`BookProof.NsScalarFourier.nsScalarFourier_prodMk_eq` (a : Lp ℂ 2 (volume : Measure V)) (c : Lp ℂ 2 (volume : Measure W)) : nsScalarFourier V W (prodMk a c) = curryLI (nsPartialFou

Proved

BookProof.NsScalarFourier.nsScalarFourier_prodMk_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsScalarFourier.

BookProof.NsScalarFourier.nsScalarFourier_prodMk_eq (a : Lp ℂ 2 (volume : Measure V)) (c : Lp ℂ 2 (volume : Measure W)) : nsScalarFourier V W (prodMk a c) = curryLI (nsPartialFourier V W (fibMk a c))

Formalization note: Lean 4 identifier BookProof.NsScalarFourier.nsScalarFourier_prodMk_eq.

Preamble

-- Generated from ChapterNsScalarFourier.lean — theorem BookProof.NsScalarFourier.nsScalarFourier_prodMk_eq
import Definitions.Def_ChapterNsScalarVectorCurry
import Mathlib
import Definitions.Def_ChapterNsScalarFourier
import Definitions.Def_ChapterNsPartialFourier
open BookProof.NsPartialFourier
open BookProof.NsScalarFourier


open MeasureTheory


open BookProof.NsPartialFourier BookProof.NsScalarVectorCurry

noncomputable section

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

Formal statement

theorem BookProof.NsScalarFourier.nsScalarFourier_prodMk_eq (a : Lp ℂ 2 (volume : Measure V))
    (c : Lp ℂ 2 (volume : Measure W)) :
    nsScalarFourier V W (prodMk a c) = curryLI (nsPartialFourier V W (fibMk a c)) := by sorry

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