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