∀ {α : Type u_1} [inst : SemilatticeInf α] {s t : Finset α} {a : α} [inst_1 : DecidableLE α] [inst_2 : BoundedOrder α]
  [inst_3 : DecidableEq α],
  a ∈ upperClosure ↑s → a ∈ upperClosure ↑t → (s ∪ t).truncatedInf a = s.truncatedInf a ⊓ t.truncatedInf a