ext x
α : Type u_1
X : Set (Set α)
a : α
⊢ insert a (⋂₀ 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 ∈ insert a (⋂₀ X) ↔ x ∈ ⋂₀ {x | ∃ x_1 ∈ X, insert a x_1 = x}