apply frequently_congr
α✝ : Type ?u.2106
α : Type u_1
inst✝ : TopologicalSpace α
s t : Set α
hst : s ⊆ t
J : Set ↑s
a : ↑s
⊢ (∃ᶠ (b : α) in nhds ↑a, ∃ a, ↑a = b ∧ a ∈ J) ↔
    ∃ᶠ (b : α) in nhds ↑a, ∃ a, ↑a = b ∧ ∃ (h : ↑a ∈ s), { val := ↑a, property := h } ∈ J
case h
α✝ : Type ?u.2106
α : Type u_1
inst✝ : TopologicalSpace α
s t : Set α
hst : s ⊆ t
J : Set ↑s
a : ↑s
⊢ ∀ᶠ (x : α) in nhds ↑a, (∃ a, ↑a = x ∧ a ∈ J) ↔ ∃ a, ↑a = x ∧ ∃ (h : ↑a ∈ s), { val := ↑a, property := h } ∈ J