Prove2Me

`BookProof.NsPartialFourier.nsPartialFourier_comp_fibreFourier_eq` : ((nsPartialFourier V W).toLinearIsometry.toContinuousLinearMap).comp (fibreOp V (fibreFourierCLM W)) = (fibreOp

Proved
BookProof.NsPartialFourier.nsPartialFourier_comp_fibreFourier_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsPartialFourier.

BookProof.NsPartialFourier.nsPartialFourier_comp_fibreFourier_eq : ((nsPartialFourier V W).toLinearIsometry.toContinuousLinearMap).comp (fibreOp V (fibreFourierCLM W)) = (fibreOp V (fibreFourierCLM W)).comp ((nsPartialFourier V W).toLinearIsometry.toContinuousLinearMap)

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

Preamble
-- Generated from ChapterNsPartialFourier.lean — theorem BookProof.NsPartialFourier.nsPartialFourier_comp_fibreFourier_eq
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_comp_fibreFourier_eq :
    ((nsPartialFourier V W).toLinearIsometry.toContinuousLinearMap).comp
        (fibreOp V (fibreFourierCLM W))
      = (fibreOp V (fibreFourierCLM W)).comp
        ((nsPartialFourier V W).toLinearIsometry.toContinuousLinearMap) := by sorry

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