`BookProof.ChapterNumericalRangeCrouzeix.numRadiusLE_pow` {A : E →L[ℂ] E} {r : ℝ} (hr : 0 ≤ r) (h : NumRadiusLE A r) (n : ℕ) (hn : 0 < n) : NumRadiusLE (A ^ n) (r ^ n)

Proved

BookProof.ChapterNumericalRangeCrouzeix.numRadiusLE_pow

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNumericalRangeCrouzeix.

BookProof.ChapterNumericalRangeCrouzeix.numRadiusLE_pow {A : E →L[ℂ] E} {r : ℝ} (hr : 0 ≤ r) (h : NumRadiusLE A r) (n : ℕ) (hn : 0 < n) : NumRadiusLE (A ^ n) (r ^ n)

Formalization note: Lean 4 identifier BookProof.ChapterNumericalRangeCrouzeix.numRadiusLE_pow.

Preamble

-- Generated from ChapterNumericalRangeCrouzeix.lean — theorem BookProof.ChapterNumericalRangeCrouzeix.numRadiusLE_pow
import Mathlib
import Definitions.Def_ChapterNumericalRangeCrouzeix
open BookProof.ChapterNumericalRangeCrouzeix


open scoped InnerProductSpace


variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E]

Formal statement

theorem BookProof.ChapterNumericalRangeCrouzeix.numRadiusLE_pow {A : E →L[ℂ] E} {r : ℝ} (hr : 0 ≤ r) (h : NumRadiusLE A r) (n : ℕ)
    (hn : 0 < n) : NumRadiusLE (A ^ n) (r ^ n) := by sorry

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