`BookProof.ChapterCayleyTransform.op_eq_cayley` (x : T.domain) : T.op x = (2 : ℂ)⁻¹ • (T.shift (-1) x + cayley T (T.shift (-1) x))

Proved

BookProof.ChapterCayleyTransform.op_eq_cayley

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterCayleyTransform.

BookProof.ChapterCayleyTransform.op_eq_cayley (x : T.domain) : T.op x = (2 : ℂ)⁻¹ • (T.shift (-1) x + cayley T (T.shift (-1) x))

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

Preamble

-- Generated from ChapterCayleyTransform.lean — theorem BookProof.ChapterCayleyTransform.op_eq_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.op_eq_cayley (x : T.domain) :
    T.op x = (2 : ℂ)⁻¹ • (T.shift (-1) x + cayley T (T.shift (-1) x)) := by sorry

View graph