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`BookProof.ChapterSpectralEnergyBound.norm_deriv_evolve_le` (f : n → ℝ) (E : ℝ) (v : EuclideanSpace ℂ n) (h : ∀ i, v i ≠ 0 → |f i| ≤ E) (t : ℝ) : ‖-Complex.I • diagOp f...

Proved
BookProof.ChapterSpectralEnergyBound.norm_deriv_evolve_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterSpectralEnergyBound.

BookProof.ChapterSpectralEnergyBound.norm_deriv_evolve_le (f : n → ℝ) (E : ℝ) (v : EuclideanSpace ℂ n) (h : ∀ i, v i ≠ 0 → |f i| ≤ E) (t : ℝ) : ‖-Complex.I • diagOp f (evolve f t v)‖ ≤ E * ‖v‖

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

Preamble
-- Generated from ChapterSpectralEnergyBound.lean — theorem BookProof.ChapterSpectralEnergyBound.norm_deriv_evolve_le
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.norm_deriv_evolve_le (f : n → ℝ) (E : ℝ) (v : EuclideanSpace ℂ n)
    (h : ∀ i, v i ≠ 0 → |f i| ≤ E) (t : ℝ) :
    ‖-Complex.I • diagOp f (evolve f t v)‖ ≤ E * ‖v‖ := by sorry

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