Prove2Me

`BookProof.NsFieldMomentumInverse.isMomInverse_momentumOp` (m : W) (f : 𝓢(W, ℂ)) : IsMomInverse m (l2Fourier W (opL2 (momentumOp m) (schwartzEquiv W f))) (l2Fourier W (f.toLp 2 (vo

Proved
BookProof.NsFieldMomentumInverse.isMomInverse_momentumOp

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsFieldMomentumInverse.

BookProof.NsFieldMomentumInverse.isMomInverse_momentumOp (m : W) (f : 𝓢(W, ℂ)) : IsMomInverse m (l2Fourier W (opL2 (momentumOp m) (schwartzEquiv W f))) (l2Fourier W (f.toLp 2 (volume : Measure W)))

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

Preamble
-- Generated from ChapterNsFieldMomentumInverse.lean — theorem BookProof.NsFieldMomentumInverse.isMomInverse_momentumOp
import Mathlib
import Definitions.Def_ChapterNsFieldMomentumInverse
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterFourierMultiplierEsa
import Definitions.Def_ChapterNsSpatialMomentumMultiplier
import Definitions.Def_ChapterStrichartzWave
open BookProof.FarisLavine
open BookProof.FourierMultiplierEsa
open BookProof.NsSpatialMultiplier
open BookProof.StrichartzWave
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.isMomInverse_momentumOp (m : W) (f : 𝓢(W, ℂ)) :
    IsMomInverse m (l2Fourier W (opL2 (momentumOp m) (schwartzEquiv W f)))
      (l2Fourier W (f.toLp 2 (volume : Measure W))) := by sorry

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