∀ {I : Type u} (C : Set (I → Bool)) [inst : LinearOrder I] [inst_1 : WellFoundedLT I] {o : Ordinal.{u}},
  IsClosed C → ∀ (ho : o < Ordinal.type fun x1 x2 => x1 < x2), IsClosed (Profinite.NobelingProof.C0 C ho)