(mu : ℝ) (x : lpFiniteModes Vel) : quadForm ((polyGaussCore (d

-- Generated from ChapterNavierStokesDiffFarisLavine.lean — theorem BookProof.NavierStokesFlow.DiffFarisLavine.quadForm_nsDiffN_embedCore
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
open BookProof.NavierStokesFlow.ThreeComponent
open BookProof.NavierStokesFlow.IkebeKato

noncomputable section

















variable (A : Matrix (Fin 3) (Fin 3) ℝ) (c : Fin 3 → ℝ)

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.quadForm_nsDiffN_embedCore (mu : ℝ) (x : lpFiniteModes Vel) :
    quadForm ((polyGaussCore (d := 3)).subtype.comp (nsDiffN mu)) (embedCore x)
      = quadForm (diagMax (velSym mu))
          (Submodule.inclusion (finiteModes_le_maxDom (velSym mu)) x) := by sorry