∀ {F : Type u_2} {α : Type u_3} {β : Type u_4} [inst : FunLike F α β] [inst_1 : AddGroup α] [inst_2 : AddCommMonoid β]
  [inst_3 : PartialOrder β] [AddGroupNormClass F α β] (f : F) {x : α}, f x = 0 ↔ x = 0