Prove2Me

`BookProof.MixedLinearEsa.hasCompactSupport_cutSchwartz` (g : V → ℝ) (hg : ContDiff ℝ ((⊤ : ℕ∞) : WithTop ℕ∞) g) (hgcs : HasCompactSupport g) (f : 𝓢(V, ℂ)) :...

Proved
BookProof.MixedLinearEsa.hasCompactSupport_cutSchwartz

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMixedLinearEsa.

BookProof.MixedLinearEsa.hasCompactSupport_cutSchwartz (g : V → ℝ) (hg : ContDiff ℝ ((⊤ : ℕ∞) : WithTop ℕ∞) g) (hgcs : HasCompactSupport g) (f : 𝓢(V, ℂ)) : HasCompactSupport ((cutSchwartz g hg hgcs f : V → ℂ))

Formalization note: Lean 4 identifier BookProof.MixedLinearEsa.hasCompactSupport_cutSchwartz.

Preamble
-- Generated from ChapterMixedLinearEsa.lean — theorem BookProof.MixedLinearEsa.hasCompactSupport_cutSchwartz
import Definitions.Def_ChapterStrichartzWave
import Definitions.Def_ChapterFourierMultiplierEsa
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterMixedLinearEsa
open BookProof.MixedLinearEsa



open MeasureTheory SchwartzMap FourierTransform ComplexInnerProductSpace LineDeriv
open BookProof.StrichartzWave BookProof.FourierMultiplierEsa BookProof.FarisLavine

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [FiniteDimensional ℝ V]
  [MeasurableSpace V] [BorelSpace V]


omit [FiniteDimensional ℝ V] [MeasurableSpace V] [BorelSpace V] in
Formal statement
theorem BookProof.MixedLinearEsa.hasCompactSupport_cutSchwartz (g : V → ℝ) (hg : ContDiff ℝ ((⊤ : ℕ∞) : WithTop ℕ∞) g)
    (hgcs : HasCompactSupport g) (f : 𝓢(V, ℂ)) :
    HasCompactSupport ((cutSchwartz g hg hgcs f : V → ℂ)) := by sorry

View graph