Prove2Me

`BookProof.NsFieldMomentumInverse.cut_mem_momDomain` {m : W} (hm : m ≠ 0) (n : ℕ) (f : Lp ℂ 2 (volume : Measure W)) : cut m n f ∈ momDomain m

Proved
BookProof.NsFieldMomentumInverse.cut_mem_momDomain

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsFieldMomentumInverse.

BookProof.NsFieldMomentumInverse.cut_mem_momDomain {m : W} (hm : m ≠ 0) (n : ℕ) (f : Lp ℂ 2 (volume : Measure W)) : cut m n f ∈ momDomain m

Formalization note: Lean 4 identifier BookProof.NsFieldMomentumInverse.cut_mem_momDomain.

Preamble
-- Generated from ChapterNsFieldMomentumInverse.lean — theorem BookProof.NsFieldMomentumInverse.cut_mem_momDomain
import Definitions.Def_ChapterNsSpatialMomentumMultiplier
import Definitions.Def_ChapterFourierMultiplierEsa
import Definitions.Def_ChapterStrichartzWave
import Mathlib
import Definitions.Def_ChapterNsFieldMomentumInverse
open BookProof.NsFieldMomentumInverse



open MeasureTheory SchwartzMap FourierTransform
open BookProof.NsSpatialMultiplier BookProof.FourierMultiplierEsa BookProof.StrichartzWave

noncomputable section

variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℝ W] [FiniteDimensional ℝ W]
  [MeasurableSpace W] [BorelSpace W]
Formal statement
theorem BookProof.NsFieldMomentumInverse.cut_mem_momDomain {m : W} (hm : m ≠ 0) (n : ℕ) (f : Lp ℂ 2 (volume : Measure W)) :
    cut m n f ∈ momDomain m := by sorry

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