Prove2Me

`BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.hasDerivAt_stoneU_zero` (x : T.domain) : HasDerivAt (fun t : ℝ => T.stoneU t (x : H)) ((-Complex.I) • T.op x) 0

Proved
BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.hasDerivAt_stoneU_zero

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterStoneGenerator.

BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.hasDerivAt_stoneU_zero (x : T.domain) : HasDerivAt (fun t : ℝ => T.stoneU t (x : H)) ((-Complex.I) • T.op x) 0

Formalization note: Lean 4 identifier BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.hasDerivAt_stoneU_zero.

Preamble
-- Generated from ChapterStoneGenerator.lean — theorem BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.hasDerivAt_stoneU_zero
import Mathlib
import Definitions.Def_ChapterStoneGenerator
import Definitions.Def_ChapterStoneEvolution
import Definitions.Def_ChapterStoneGroup
import Definitions.Def_ChapterStoneResolvent
import Definitions.Def_ChapterStoneUnitary
import Definitions.Def_ChapterSirkTrotterKato
open BookProof.ChapterStoneResolvent
open BookProof.ChapterStoneResolvent


open scoped InnerProductSpace
open Filter Topology NormedSpace


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


variable (T : UnboundedSelfAdjoint H)
Formal statement
theorem BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.hasDerivAt_stoneU_zero (x : T.domain) :
    HasDerivAt (fun t : ℝ => T.stoneU t (x : H)) ((-Complex.I) • T.op x) 0 := by sorry

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