`BookProof.ChapterF2.bargmann_numberOp_re` (p : ℂ[X]) : (bargmann p (numberOp p)).re = ∑ n ∈ p.support, ((n : ℝ) * n.factorial) * Complex.normSq (p.coeff n)

Proved

BookProof.ChapterF2.bargmann_numberOp_re

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF2.

BookProof.ChapterF2.bargmann_numberOp_re (p : ℂ[X]) : (bargmann p (numberOp p)).re = ∑ n ∈ p.support, ((n : ℝ) * n.factorial) * Complex.normSq (p.coeff n)

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

Preamble

-- Generated from ChapterF2.lean — theorem BookProof.ChapterF2.bargmann_numberOp_re
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.bargmann_numberOp_re (p : ℂ[X]) :
    (bargmann p (numberOp p)).re
      = ∑ n ∈ p.support, ((n : ℝ) * n.factorial) * Complex.normSq (p.coeff n) := by sorry

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