∀ {α : Type u_3} {β : Type u_4} [inst : AddGroup α] (a : α) [inst_1 : AddAction α β] (b : β)
  [inst_2 : Fintype ↑(AddAction.orbit (↥(AddSubgroup.zmultiples a)) b)],
  Function.minimalPeriod (fun x => a +ᵥ x) b = Fintype.card ↑(AddAction.orbit (↥(AddSubgroup.zmultiples a)) b)