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feat: fix typo (eventually_nhds_subtype_if -> eventually_nhds_subtype…
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…_iff) (#10124)

This was unnoticed during the review of #7568
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ADedecker committed Jan 31, 2024
1 parent 18b19cc commit bb85b99
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions Mathlib/Topology/ContinuousOn.lean
Expand Up @@ -505,13 +505,13 @@ theorem preimage_coe_mem_nhds_subtype {s t : Set α} {a : s} : (↑) ⁻¹' t
rw [← map_nhds_subtype_val, mem_map]
#align preimage_coe_mem_nhds_subtype preimage_coe_mem_nhds_subtype

theorem eventually_nhds_subtype_if (s : Set α) (a : s) (P : α → Prop) :
theorem eventually_nhds_subtype_iff (s : Set α) (a : s) (P : α → Prop) :
(∀ᶠ x : s in 𝓝 a, P x) ↔ ∀ᶠ x in 𝓝[s] a, P x :=
preimage_coe_mem_nhds_subtype

theorem frequently_nhds_subtype_iff (s : Set α) (a : s) (P : α → Prop) :
(∃ᶠ x : s in 𝓝 a, P x) ↔ ∃ᶠ x in 𝓝[s] a, P x :=
eventually_nhds_subtype_if s a (¬ P ·) |>.not
eventually_nhds_subtype_iff s a (¬ P ·) |>.not

theorem tendsto_nhdsWithin_iff_subtype {s : Set α} {a : α} (h : a ∈ s) (f : α → β) (l : Filter β) :
Tendsto f (𝓝[s] a) l ↔ Tendsto (s.restrict f) (𝓝 ⟨a, h⟩) l := by
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