`BookProof.ChapterUnitaryTransport.transported_position_domain_dense` (f : ℤ → ℝ) (W : L2Z ≃ₗᵢ[ℂ] K) : Dense ((transportDomain W (mulDomain f) : Submodule ℂ K) : Set K)
ProvedBookProof.ChapterUnitaryTransport.transported_position_domain_densetheoremstimepiece
Prove the following Lean 4 theorem from ChapterUnitaryTransport.
BookProof.ChapterUnitaryTransport.transported_position_domain_dense (f : ℤ → ℝ) (W : L2Z ≃ₗᵢ[ℂ] K) : Dense ((transportDomain W (mulDomain f) : Submodule ℂ K) : Set K)
Formalization note: Lean 4 identifier BookProof.ChapterUnitaryTransport.transported_position_domain_dense.
Preamble
-- Generated from ChapterUnitaryTransport.lean — theorem BookProof.ChapterUnitaryTransport.transported_position_domain_dense
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_domain_dense (f : ℤ → ℝ) (W : L2Z ≃ₗᵢ[ℂ] K) :
Dense ((transportDomain W (mulDomain f) : Submodule ℂ K) : Set K) := by sorry