∀ {α : Type u_1} [inst : DecidableEq α] (s t u : Finset α),
  u ∈
      (fun s t =>
          if s ⊆ t then Finset.map { toFun := fun u => (↑u).disjUnion s ⋯, inj' := ⋯ } (t \ s).powerset.attach else ∅)
        s t ↔
    s ≤ u ∧ u ≤ t