`BookProof.ChapterStoneSeparable.stone_exists_unique_group` (T : UnboundedSelfAdjoint H) : ∃! G : WeakMeasurableUnitaryGroup H, ∀ x : T.domain, HasDerivAt (fun t : ℝ => G.U t (x :

Proved

BookProof.ChapterStoneSeparable.stone_exists_unique_group

by leonardopedro · Oct 20, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterStoneSeparable.

BookProof.ChapterStoneSeparable.stone_exists_unique_group (T : UnboundedSelfAdjoint H) : ∃! G : WeakMeasurableUnitaryGroup H, ∀ x : T.domain, HasDerivAt (fun t : ℝ => G.U t (x : H)) ((-Complex.I) • T.op x) 0

Formalization note: Lean 4 identifier BookProof.ChapterStoneSeparable.stone_exists_unique_group.

Preamble

-- Generated from ChapterStoneSeparable.lean — theorem BookProof.ChapterStoneSeparable.stone_exists_unique_group
import Definitions.Def_ChapterSirkTrotterKato
import Definitions.Def_ChapterStoneConverse
import Mathlib
import Definitions.Def_ChapterStoneSeparable
import Definitions.Def_ChapterStoneMeasurable
import Definitions.Def_ChapterStoneResolvent
import Definitions.Def_ChapterStoneTheorem
open BookProof.ChapterStoneTheorem
open BookProof.ChapterStoneSeparable


open scoped InnerProductSpace
open Filter Topology


open BookProof.ChapterStoneResolvent BookProof.ChapterStoneMeasurable

variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H]
  [TopologicalSpace.SeparableSpace H]

Formal statement

theorem BookProof.ChapterStoneSeparable.stone_exists_unique_group (T : UnboundedSelfAdjoint H) :
    ∃! G : WeakMeasurableUnitaryGroup H,
      ∀ x : T.domain, HasDerivAt (fun t : ℝ => G.U t (x : H)) ((-Complex.I) • T.op x) 0 := by sorry

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