The Lean 4 theorem `nsDiffH_symmetricOn` in the `ChapterNavierStokesDiffHashimoto` chapter of the timepiece formalization

-- Generated from ChapterNavierStokesDiffHashimoto.lean — theorem BookProof.NavierStokesFlow.DiffHashimoto.nsDiffH_symmetricOn
import Mathlib
import Definitions.Def_ChapterNavierStokesDiffHashimoto
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.DiffHashimoto







open Filter Topology



open MvPolynomial
open BookProof.FarisLavine BookProof.HashimotoShiftInvert BookProof.EsaClosure
open BookProof.HermiteGalerkin
open BookProof.HermiteProductCore BookProof.HermiteProductBasis
open BookProof.HermiteRelative
open BookProof.NavierStokesFlow.DifferentialL2

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.DiffHashimoto.nsDiffH_symmetricOn :
    SymmetricOn (polyGaussCore (d := 3))
      ((polyGaussCore (d := 3)).subtype.comp (nsDiffH A c)) := by sorry