Prove2Me

`BookProof.MixedLinearEsa.momentumOp_apply` (m : V) (f : ๐“ข(V, โ„‚)) (x : V) : (momentumOp m f) x = (-Complex.I) * (fderiv โ„ f x m)

Proved
BookProof.MixedLinearEsa.momentumOp_apply

by leonardopedro ยท Oct 9, 2026 ยท Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMixedLinearEsa.

BookProof.MixedLinearEsa.momentumOp_apply (m : V) (f : ๐“ข(V, โ„‚)) (x : V) : (momentumOp m f) x = (-Complex.I) * (fderiv โ„ f x m)

Formalization note: Lean 4 identifier BookProof.MixedLinearEsa.momentumOp_apply.

Preamble
-- Generated from ChapterMixedLinearEsa.lean โ€” theorem BookProof.MixedLinearEsa.momentumOp_apply
import Definitions.Def_ChapterStrichartzWave
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterMixedLinearEsa
import Definitions.Def_ChapterFourierMultiplierEsa
open BookProof.FourierMultiplierEsa
open BookProof.MixedLinearEsa



open MeasureTheory SchwartzMap FourierTransform ComplexInnerProductSpace LineDeriv
open BookProof.StrichartzWave BookProof.FourierMultiplierEsa BookProof.FarisLavine

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace โ„ V] [FiniteDimensional โ„ V]
  [MeasurableSpace V] [BorelSpace V]
Formal statement
theorem BookProof.MixedLinearEsa.momentumOp_apply (m : V) (f : ๐“ข(V, โ„‚)) (x : V) :
    (momentumOp m f) x = (-Complex.I) * (fderiv โ„ f x m) := by sorry

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