(mu : ℝ) : nsDiffN mu = (((2 * mu : ℝ) : ℂ)) • (∑ i, (creOp i).comp (annOp i)) + (((3 * mu + 1 : ℝ) : ℂ)) • LinearMap.id

-- Generated from ChapterNavierStokesDiffFarisLavine.lean — theorem BookProof.NavierStokesFlow.DiffFarisLavine.nsDiffN_eq_ladder
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.nsDiffN_eq_ladder (mu : ℝ) :
    nsDiffN mu = (((2 * mu : ℝ) : ℂ)) • (∑ i, (creOp i).comp (annOp i))
      + (((3 * mu + 1 : ℝ) : ℂ)) • LinearMap.id := by sorry