∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : Preorder β] [inst_2 : Add α] [inst_3 : One α]
  [inst_4 : SuccAddOrder α] [IsSuccArchimedean α] {f : α → β}, (∀ (a : α), ¬IsMax a → f (a + 1) < f a) → StrictAnti f