apply List.mem_fold_union_iff.mpr
case mpr.mk
β : Type u_2
inst✝ : DecidableEq β
α : Type u_1
e : β
s : Finset α
f : α → Finset β
x : α
h₂ : e ∈ f x
l : List α
nodup✝ : Multiset.Nodup (Quot.mk Setoid.r l)
h : x ∈ { val := Quot.mk Setoid.r l, nodup := nodup✝ }
⊢ e ∈ List.foldr Union.union ∅ (List.map f l)
case mpr.mk
β : Type u_2
inst✝ : DecidableEq β
α : Type u_1
e : β
s : Finset α
f : α → Finset β
x : α
h₂ : e ∈ f x
l : List α
nodup✝ : Multiset.Nodup (Quot.mk Setoid.r l)
h : x ∈ { val := Quot.mk Setoid.r l, nodup := nodup✝ }
⊢ ∃ s ∈ List.map f l, e ∈ s