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feat: fix typo (eventually_nhds_subtype_if -> eventually_nhds_subtype_iff) (#10124)
This was unnoticed during the review of #7568
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Mathlib/Topology/ContinuousOn.lean

Lines changed: 2 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -505,13 +505,13 @@ theorem preimage_coe_mem_nhds_subtype {s t : Set α} {a : s} : (↑) ⁻¹' t
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rw [← map_nhds_subtype_val, mem_map]
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#align preimage_coe_mem_nhds_subtype preimage_coe_mem_nhds_subtype
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theorem eventually_nhds_subtype_if (s : Set α) (a : s) (P : α → Prop) :
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theorem eventually_nhds_subtype_iff (s : Set α) (a : s) (P : α → Prop) :
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(∀ᶠ x : s in 𝓝 a, P x) ↔ ∀ᶠ x in 𝓝[s] a, P x :=
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preimage_coe_mem_nhds_subtype
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theorem frequently_nhds_subtype_iff (s : Set α) (a : s) (P : α → Prop) :
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(∃ᶠ x : s in 𝓝 a, P x) ↔ ∃ᶠ x in 𝓝[s] a, P x :=
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eventually_nhds_subtype_if s a (¬ P ·) |>.not
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eventually_nhds_subtype_iff s a (¬ P ·) |>.not
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theorem tendsto_nhdsWithin_iff_subtype {s : Set α} {a : α} (h : a ∈ s) (f : α → β) (l : Filter β) :
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Tendsto f (𝓝[s] a) l ↔ Tendsto (s.restrict f) (𝓝 ⟨a, h⟩) l := by

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