(a : Fin 3 →₀ ℕ) : hermiteMvLp a ∈ Submodule.map ((polyGaussCore (d

-- Generated from ChapterNavierStokesDiffFarisLavine.lean — theorem BookProof.NavierStokesFlow.DiffFarisLavine.hermiteMvLp_mem_range
import Mathlib
import Definitions.Def_ChapterNavierStokesDiffFarisLavine
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterHermiteProductBasis
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.DiffFarisLavine













open MvPolynomial
open BookProof.HermiteProductCore BookProof.HermiteProductBasis
open BookProof.NavierStokesFlow.LpNat BookProof.FarisLavine BookProof.NavierStokesFlow.IkebeKato BookProof.NavierStokesFlow.ThreeComponent BookProof.NavierStokesFlow.CanonicalVector BookProof.NavierStokesFlow.DifferentialL2

noncomputable section

set_option maxHeartbeats 4000000 in
-- The core operators unfold through several linear equivalences on a submodule of `L²(ℝ³)`,
-- so the default heartbeat budget is not enough.

theorem BookProof.NavierStokesFlow.DiffFarisLavine.hermiteMvLp_mem_range (a : Fin 3 →₀ ℕ) :
    hermiteMvLp a
      ∈ Submodule.map ((polyGaussCore (d := 3)).subtype) (LinearMap.range embedCore) := by sorry