rintro a t has - - ⟨u, huC, htu⟩
α : Type u_1
s : Set α
hs : s.Finite
C : Set (Set α)
hC : DirectedOn (fun x x_1 => x ⊆ x_1) C
hne : C.Nonempty
h : s ⊆ ⋃₀ C
⊢ ∀ {a : α} {s_1 : Set α}, a ∈ s → s_1 ⊆ s → a ∉ s_1 → (∃ u ∈ C, s_1 ⊆ u) → ∃ u ∈ C, insert a s_1 ⊆ u
case intro.intro
α : Type u_1
s : Set α
hs : s.Finite
C : Set (Set α)
hC : DirectedOn (fun x x_1 => x ⊆ x_1) C
hne : C.Nonempty
h : s ⊆ ⋃₀ C
a : α
t : Set α
has : a ∈ s
u : Set α
huC : u ∈ C
htu : t ⊆ u
⊢ ∃ u ∈ C, insert a t ⊆ u