`BookProof.ChapterCayleyInverse.cayley_ofUnitary` (hdense : Dense ((invCayleyDomain V : Submodule ℂ H) : Set H)) (y : H) : cayley (ofUnitary V hinj hdense) y = V y

Proved

BookProof.ChapterCayleyInverse.cayley_ofUnitary

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCayleyInverse.

BookProof.ChapterCayleyInverse.cayley_ofUnitary (hdense : Dense ((invCayleyDomain V : Submodule ℂ H) : Set H)) (y : H) : cayley (ofUnitary V hinj hdense) y = V y

Formalization note: Lean 4 identifier BookProof.ChapterCayleyInverse.cayley_ofUnitary.

Preamble

-- Generated from ChapterCayleyInverse.lean — theorem BookProof.ChapterCayleyInverse.cayley_ofUnitary
import Definitions.Def_ChapterUnitaryTransport
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterCayleyInverse
import Definitions.Def_ChapterCayleyTransform
import Definitions.Def_ChapterStoneResolvent
open BookProof.ChapterCayleyTransform
open BookProof.ChapterCayleyInverse


open scoped InnerProductSpace


open BookProof.ChapterUnitaryTransport BookProof.ChapterStoneResolvent
open BookProof.ChapterCayleyTransform

variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H]

variable (V : H ≃ₗᵢ[ℂ] H)
variable (hinj : Function.Injective (oneSubU V))
variable [CompleteSpace H]

Formal statement

theorem BookProof.ChapterCayleyInverse.cayley_ofUnitary (hdense : Dense ((invCayleyDomain V : Submodule ℂ H) : Set H))
    (y : H) : cayley (ofUnitary V hinj hdense) y = V y := by sorry

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