∀ {I : Type u} (C : Set (I → Bool)) [inst : LinearOrder I] [inst_1 : WellFoundedLT I] {o : Ordinal.{u}},
  Profinite.NobelingProof.contained C (Order.succ o) →
    ∀ (ho : o < Ordinal.type fun x1 x2 => x1 < x2),
      LinearIndependent ℤ (Profinite.NobelingProof.GoodProducts.eval C) ↔
        LinearIndependent ℤ (Profinite.NobelingProof.GoodProducts.SumEval C ho)