`BookProof.GaussCoordCombo.pderiv_aeval_self` (i : Fin d) (f : Polynomial ℂ) : pderiv i (Polynomial.aeval (X i : MvPolynomial (Fin d) ℂ) f) = Polynomial.aeval (X i : MvPolynomial (

Proved

BookProof.GaussCoordCombo.pderiv_aeval_self

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaussCoordCombo.

BookProof.GaussCoordCombo.pderiv_aeval_self (i : Fin d) (f : Polynomial ℂ) : pderiv i (Polynomial.aeval (X i : MvPolynomial (Fin d) ℂ) f) = Polynomial.aeval (X i : MvPolynomial (Fin d) ℂ) (Polynomial.derivative f)

Formalization note: Lean 4 identifier BookProof.GaussCoordCombo.pderiv_aeval_self.

Preamble

-- Generated from ChapterGaussCoordCombo.lean — theorem BookProof.GaussCoordCombo.pderiv_aeval_self
import Definitions.Def_ChapterHermiteProductCore
import Mathlib
import Definitions.Def_ChapterGaussCoordCombo
open BookProof.GaussCoordCombo



open MvPolynomial BookProof.HermiteProductCore

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.GaussCoordCombo.pderiv_aeval_self (i : Fin d) (f : Polynomial ℂ) :
    pderiv i (Polynomial.aeval (X i : MvPolynomial (Fin d) ℂ) f)
      = Polynomial.aeval (X i : MvPolynomial (Fin d) ℂ) (Polynomial.derivative f) := by sorry

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