∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop} [inst : IsWellOrder α r]
  [inst_1 : IsWellOrder β s]
  (motive : Ordinal.lift.{max u_2 u_3, u_1} (Ordinal.type r) < Ordinal.lift.{max u_1 u_3, u_2} (Ordinal.type s) → Prop)
  (x : Ordinal.lift.{max u_2 u_3, u_1} (Ordinal.type r) < Ordinal.lift.{max u_1 u_3, u_2} (Ordinal.type s)),
  (∀
      (f :
        PrincipalSeg (ULift.down ⁻¹'o { α := α, r := r, wo := inst }.r)
          (ULift.down ⁻¹'o { α := β, r := s, wo := inst_1 }.r)),
      motive ⋯) →
    motive x