tendsto_of_monotone — Mathlib

English

A duplicate instance asserting the product of SupConvergenceClass objects.

Русский

Дубликат утверждения о произведении суперконвергенции.

LaTeX

$$$ \text{Prod SupConvergence} \;\Rightarrow\; \SupConvergenceClass(\alpha \times \beta) $$$

Lean4

theorem tendsto_of_monotone {ι α : Type*} [Preorder ι] [TopologicalSpace α] [ConditionallyCompleteLinearOrder α]
    [OrderTopology α] {f : ι → α} (h_mono : Monotone f) : Tendsto f atTop atTop ∨ ∃ l, Tendsto f atTop (𝓝 l) := by
  classical
    exact
    if H : BddAbove (range f) then Or.inr ⟨_, tendsto_atTop_ciSup h_mono H⟩
    else Or.inl <| tendsto_atTop_atTop_of_monotone' h_mono H

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