∀ {α : Type u_3} {β : Type u_4} [inst : AddGroup α] (a : α) [inst_1 : AddAction α β] (b : β)
  [Finite ↑(AddAction.orbit (↥(AddSubgroup.zmultiples a)) b)], NeZero (Function.minimalPeriod (fun x => a +ᵥ x) b)