`BookProof.ChapterF1.ccr_mv` {n : ℕ} (i j : Fin n) (p : MvPolynomial (Fin n) ℂ) : (MvPolynomial.pderiv i) (MvPolynomial.X j * p) - MvPolynomial.X j * (MvPolynomial.pderiv i) p = (i

Proved

BookProof.ChapterF1.ccr_mv

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF1.

BookProof.ChapterF1.ccr_mv {n : ℕ} (i j : Fin n) (p : MvPolynomial (Fin n) ℂ) : (MvPolynomial.pderiv i) (MvPolynomial.X j * p) - MvPolynomial.X j * (MvPolynomial.pderiv i) p = (if i = j then p else 0)

Formalization note: Lean 4 identifier BookProof.ChapterF1.ccr_mv.

Preamble

-- Generated from ChapterF1.lean — theorem BookProof.ChapterF1.ccr_mv
import Mathlib
import Definitions.Def_ChapterF1
open BookProof.ChapterF1


open Polynomial Finset
open scoped BigOperators


noncomputable section

Formal statement

theorem BookProof.ChapterF1.ccr_mv {n : ℕ} (i j : Fin n) (p : MvPolynomial (Fin n) ℂ) :
    (MvPolynomial.pderiv i) (MvPolynomial.X j * p)
      - MvPolynomial.X j * (MvPolynomial.pderiv i) p
      = (if i = j then p else 0) := by sorry

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