`BookProof.NsFieldMomentumInverse.eq_div_of_mul_eq_ae` {m : W} (hm : m ≠ 0) (t : W → ℂ) (p : ℂ) (h : ∀ᵐ ξ ∂(volume : Measure W), ((momSymbol m ξ : ℝ) : ℂ) * t ξ = p) :...

Proved

BookProof.NsFieldMomentumInverse.eq_div_of_mul_eq_ae

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsFieldMomentumInverse.

BookProof.NsFieldMomentumInverse.eq_div_of_mul_eq_ae {m : W} (hm : m ≠ 0) (t : W → ℂ) (p : ℂ) (h : ∀ᵐ ξ ∂(volume : Measure W), ((momSymbol m ξ : ℝ) : ℂ) * t ξ = p) : ∀ᵐ ξ ∂(volume : Measure W), t ξ = p / ((momSymbol m ξ : ℝ) : ℂ)

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

Preamble

-- Generated from ChapterNsFieldMomentumInverse.lean — theorem BookProof.NsFieldMomentumInverse.eq_div_of_mul_eq_ae
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.eq_div_of_mul_eq_ae {m : W} (hm : m ≠ 0) (t : W → ℂ) (p : ℂ)
    (h : ∀ᵐ ξ ∂(volume : Measure W), ((momSymbol m ξ : ℝ) : ℂ) * t ξ = p) :
    ∀ᵐ ξ ∂(volume : Measure W), t ξ = p / ((momSymbol m ξ : ℝ) : ℂ) := by sorry

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