Prove2Me

`BookProof.ChapterStoneSeparable.stone_exists_unique_generator` (G : WeakMeasurableUnitaryGroup H) : ∃! T : UnboundedSelfAdjoint H, ∀ t : ℝ, T.stoneU t = G.U t

Proved
BookProof.ChapterStoneSeparable.stone_exists_unique_generator

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_generator (G : WeakMeasurableUnitaryGroup H) : ∃! T : UnboundedSelfAdjoint H, ∀ t : ℝ, T.stoneU t = G.U t

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

Preamble
-- Generated from ChapterStoneSeparable.lean — theorem BookProof.ChapterStoneSeparable.stone_exists_unique_generator
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterStoneSeparable
import Definitions.Def_ChapterStoneConverse
import Definitions.Def_ChapterStoneMeasurable
import Definitions.Def_ChapterStoneResolvent
import Definitions.Def_ChapterStoneTheorem
import Definitions.Def_ChapterStoneUnitary
open BookProof.ChapterStoneMeasurable
open BookProof.ChapterStoneMeasurable
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_generator (G : WeakMeasurableUnitaryGroup H) :
    ∃! T : UnboundedSelfAdjoint H, ∀ t : ℝ, T.stoneU t = G.U t := by sorry

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