∀ (q : Quot ⇑Ordinal.isEquivalent),
  Quotient.liftOn₂ q q
    (fun x x_1 =>
      match x with
      | { α := α, r := r, wo := wo } =>
        match x_1 with
        | { α := α_1, r := s, wo := wo } => Nonempty (InitialSeg r s))
    Ordinal.partialOrder._proof_1