`BookProof.OdeUnitaryFlow.hasDerivAt_odeKoop_zero` (ψ : ℝ → ℂ) (x : ℝ) (d : ℂ) (hψ : HasDerivAt ψ d x) : HasDerivAt (fun t : ℝ => odeKoop t ψ x) (-((x : ℂ) ^ 2 * d + (x : ℂ)...

Proved

BookProof.OdeUnitaryFlow.hasDerivAt_odeKoop_zero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterOdeUnitaryFlow.

BookProof.OdeUnitaryFlow.hasDerivAt_odeKoop_zero (ψ : ℝ → ℂ) (x : ℝ) (d : ℂ) (hψ : HasDerivAt ψ d x) : HasDerivAt (fun t : ℝ => odeKoop t ψ x) (-((x : ℂ) ^ 2 * d + (x : ℂ) * ψ x)) 0

Formalization note: Lean 4 identifier BookProof.OdeUnitaryFlow.hasDerivAt_odeKoop_zero.

Preamble

-- Generated from ChapterOdeUnitaryFlow.lean — theorem BookProof.OdeUnitaryFlow.hasDerivAt_odeKoop_zero
import Mathlib
import Definitions.Def_ChapterOdeUnitaryFlow
open BookProof.OdeUnitaryFlow



open MeasureTheory Filter Set
open scoped Topology ENNReal

Formal statement

theorem BookProof.OdeUnitaryFlow.hasDerivAt_odeKoop_zero (ψ : ℝ → ℂ) (x : ℝ) (d : ℂ) (hψ : HasDerivAt ψ d x) :
    HasDerivAt (fun t : ℝ => odeKoop t ψ x) (-((x : ℂ) ^ 2 * d + (x : ℂ) * ψ x)) 0 := by sorry

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