`BookProof.NsPartialFourier.nsPartialFourier_fibreOp` (T : Lp ℂ 2 (volume : Measure W) →L[ℂ] Lp ℂ 2 (volume : Measure W)) (f : Lp (Lp ℂ 2 (volume : Measure W)) 2 (volume : Measure

Proved

BookProof.NsPartialFourier.nsPartialFourier_fibreOp

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsPartialFourier.

BookProof.NsPartialFourier.nsPartialFourier_fibreOp (T : Lp ℂ 2 (volume : Measure W) →L[ℂ] Lp ℂ 2 (volume : Measure W)) (f : Lp (Lp ℂ 2 (volume : Measure W)) 2 (volume : Measure V)) : nsPartialFourier V W (fibreOp V T f) = fibreOp V T (nsPartialFourier V W f)

Formalization note: Lean 4 identifier BookProof.NsPartialFourier.nsPartialFourier_fibreOp.

Preamble

-- Generated from ChapterNsPartialFourier.lean — theorem BookProof.NsPartialFourier.nsPartialFourier_fibreOp
import Mathlib
import Definitions.Def_ChapterNsPartialFourier
open BookProof.NsPartialFourier



open MeasureTheory SchwartzMap FourierTransform LineDeriv

noncomputable section

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

variable {F G : Type*} [NormedAddCommGroup F] [NormedSpace ℂ F]
  [NormedAddCommGroup G] [NormedSpace ℂ G]
variable {F G : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]
  [NormedAddCommGroup G] [InnerProductSpace ℂ G] [CompleteSpace G]
variable {W : Type*} [NormedAddCommGroup W] [InnerProductSpace ℝ W] [FiniteDimensional ℝ W]
  [MeasurableSpace W] [BorelSpace W]

Formal statement

theorem BookProof.NsPartialFourier.nsPartialFourier_fibreOp (T : Lp ℂ 2 (volume : Measure W) →L[ℂ] Lp ℂ 2 (volume : Measure W))
    (f : Lp (Lp ℂ 2 (volume : Measure W)) 2 (volume : Measure V)) :
    nsPartialFourier V W (fibreOp V T f) = fibreOp V T (nsPartialFourier V W f) := by sorry

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