∀ {R : Type u_1} [inst : Semiring R] [inst_1 : LinearOrder R] {F : Type u_2} {α : Type u_3} [inst_2 : AddGroup α]
  [inst_3 : FunLike F α R] [AddGroupSeminormClass F α R] {f : F},
  IsNonarchimedean ⇑f → ∀ {x y : α}, f x ≠ f y → f (x + y) = max (f x) (f y)