Check alpha_nat_congruence_1.
Section congruence_2.
(** This section might notbe needed anymore *)
Variable (b : nat) (Hb : b - 2 <> 0).
Notation "〚 x 〛" := (Z2Zp Hb x).  (* congruence class modulo (b-2) *)
Hint Resolve Zle_0_nat.
Open Scope Z_scope.

Theorem alpha_Z_b_2 n : 〚 alpha_Z b n 〛 = Zp_plus Hb 〚 Z.of_nat n 〛〚 -1 〛.
End congruence_2.