∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : LinearOrder β] {f : α → β},
  Order.IsNormal f ↔ StrictMono f ∧ ∀ (o : α), Order.IsSuccLimit o → ∀ (a : β), (∀ b < o, f b ≤ a) → f o ≤ a