The Lean 4 theorem `momOp_apply_eq_differential` in the `ChapterNavierStokesDifferentialL2` chapter of the timepiece formalization

-- Generated from ChapterNavierStokesDifferentialL2.lean — theorem BookProof.NavierStokesFlow.DifferentialL2.momOp_apply_eq_differential
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesDeficiency
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterNavierStokesThreeComponent
import Definitions.Def_ChapterNavierStokesCanonicalVector
import Definitions.Def_ChapterNavierStokesLagrangianEsa
import Mathlib
import Definitions.Def_ChapterNavierStokesDifferentialL2
import Definitions.Def_ChapterHermiteProductCore
open BookProof.HermiteProductCore
open BookProof.NavierStokesFlow.DifferentialL2

variable {d : ℕ}



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

noncomputable section

theorem BookProof.NavierStokesFlow.DifferentialL2.momOp_apply_eq_differential (i : Fin d) (p : MvPolynomial (Fin d) ℂ) (x : Vd d) :
    pgFun (momPoly i p) x
      = -Complex.I * deriv (fun t : ℝ => pgFun p (sec i x t)) (x i) := by sorry