∀ {I : Type u} [inst : LinearOrder I] [inst_1 : WellFoundedLT I] {l m : Profinite.NobelingProof.Products I}
  {o : Ordinal.{u}},
  m < l → (∀ i ∈ ↑l, Profinite.NobelingProof.ord I i < o) → ∀ i ∈ ↑m, Profinite.NobelingProof.ord I i < o