    DeficiencyTrivialAt (lpFiniteModes (ℕ × J)) (bilH κ) z := by sorry

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