`BookProof.ChapterF2.hamiltonian_expectation_nonneg` (p : ℂ[X]) : 0 ≤ (bargmann p (numberOp p)).re

Proved

BookProof.ChapterF2.hamiltonian_expectation_nonneg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF2.

BookProof.ChapterF2.hamiltonian_expectation_nonneg (p : ℂ[X]) : 0 ≤ (bargmann p (numberOp p)).re

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

Preamble

-- Generated from ChapterF2.lean — theorem BookProof.ChapterF2.hamiltonian_expectation_nonneg
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.hamiltonian_expectation_nonneg (p : ℂ[X]) :
    0 ≤ (bargmann p (numberOp p)).re := by sorry

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