`BookProof.ChapterCayleyTransform.range_one_sub_cayley` : Set.range (fun y : H => y - cayley T y) = (T.domain : Set H)

Proved

BookProof.ChapterCayleyTransform.range_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.range_one_sub_cayley : Set.range (fun y : H => y - cayley T y) = (T.domain : Set H)

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

Preamble

-- Generated from ChapterCayleyTransform.lean — theorem BookProof.ChapterCayleyTransform.range_one_sub_cayley
import Definitions.Def_ChapterUnitaryTransport
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterCayleyTransform
import Definitions.Def_ChapterStoneResolvent
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.range_one_sub_cayley :
    Set.range (fun y : H => y - cayley T y) = (T.domain : Set H) := by sorry

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