`BookProof.BrstUnboundedLeakage.hasDerivAt_flow` (B : H →L[ℂ] H) (x : H) (u : ℝ) : HasDerivAt (fun v : ℝ => flow B v x) ((-Complex.I) • B (flow B u x)) u

Proved

BookProof.BrstUnboundedLeakage.hasDerivAt_flow

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterBrstUnboundedLeakage.

BookProof.BrstUnboundedLeakage.hasDerivAt_flow (B : H →L[ℂ] H) (x : H) (u : ℝ) : HasDerivAt (fun v : ℝ => flow B v x) ((-Complex.I) • B (flow B u x)) u

Formalization note: Lean 4 identifier BookProof.BrstUnboundedLeakage.hasDerivAt_flow.

Preamble

-- Generated from ChapterBrstUnboundedLeakage.lean — theorem BookProof.BrstUnboundedLeakage.hasDerivAt_flow
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterBrstUnboundedLeakage
import Definitions.Def_ChapterBrstTruncationLeakage
open BookProof.BrstLeakage
open BookProof.BrstUnboundedLeakage


open NormedSpace Filter Topology
open scoped InnerProductSpace


open BookProof.BrstLeakage BookProof.ChapterStoneResolvent

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

Formal statement

theorem BookProof.BrstUnboundedLeakage.hasDerivAt_flow (B : H →L[ℂ] H) (x : H) (u : ℝ) :
    HasDerivAt (fun v : ℝ => flow B v x) ((-Complex.I) • B (flow B u x)) u := by sorry

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