The Lean 4 theorem `inner_toLp_eq_integral_fourier` in the `ChapterStrichartzWave` chapter of the timepiece formalization

-- Generated from ChapterStrichartzWave.lean — theorem BookProof.StrichartzWave.inner_toLp_eq_integral_fourier
import Mathlib
import Definitions.Def_ChapterStrichartzWave
open BookProof.StrichartzWave










open MeasureTheory SchwartzMap FourierTransform ComplexInnerProductSpace LineDeriv

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

theorem BookProof.StrichartzWave.inner_toLp_eq_integral_fourier (f g : 𝓢(V, ℂ)) :
    (inner ℂ (f.toLp 2 (volume : Measure V)) (g.toLp 2 (volume : Measure V)) : ℂ)
      = ∫ x, (starRingEnd ℂ) ((𝓕 f : 𝓢(V, ℂ)) x) * ((𝓕 g : 𝓢(V, ℂ)) x) := by sorry