∀ (x x_1 : WellOrder)
  (motive :
    ⟦x⟧.liftOn₂ ⟦x_1⟧
        (fun x x_2 =>
          match x with
          | { α := α, r := r, wo := wo } =>
            match x_2 with
            | { α := α_1, r := s, wo := wo } => Nonempty (InitialSeg r s))
        ⋯ →
      Prop)
  (x_2 :
    ⟦x⟧.liftOn₂ ⟦x_1⟧
      (fun x x_2 =>
        match x with
        | { α := α, r := r, wo := wo } =>
          match x_2 with
          | { α := α_1, r := s, wo := wo } => Nonempty (InitialSeg r s))
      ⋯),
  (∀ (g : InitialSeg x.r x_1.r), motive ⋯) → motive x_2