The Lean 4 theorem `hasDerivAt_pgFun_coord` in the `ChapterQgHermiteFriedrichs` chapter of the timepiece formalization

-- Generated from ChapterQgHermiteFriedrichs.lean — theorem BookProof.QgHermiteFriedrichs.hasDerivAt_pgFun_coord
import Mathlib
import Definitions.Def_ChapterQgHermiteFriedrichs
import Definitions.Def_ChapterSirkBandLedger
import Definitions.Def_ChapterRitzCertificate
open BookProof.QgHermiteFriedrichs







open MeasureTheory Complex MvPolynomial
open BookProof.HermiteProductCore BookProof.QgHermiteCore BookProof.Starobinsky
open BookProof.FarisLavine BookProof.YangMillsFriedrichs BookProof.FriedrichsExtension

noncomputable section

variable {d : ℕ}































variable (W : Vd d → ℝ)

theorem BookProof.QgHermiteFriedrichs.hasDerivAt_pgFun_coord (p : MvPolynomial (Fin d) ℂ) (j : Fin d) (x : Vd d) (t : ℝ) :
    HasDerivAt (fun s : ℝ => pgFun p (coordLine x j s))
      (pgFun (coreD j p) (coordLine x j t)) t := by sorry