Prove2Me

`BookProof.NsSpatialMultiplier.foSymbolFn_add_fibre` (c : ι → ℝ) (w : ι → V) (x m : V) (hm : ∀ i, (inner ℝ m (w i) : ℝ) = 0) (t : ℝ) : foSymbolFn c w (x + t • m) = foSymbolFn c w x

Proved
BookProof.NsSpatialMultiplier.foSymbolFn_add_fibre

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsSpatialMomentumMultiplier.

BookProof.NsSpatialMultiplier.foSymbolFn_add_fibre (c : ι → ℝ) (w : ι → V) (x m : V) (hm : ∀ i, (inner ℝ m (w i) : ℝ) = 0) (t : ℝ) : foSymbolFn c w (x + t • m) = foSymbolFn c w x

Formalization note: Lean 4 identifier BookProof.NsSpatialMultiplier.foSymbolFn_add_fibre.

Preamble
-- Generated from ChapterNsSpatialMomentumMultiplier.lean — theorem BookProof.NsSpatialMultiplier.foSymbolFn_add_fibre
import Definitions.Def_ChapterStrichartzWave
import Mathlib
import Definitions.Def_ChapterNsSpatialMomentumMultiplier
import Definitions.Def_ChapterFourierMultiplierEsa
open BookProof.FourierMultiplierEsa
open BookProof.NsSpatialMultiplier



open MeasureTheory SchwartzMap FourierTransform
open BookProof.StrichartzWave BookProof.FourierMultiplierEsa

noncomputable section

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

variable (V) in
Formal statement
theorem BookProof.NsSpatialMultiplier.foSymbolFn_add_fibre (c : ι → ℝ) (w : ι → V) (x m : V)
    (hm : ∀ i, (inner ℝ m (w i) : ℝ) = 0) (t : ℝ) :
    foSymbolFn c w (x + t • m) = foSymbolFn c w x := by sorry

View graph