`BookProof.HarmonicOscillator.hasDerivAt_polyGaussC` (p : Polynomial ℝ) (x : ℝ) : HasDerivAt (polyGaussC p) ((((derivative p - C (1 / 2 : ℝ) * (X * p)).eval x * gaussH x : ℝ) : ℂ))

Proved

BookProof.HarmonicOscillator.hasDerivAt_polyGaussC

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterHarmonicOscillatorEsa.

BookProof.HarmonicOscillator.hasDerivAt_polyGaussC (p : Polynomial ℝ) (x : ℝ) : HasDerivAt (polyGaussC p) ((((derivative p - C (1 / 2 : ℝ) * (X * p)).eval x * gaussH x : ℝ) : ℂ)) x

Formalization note: Lean 4 identifier BookProof.HarmonicOscillator.hasDerivAt_polyGaussC.

Preamble

-- Generated from ChapterHarmonicOscillatorEsa.lean — theorem BookProof.HarmonicOscillator.hasDerivAt_polyGaussC
import Definitions.Def_ChapterStrichartzHermiteQG
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterHarmonicOscillatorEsa
import Definitions.Def_ChapterHermiteFunctions
open BookProof.HermiteCore
open BookProof.HarmonicOscillator



open MeasureTheory Polynomial BookProof.HermiteCore BookProof.HermiteStrichartzQG
open BookProof.FarisLavine

Formal statement

theorem BookProof.HarmonicOscillator.hasDerivAt_polyGaussC (p : Polynomial ℝ) (x : ℝ) :
    HasDerivAt (polyGaussC p)
      ((((derivative p - C (1 / 2 : ℝ) * (X * p)).eval x * gaussH x : ℝ) : ℂ)) x := by sorry

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