`BookProof.ChapterNumericalRangeSemigroup.norm_exp_le` {A : E →L[ℂ] E} {ω : ℝ} (h : NumReLE A ω) {t : ℝ} (ht : 0 ≤ t) : ‖NormedSpace.exp (t • A)‖ ≤ Real.exp (ω * t)

Proved

BookProof.ChapterNumericalRangeSemigroup.norm_exp_le

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNumericalRangeSemigroup.

BookProof.ChapterNumericalRangeSemigroup.norm_exp_le {A : E →L[ℂ] E} {ω : ℝ} (h : NumReLE A ω) {t : ℝ} (ht : 0 ≤ t) : ‖NormedSpace.exp (t • A)‖ ≤ Real.exp (ω * t)

Formalization note: Lean 4 identifier BookProof.ChapterNumericalRangeSemigroup.norm_exp_le.

Preamble

-- Generated from ChapterNumericalRangeSemigroup.lean — theorem BookProof.ChapterNumericalRangeSemigroup.norm_exp_le
import Mathlib
import Definitions.Def_ChapterNumericalRangeSemigroup
open BookProof.ChapterNumericalRangeSemigroup


open scoped InnerProductSpace


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

Formal statement

theorem BookProof.ChapterNumericalRangeSemigroup.norm_exp_le {A : E →L[ℂ] E} {ω : ℝ} (h : NumReLE A ω) {t : ℝ} (ht : 0 ≤ t) :
    ‖NormedSpace.exp (t • A)‖ ≤ Real.exp (ω * t) := by sorry

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