`BookProof.NsPartialFourier.fourier_postcompCLM_apply` [CompleteSpace F] [CompleteSpace G] (T : F →L[ℂ] G) (f : 𝓢(V, F)) (x : V) : (𝓕 (postcompCLM T f) : 𝓢(V, G)) x = T ((𝓕 f : 𝓢(V

Proved

BookProof.NsPartialFourier.fourier_postcompCLM_apply

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsPartialFourier.

BookProof.NsPartialFourier.fourier_postcompCLM_apply [CompleteSpace F] [CompleteSpace G] (T : F →L[ℂ] G) (f : 𝓢(V, F)) (x : V) : (𝓕 (postcompCLM T f) : 𝓢(V, G)) x = T ((𝓕 f : 𝓢(V, F)) x)

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

Preamble

-- Generated from ChapterNsPartialFourier.lean — theorem BookProof.NsPartialFourier.fourier_postcompCLM_apply
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]

Formal statement

theorem BookProof.NsPartialFourier.fourier_postcompCLM_apply [CompleteSpace F] [CompleteSpace G]
    (T : F →L[ℂ] G) (f : 𝓢(V, F)) (x : V) :
    (𝓕 (postcompCLM T f) : 𝓢(V, G)) x = T ((𝓕 f : 𝓢(V, F)) x) := by sorry

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