∀ {α : Type u_1} {β : Type u_2} [inst : PartialOrder α] [inst_1 : PartialOrder β] [inst_2 : SuccOrder α] [NoMaxOrder α]
  [inst_4 : SuccOrder β] (f : InitialSeg (fun x1 x2 => x1 < x2) fun x1 x2 => x1 < x2) (a : α),
  f (Order.succ a) = Order.succ (f a)