`BookProof.ChapterCayleyTransform.cayley_shift` (x : T.domain) : cayley T (T.shift (-1) x) = T.shift 1 x
ProvedBookProof.ChapterCayleyTransform.cayley_shifttheoremstimepiece
Prove the following Lean 4 theorem from ChapterCayleyTransform.
BookProof.ChapterCayleyTransform.cayley_shift (x : T.domain) : cayley T (T.shift (-1) x) = T.shift 1 x
Formalization note: Lean 4 identifier BookProof.ChapterCayleyTransform.cayley_shift.
Preamble
-- Generated from ChapterCayleyTransform.lean — theorem BookProof.ChapterCayleyTransform.cayley_shift
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.cayley_shift (x : T.domain) : cayley T (T.shift (-1) x) = T.shift 1 x := by sorry