Prove2Me

`BookProof.NsFieldMomentumInverse.isMomInverse_of_memLp` {m : W} (hm : m ≠ 0) (f : Lp ℂ 2 (volume : Measure W)) (hf : MemLp (fun ξ => (f : W → ℂ) ξ / ((momSymbol m ξ : ℝ) : ℂ)) 2 (

Proved
BookProof.NsFieldMomentumInverse.isMomInverse_of_memLp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsFieldMomentumInverse.

BookProof.NsFieldMomentumInverse.isMomInverse_of_memLp {m : W} (hm : m ≠ 0) (f : Lp ℂ 2 (volume : Measure W)) (hf : MemLp (fun ξ => (f : W → ℂ) ξ / ((momSymbol m ξ : ℝ) : ℂ)) 2 (volume : Measure W)) : IsMomInverse m f hf.toLp

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

Preamble
-- Generated from ChapterNsFieldMomentumInverse.lean — theorem BookProof.NsFieldMomentumInverse.isMomInverse_of_memLp
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.isMomInverse_of_memLp {m : W} (hm : m ≠ 0) (f : Lp ℂ 2 (volume : Measure W))
    (hf : MemLp (fun ξ => (f : W → ℂ) ξ / ((momSymbol m ξ : ℝ) : ℂ)) 2 (volume : Measure W)) :
    IsMomInverse m f hf.toLp := by sorry

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