`BookProof.ChapterF7.continuityHamiltonian_l2Symmetric` (v : ℝ → ℝ) (hv : Function.HasTemperateGrowth (fun x => (v x : ℂ))) : IsL2Symmetric (((1 : ℂ) / 2) • (momentum.comp (mulOp v

Proved

BookProof.ChapterF7.continuityHamiltonian_l2Symmetric

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF7.

BookProof.ChapterF7.continuityHamiltonian_l2Symmetric (v : ℝ → ℝ) (hv : Function.HasTemperateGrowth (fun x => (v x : ℂ))) : IsL2Symmetric (((1 : ℂ) / 2) • (momentum.comp (mulOp v hv) + (mulOp v hv).comp momentum))

Formalization note: Lean 4 identifier BookProof.ChapterF7.continuityHamiltonian_l2Symmetric.

Preamble

-- Generated from ChapterF7.lean — theorem BookProof.ChapterF7.continuityHamiltonian_l2Symmetric
import Mathlib
import Definitions.Def_ChapterF7
import Definitions.Def_ChapterContinuityUnitary
open BookProof.ChapterContinuityUnitary
open BookProof.ChapterF7


open SchwartzMap MeasureTheory Complex
open scoped BigOperators


noncomputable section

Formal statement

theorem BookProof.ChapterF7.continuityHamiltonian_l2Symmetric (v : ℝ → ℝ)
    (hv : Function.HasTemperateGrowth (fun x => (v x : ℂ))) :
    IsL2Symmetric
      (((1 : ℂ) / 2) • (momentum.comp (mulOp v hv) + (mulOp v hv).comp momentum)) := by sorry

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