`BookProof.ChapterSpectralEnergyBound.hasDerivAt_evolve` (f : n → ℝ) (v : EuclideanSpace ℂ n) (t : ℝ) : HasDerivAt (fun s : ℝ => evolve f s v) (-Complex.I • diagOp f (evolve f t v)

Proved

BookProof.ChapterSpectralEnergyBound.hasDerivAt_evolve

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSpectralEnergyBound.

BookProof.ChapterSpectralEnergyBound.hasDerivAt_evolve (f : n → ℝ) (v : EuclideanSpace ℂ n) (t : ℝ) : HasDerivAt (fun s : ℝ => evolve f s v) (-Complex.I • diagOp f (evolve f t v)) t

Formalization note: Lean 4 identifier BookProof.ChapterSpectralEnergyBound.hasDerivAt_evolve.

Preamble

-- Generated from ChapterSpectralEnergyBound.lean — theorem BookProof.ChapterSpectralEnergyBound.hasDerivAt_evolve
import Mathlib
import Definitions.Def_ChapterSpectralEnergyBound
import Definitions.Def_ChapterAbelianDiagonalCountable
import Definitions.Def_ChapterBornMeasure
open BookProof.ChapterAbelianDiagonalCountable
open BookProof.ChapterBornMeasure
open BookProof.ChapterSpectralEnergyBound



variable {n : Type*} [Fintype n]

Formal statement

theorem BookProof.ChapterSpectralEnergyBound.hasDerivAt_evolve (f : n → ℝ) (v : EuclideanSpace ℂ n) (t : ℝ) :
    HasDerivAt (fun s : ℝ => evolve f s v)
      (-Complex.I • diagOp f (evolve f t v)) t := by sorry

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