simp
case h
α : Type u_1
X : Set (Set α)
a x : α
⊢ x ∈ insert a (⋂₀ X) ↔ x ∈ ⋂₀ {x | ∃ x_1 ∈ X, insert a x_1 = x}
case h
α : Type u_1
X : Set (Set α)
a x : α
⊢ (x = a ∨ ∀ t ∈ X, x ∈ t) ↔ ∀ a_1 ∈ X, x = a ∨ x ∈ a_1