∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : Preorder β] [inst_2 : Sub α] [inst_3 : One α]
  [inst_4 : PredSubOrder α] [IsPredArchimedean α] {f : α → β}, (∀ (a : α), ¬IsMin a → f a < f (a - 1)) → StrictAnti f