∀ {I : Type u} [inst : LinearOrder I] [inst_1 : WellFoundedLT I] {o : Ordinal.{u}}
  (ho : o < Ordinal.type fun x1 x2 => x1 < x2) (i : I),
  Profinite.NobelingProof.ord I i = o ↔ Profinite.NobelingProof.term I ho = i