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theorem proved term proof

runningMax_tendsto_atTop

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formal statement (Lean)

  53theorem runningMax_tendsto_atTop (a : ℕ → ℝ) (h : Tendsto a atTop atTop) :
  54    Tendsto (runningMax a) atTop atTop := by

proof body

Term-mode proof.

  55  rw [Filter.tendsto_atTop_atTop]
  56  intro b
  57  rw [Filter.tendsto_atTop_atTop] at h
  58  obtain ⟨N, hN⟩ := h b
  59  exact ⟨N, fun n hn => le_trans (hN N le_rfl) (le_trans (runningMax_ge a N) (runningMax_mono a hn))⟩
  60
  61/-- The running maximum is positive if any element is positive. -/

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