∀ {α : Type u_1} {β : Type u_2} (r : α → α → Prop) (s : β → β → Prop) [IsWellOrder α r] [IsWellOrder β s]
  (f : PrincipalSeg r (Sum.Lex r s)) (g : PrincipalSeg s (Sum.Lex r s)), Nonempty (InitialSeg r s ⊕ InitialSeg s r)