Section in_nat.
Notation "〚 x 〛" := (nat2Zp Hak x).  (* congruence class modulo alpha_nat b k *)
End in_nat.
End equation.
(* This is property 3.23 *)

Theorem alpha_nat_divides_k_ge_1 m : alpha_nat b k │ alpha_nat b m <-> k │ m.