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`BookProof.ChapterUnitaryTransport.transported_position_group` (f : ℤ → ℝ) (W : L2Z ≃ₗᵢ[ℂ] K) (s t : ℝ) (y : K) : transportUnitary W (phaseUnitary f (s + t)) y = transportUnitary W

Proved
BookProof.ChapterUnitaryTransport.transported_position_group

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterUnitaryTransport.

BookProof.ChapterUnitaryTransport.transported_position_group (f : ℤ → ℝ) (W : L2Z ≃ₗᵢ[ℂ] K) (s t : ℝ) (y : K) : transportUnitary W (phaseUnitary f (s + t)) y = transportUnitary W (phaseUnitary f s) (transportUnitary W (phaseUnitary f t) y)

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

Preamble
-- Generated from ChapterUnitaryTransport.lean — theorem BookProof.ChapterUnitaryTransport.transported_position_group
import Mathlib
import Definitions.Def_ChapterUnitaryTransport
import Definitions.Def_ChapterContinuityUnitaryInfinite
import Definitions.Def_ChapterUnboundedPosition
open BookProof.ChapterContinuityUnitaryInfinite
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.transported_position_group (f : ℤ → ℝ) (W : L2Z ≃ₗᵢ[ℂ] K) (s t : ℝ) (y : K) :
    transportUnitary W (phaseUnitary f (s + t)) y
      = transportUnitary W (phaseUnitary f s) (transportUnitary W (phaseUnitary f t) y) := by sorry

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