Prove2Me

`BookProof.StrichartzWave.wave_add_potentialOp_symmetric` (n : ℕ) (W : SpaceTime n → ℝ) (hW : Function.HasTemperateGrowth W) : BookProof.FarisLavine.SymmetricOn (schwartzDomain (Sp

Proved
BookProof.StrichartzWave.wave_add_potentialOp_symmetric

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWaveUnboundedPotential.

BookProof.StrichartzWave.wave_add_potentialOp_symmetric (n : ℕ) (W : SpaceTime n → ℝ) (hW : Function.HasTemperateGrowth W) : BookProof.FarisLavine.SymmetricOn (schwartzDomain (SpaceTime n)) (opL2 (waveOp n 0 + potentialOp W))

Formalization note: Lean 4 identifier BookProof.StrichartzWave.wave_add_potentialOp_symmetric.

Preamble
-- Generated from ChapterWaveUnboundedPotential.lean — theorem BookProof.StrichartzWave.wave_add_potentialOp_symmetric
import Mathlib
import Definitions.Def_ChapterWaveUnboundedPotential
import Definitions.Def_ChapterFarisLavineCore
import Definitions.Def_ChapterStrichartzWave
open BookProof.StrichartzWave



open MeasureTheory SchwartzMap FourierTransform ComplexInnerProductSpace ENNReal

variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [FiniteDimensional ℝ V]
  [MeasurableSpace V] [BorelSpace V]
Formal statement
theorem BookProof.StrichartzWave.wave_add_potentialOp_symmetric (n : ℕ) (W : SpaceTime n → ℝ)
    (hW : Function.HasTemperateGrowth W) :
    BookProof.FarisLavine.SymmetricOn (schwartzDomain (SpaceTime n))
      (opL2 (waveOp n 0 + potentialOp W)) := by sorry

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