Prove2Me

`BookProof.NsSpatialMultiplier.foSymbolFn_congr_of_inner_eq` (c : ι → ℝ) (w : ι → V) {x y : V} (h : ∀ i, (inner ℝ x (w i) : ℝ) = inner ℝ y (w i)) : foSymbolFn c w x = foSymbolFn c

Proved
BookProof.NsSpatialMultiplier.foSymbolFn_congr_of_inner_eq

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNsSpatialMomentumMultiplier.

BookProof.NsSpatialMultiplier.foSymbolFn_congr_of_inner_eq (c : ι → ℝ) (w : ι → V) {x y : V} (h : ∀ i, (inner ℝ x (w i) : ℝ) = inner ℝ y (w i)) : foSymbolFn c w x = foSymbolFn c w y

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

Preamble
-- Generated from ChapterNsSpatialMomentumMultiplier.lean — theorem BookProof.NsSpatialMultiplier.foSymbolFn_congr_of_inner_eq
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_congr_of_inner_eq (c : ι → ℝ) (w : ι → V) {x y : V}
    (h : ∀ i, (inner ℝ x (w i) : ℝ) = inner ℝ y (w i)) :
    foSymbolFn c w x = foSymbolFn c w y := by sorry

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