`BookProof.NsScalarFourier.scalarFibreOp_prodMk` (T : Lp ℂ 2 (volume : Measure W) →L[ℂ] Lp ℂ 2 (volume : Measure W)) (a : Lp ℂ 2 (volume : Measure V)) (c : Lp ℂ 2 (volume : Measure

Proved

BookProof.NsScalarFourier.scalarFibreOp_prodMk

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsScalarFourier.

BookProof.NsScalarFourier.scalarFibreOp_prodMk (T : Lp ℂ 2 (volume : Measure W) →L[ℂ] Lp ℂ 2 (volume : Measure W)) (a : Lp ℂ 2 (volume : Measure V)) (c : Lp ℂ 2 (volume : Measure W)) : scalarFibreOp V T (prodMk a c) = prodMk a (T c)

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

Preamble

-- Generated from ChapterNsScalarFourier.lean — theorem BookProof.NsScalarFourier.scalarFibreOp_prodMk
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.scalarFibreOp_prodMk (T : Lp ℂ 2 (volume : Measure W) →L[ℂ] Lp ℂ 2 (volume : Measure W))
    (a : Lp ℂ 2 (volume : Measure V)) (c : Lp ℂ 2 (volume : Measure W)) :
    scalarFibreOp V T (prodMk a c) = prodMk a (T c) := by sorry

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