∀ {I : Type u} (C : Set (I → Bool)) [inst : LinearOrder I] [inst_1 : WellFoundedLT I] {o : Ordinal.{u}},
  Order.IsSuccLimit o →
    Profinite.NobelingProof.contained C o →
      Profinite.NobelingProof.GoodProducts.range C = ⋃ e, Profinite.NobelingProof.GoodProducts.smaller C ↑e