Prove2Me

`BookProof.ChapterUnitaryTransport.tendsto_slope_transported_position` (f : ℤ → ℝ) (W : L2Z ≃ₗᵢ[ℂ] K) (y : transportDomain W (mulDomain f)) : Filter.Tendsto (fun t : ℝ => (t⁻¹...

Proved
BookProof.ChapterUnitaryTransport.tendsto_slope_transported_position

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterUnitaryTransport.

BookProof.ChapterUnitaryTransport.tendsto_slope_transported_position (f : ℤ → ℝ) (W : L2Z ≃ₗᵢ[ℂ] K) (y : transportDomain W (mulDomain f)) : Filter.Tendsto (fun t : ℝ => (t⁻¹ : ℝ) • (transportUnitary W (phaseUnitary f t) (y : K) - (y : K))) (nhdsWithin 0 {0}ᶜ) (nhds (Complex.I • transportOp W (mulDomain f) (mulOp f) y))

Formalization note: Lean 4 identifier BookProof.ChapterUnitaryTransport.tendsto_slope_transported_position.

Preamble
-- Generated from ChapterUnitaryTransport.lean — theorem BookProof.ChapterUnitaryTransport.tendsto_slope_transported_position
import Mathlib
import Definitions.Def_ChapterUnitaryTransport
import Definitions.Def_ChapterContinuityUnitaryInfinite
import Definitions.Def_ChapterF7
import Definitions.Def_ChapterUnboundedPosition
open BookProof.ChapterContinuityUnitaryInfinite
open BookProof.ChapterF7
open BookProof.ChapterUnboundedPosition
open BookProof.ChapterUnitaryTransport


open scoped InnerProductSpace


variable {H K : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H]
  [NormedAddCommGroup K] [InnerProductSpace ℂ K]
Formal statement
theorem BookProof.ChapterUnitaryTransport.tendsto_slope_transported_position (f : ℤ → ℝ) (W : L2Z ≃ₗᵢ[ℂ] K)
    (y : transportDomain W (mulDomain f)) :
    Filter.Tendsto
      (fun t : ℝ => (t⁻¹ : ℝ) • (transportUnitary W (phaseUnitary f t) (y : K) - (y : K)))
      (nhdsWithin 0 {0}ᶜ) (nhds (Complex.I • transportOp W (mulDomain f) (mulOp f) y)) := by sorry

View graph