`BookProof.NavierStokesFlow.AffineBlock.deficiencyTrivialAt_affBlockH` (κ c : J → ℝ) (hκ : ∀ j, 0 ≤ κ j) (hc : ∀ j, 0 ≤ c j) (z : ℂ) (hblk : ∀ j, DeficiencyTrivialAt (lpFiniteModes

Proved

BookProof.NavierStokesFlow.AffineBlock.deficiencyTrivialAt_affBlockH

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesAffineBlockEsa.

BookProof.NavierStokesFlow.AffineBlock.deficiencyTrivialAt_affBlockH (κ c : J → ℝ) (hκ : ∀ j, 0 ≤ κ j) (hc : ∀ j, 0 ≤ c j) (z : ℂ) (hblk : ∀ j, DeficiencyTrivialAt (lpFiniteModes ℕ) ((affH (hκ j) (hc j)).comp (Submodule.inclusion (finiteModes_le_maxDom (oscSymbol (affMu (κ j) (c j)))))) z) : DeficiencyTrivialAt (lpFiniteModes (ℕ × J)) (affBlockH κ c hκ hc) z

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.AffineBlock.deficiencyTrivialAt_affBlockH.

Preamble

-- Generated from ChapterNavierStokesAffineBlockEsa.lean — theorem BookProof.NavierStokesFlow.AffineBlock.deficiencyTrivialAt_affBlockH
import Mathlib
import Definitions.Def_ChapterNavierStokesAffineBlockEsa
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.AffineFiber.PairShift
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.AffineBlock


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato HermiteFarisLavine ShiftHamiltonian AffineFiber BilinearEsa

variable {J : Type*}

Formal statement

theorem BookProof.NavierStokesFlow.AffineBlock.deficiencyTrivialAt_affBlockH (κ c : J → ℝ) (hκ : ∀ j, 0 ≤ κ j) (hc : ∀ j, 0 ≤ c j)
    (z : ℂ)
    (hblk : ∀ j, DeficiencyTrivialAt (lpFiniteModes ℕ)
      ((affH (hκ j) (hc j)).comp
        (Submodule.inclusion (finiteModes_le_maxDom (oscSymbol (affMu (κ j) (c j)))))) z) :
    DeficiencyTrivialAt (lpFiniteModes (ℕ × J)) (affBlockH κ c hκ hc) z := by sorry

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