α : Type u_1
β : Type u_2
γ : Type ?u.188629
δ : Type ?u.188632
inst✝ : TopologicalSpace α
f : β → α
a : α
s : Set α
l : Filter β
h : ∀ (i : Set α), a ∈ i ∧ IsOpen i → (∀ᶠ (x : β) in l, f x ∈ i) ∧ ∀ᶠ (x : β) in l, f x ∈ s
⊢ ∀ᶠ (i : β) in l, f i ∈ s
α : Type u_1
β : Type u_2
γ : Type ?u.188629
δ : Type ?u.188632
inst✝ : TopologicalSpace α
f : β → α
a : α
s : Set α
l : Filter β
h : Tendsto f l (𝓝[s] a)
⊢ ∀ᶠ (i : β) in l, f i ∈ s
simp_rw [nhdsWithin_eq, tendsto_iInf, mem_setOf_eq, tendsto_principal, mem_inter_iff,
  eventually_and] at h
no goals
α : Type u_1
β : Type u_2
γ : Type ?u.188629
δ : Type ?u.188632
inst✝ : TopologicalSpace α
f : β → α
a : α
s : Set α
l : Filter β
h : ∀ (i : Set α), a ∈ i ∧ IsOpen i → (∀ᶠ (x : β) in l, f x ∈ i) ∧ ∀ᶠ (x : β) in l, f x ∈ s
⊢ ∀ᶠ (i : β) in l, f i ∈ s
exact (h univ ⟨mem_univ a, isOpen_univ⟩).2