Section in_Zp.
Notation "〚 x 〛" := (Z2Zp Hak2 x).  (* congruence class modulo alpha_nat b k *)
Let Z2Zp_morph := Z2Zp_morphishm Hak2.
Open Scope Z_scope.
Let Zmult_monoid : monoid_theory Zmult 1.
End in_Zp.
Add Ring myring2 : (Zp_is_ring Hak2).
End equation.
End divisibility_2.
(* Second divisibility property *)

Theorem alpha_nat_divisibility_2 b k m :
2 <= b -> alpha_nat b k * alpha_nat b k │ alpha_nat b m <-> k*alpha_nat b k │ m.