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.

Lemma alpha_Z_ml_eq : 〚 alpha_Z b (S m) 〛
= expoZp (l-1) 〚-1〛
⊗ nat2Zp Hak2 l
⊗〚 alpha_Z b (S k) 〛
⊗ expoZp (l-1)〚 alpha_Z b k 〛.