apply Set.ext
α : Sort u_1
β : Sort u_2
f : Set (α → β)
a : α
s : Set α
⊢ (f.bind fun f => Set.map f (s.insert a)) = (Set.map (fun f => f a) f).union (f.bind fun f => Set.map f s)
case a
α : Sort u_1
β : Sort u_2
f : Set (α → β)
a : α
s : Set α
⊢ ∀ (x : β),
    (x ∈ f.bind fun f => Set.map f (s.insert a)) ↔ x ∈ (Set.map (fun f => f a) f).union (f.bind fun f => Set.map f s)