`BookProof.ChapterF7.conservativeHamiltonian_l2Symmetric` (V : ℝ → ℝ) (hV : Function.HasTemperateGrowth (fun x => (V x : ℂ))) : IsL2Symmetric (Complex.I • (kinetic.comp (mulOp V hV

Proved

BookProof.ChapterF7.conservativeHamiltonian_l2Symmetric

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF7.

BookProof.ChapterF7.conservativeHamiltonian_l2Symmetric (V : ℝ → ℝ) (hV : Function.HasTemperateGrowth (fun x => (V x : ℂ))) : IsL2Symmetric (Complex.I • (kinetic.comp (mulOp V hV) - (mulOp V hV).comp kinetic))

Formalization note: Lean 4 identifier BookProof.ChapterF7.conservativeHamiltonian_l2Symmetric.

Preamble

-- Generated from ChapterF7.lean — theorem BookProof.ChapterF7.conservativeHamiltonian_l2Symmetric
import Mathlib
import Definitions.Def_ChapterF7
open BookProof.ChapterF7


open SchwartzMap MeasureTheory Complex
open scoped BigOperators


noncomputable section

Formal statement

theorem BookProof.ChapterF7.conservativeHamiltonian_l2Symmetric (V : ℝ → ℝ)
    (hV : Function.HasTemperateGrowth (fun x => (V x : ℂ))) :
    IsL2Symmetric (Complex.I • (kinetic.comp (mulOp V hV) - (mulOp V hV).comp kinetic)) := by sorry

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