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b-mehtaReemMelamed
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feat(ENat): Nat.cast tends to in ENat (leanprover-community#40131)
A simple lemma that came up when adding new ENat tsum lemmas. (If - like me - you were surprised that this is missing, [note that `exact?` can't prove this](https://live.lean-lang.org/#codez=JYWwDg9gTgLgBAWQIYwBYBtgCMBQO0Cm0BIcMBAdgCYDOMEA%2BhSgMJJ1Oq0P1hwBccHHBFwAYsHTkoAOgAqlWvTgA5FDIDG7eBKkFZKORD4AKClxpwTgEqIBcAKJqYASmcCAvHCwBPYXAIAHkgaMAD8QA))
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Mathlib/Topology/Instances/ENat.lean

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@@ -63,6 +63,11 @@ theorem tendsto_nhds_top_iff_natCast_lt {α : Type*} {l : Filter α} {f : α →
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simp_rw [nhds_top_order, lt_top_iff_ne_top, tendsto_iInf, tendsto_principal, ENat.forall_ne_top,
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mem_Ioi]
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theorem tendsto_natCast_nhds_top : Tendsto Nat.cast atTop (𝓝 (⊤ : ℕ∞)) := by
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rw [tendsto_nhds_top_iff_natCast_lt]
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intro n
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filter_upwards [eventually_ge_atTop (n + 1)] with a ha using by simpa
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instance : ContinuousAdd ℕ∞ := by
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refine ⟨continuous_iff_continuousAt.2 fun (a, b) ↦ ?_⟩
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match a, b with

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