End in_Zp.
Local Add Ring myring2 : (Zp_is_ring Hak2).

(* Specifications: *)
Corollary alpha_square_nat : exists q, Zp_invertible Hak2 q /\ nat2Zp Hak2 (alpha_nat b m) = q ⊗ nat2Zp Hak2 l  ⊗ nat2Zp Hak2 (alpha_nat b k).
End equation.
Theorem alpha_nat_divides_2_pos m : alpha_nat b k * alpha_nat b k │ alpha_nat b m <-> k*alpha_nat b k │ m.
End divisibility_2.