∀ {α : Type u_1} [inst : Zero α] [inst_1 : LinearOrder α] {β : Type u_2} {F : Type u_3} [inst_2 : Zero β]
  [inst_3 : Preorder β] [inst_4 : DecidableLT β] [inst_5 : FunLike F α β] [ZeroHomClass F α β] {f : F},
  StrictMono ⇑f → ∀ (a : α), SignType.sign (f a) = SignType.sign a