The Lean 4 theorem `genOp_eq_op` in the `ChapterStoneTheorem` chapter of the timepiece formalization
ProvedBookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.genOp_eq_opformalizationtimepiece
Formal statement of BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.genOp_eq_op from the timepiece Lean 4 formalization.
Preamble
-- Generated from ChapterStoneTheorem.lean — theorem BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.genOp_eq_op
import Mathlib
import Definitions.Def_ChapterStoneTheorem
import Definitions.Def_ChapterStoneConverse
import Definitions.Def_ChapterStoneResolvent
import Definitions.Def_ChapterSirkTrotterKato
-- `domain_le_genDomain` is carried by this stub (no published def bundle has
-- it — leaf selection dropped it), so `genOp_eq_op`'s statement cannot
-- elaborate without the import
import Theorems.Thm_BookProof_ChapterStoneResolvent_UnboundedSelfAdjoint_domain_le_genDomain
open BookProof.ChapterStoneMeasurable
open BookProof.ChapterStoneMeasurable.WeakMeasurableUnitaryGroup
open BookProof.ChapterStoneResolvent
open scoped InnerProductSpace
variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H]
variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]Formal statement
theorem BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.genOp_eq_op (T : UnboundedSelfAdjoint H) (x : T.domain) :
T.stoneGroup.genOp ⟨(x : H), T.domain_le_genDomain x.2⟩ = T.op x := by sorrySource