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

Proved
BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.hasDerivAt_stoneU_op

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_op (x : T.domain) (t : ℝ) : HasDerivAt (fun s : ℝ => T.stoneU s (x : H)) ((-Complex.I) • T.op ⟨T.stoneU t (x : H), T.stoneU_mem_domain t x⟩) t

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

Preamble
-- Generated from ChapterStoneGenerator.lean — theorem BookProof.ChapterStoneResolvent.UnboundedSelfAdjoint.hasDerivAt_stoneU_op
import Mathlib
import Definitions.Def_ChapterStoneGenerator
import Definitions.Def_ChapterSirkTrotterKato
import Definitions.Def_ChapterStoneResolvent
import Definitions.Def_ChapterStoneUnitary
open BookProof.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_op (x : T.domain) (t : ℝ) :
    HasDerivAt (fun s : ℝ => T.stoneU s (x : H))
      ((-Complex.I) • T.op ⟨T.stoneU t (x : H), T.stoneU_mem_domain t x⟩) t := by sorry

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