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 *)
End divisibility_1.

Theorem alpha_nat_divisibility_1 b k m : 2 <= b -> alpha_nat b k │ alpha_nat b m <-> k │ m.