(i : Fin 3) (x : lpFiniteModes Vel) (β : Vel) : crd (numSeq i x) β = ((β i : ℝ) : ℂ) * crd x β

-- Generated from ChapterNavierStokesDiffFarisLavine.lean — theorem BookProof.NavierStokesFlow.DiffFarisLavine.crd_numSeq
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.crd_numSeq (i : Fin 3) (x : lpFiniteModes Vel) (β : Vel) :
    crd (numSeq i x) β = ((β i : ℝ) : ℂ) * crd x β := by sorry