`BookProof.ChapterF2.numberOp_coeff` (p : ℂ[X]) (n : ℕ) : (numberOp p).coeff n = (n : ℂ) * p.coeff n

Proved

BookProof.ChapterF2.numberOp_coeff

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF2.

BookProof.ChapterF2.numberOp_coeff (p : ℂ[X]) (n : ℕ) : (numberOp p).coeff n = (n : ℂ) * p.coeff n

Formalization note: Lean 4 identifier BookProof.ChapterF2.numberOp_coeff.

Preamble

-- Generated from ChapterF2.lean — theorem BookProof.ChapterF2.numberOp_coeff
import Definitions.Def_ChapterF1
import Mathlib
import Definitions.Def_ChapterF2
import Definitions.Def_ChapterGhostField
open BookProof.GhostField
open BookProof.ChapterF2


open Polynomial Finset
open scoped BigOperators


open BookProof.ChapterF1

noncomputable section

Formal statement

theorem BookProof.ChapterF2.numberOp_coeff (p : ℂ[X]) (n : ℕ) :
    (numberOp p).coeff n = (n : ℂ) * p.coeff n := by sorry

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