`BookProof.NsScalarFourier.scalarFibreOp_apply` (T : Lp ℂ 2 (volume : Measure W) →L[ℂ] Lp ℂ 2 (volume : Measure W)) (g : Lp ℂ 2 ((volume : Measure V).prod (volume : Measure W))) :

Proved

BookProof.NsScalarFourier.scalarFibreOp_apply

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsScalarFourier.

BookProof.NsScalarFourier.scalarFibreOp_apply (T : Lp ℂ 2 (volume : Measure W) →L[ℂ] Lp ℂ 2 (volume : Measure W)) (g : Lp ℂ 2 ((volume : Measure V).prod (volume : Measure W))) : scalarFibreOp V T g = curryLI (fibreOp V T (curryLI.symm g))

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

Preamble

-- Generated from ChapterNsScalarFourier.lean — theorem BookProof.NsScalarFourier.scalarFibreOp_apply
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_apply (T : Lp ℂ 2 (volume : Measure W) →L[ℂ] Lp ℂ 2 (volume : Measure W))
    (g : Lp ℂ 2 ((volume : Measure V).prod (volume : Measure W))) :
    scalarFibreOp V T g = curryLI (fibreOp V T (curryLI.symm g)) := by sorry

View graph