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`BookProof.ChapterCayleyTransform.denseRange_one_sub_cayley` : DenseRange (fun y : H => y - cayley T y)

Proved
BookProof.ChapterCayleyTransform.denseRange_one_sub_cayley

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCayleyTransform.

BookProof.ChapterCayleyTransform.denseRange_one_sub_cayley : DenseRange (fun y : H => y - cayley T y)

Formalization note: Lean 4 identifier BookProof.ChapterCayleyTransform.denseRange_one_sub_cayley.

Preamble
-- Generated from ChapterCayleyTransform.lean — theorem BookProof.ChapterCayleyTransform.denseRange_one_sub_cayley
import Definitions.Def_ChapterUnitaryTransport
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterCayleyTransform
import Definitions.Def_ChapterStoneConverse
import Definitions.Def_ChapterStoneResolvent
open BookProof.ChapterStoneMeasurable
open BookProof.ChapterStoneMeasurable.WeakMeasurableUnitaryGroup
open BookProof.ChapterCayleyTransform


open scoped InnerProductSpace
open Filter Topology


open BookProof.ChapterUnitaryTransport BookProof.ChapterStoneResolvent

variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]
variable (T : UnboundedSelfAdjoint H)
Formal statement
theorem BookProof.ChapterCayleyTransform.denseRange_one_sub_cayley :
    DenseRange (fun y : H => y - cayley T y) := by sorry

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