∀ {α : Type u_1} {s : Set α} (x : Set Prop),
  True ∈ x →
    False ∉ x →
      (fun x => x ∈ s) ⁻¹' x = ∅ ∨
        (fun x => x ∈ s) ⁻¹' x = s ∨ (fun x => x ∈ s) ⁻¹' x = sᶜ ∨ (fun x => x ∈ s) ⁻¹' x = Set.univ