∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}
  (motive :
    (∃ x, (∀ ⦃x_1 : Set X⦄, x_1 ∈ x → IsClosed x_1 ∧ IsNowhereDense x_1) ∧ (compl '' x).Countable ∧ s ⊆ ⋃₀ x) → Prop)
  (x : ∃ x, (∀ ⦃x_1 : Set X⦄, x_1 ∈ x → IsClosed x_1 ∧ IsNowhereDense x_1) ∧ (compl '' x).Countable ∧ s ⊆ ⋃₀ x),
  (∀ (S : Set (Set X)) (hS : ∀ ⦃x : Set X⦄, x ∈ S → IsClosed x ∧ IsNowhereDense x) (hc : (compl '' S).Countable)
      (hsub : s ⊆ ⋃₀ S), motive ⋯) →
    motive x