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).

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).