Section divisibility_1.
Variable (b : nat) (Hb : 2 <= b) (k : nat) (Hk : k <> 0).
Let Hak : alpha_nat b k <> 0.

Lemma alpha_Z_mnlk_eq : 〚 alpha_Z b (1+m) 〛 = 〚 alpha_Z b (1+n) 〛⊗ expo l〚 alpha_Z b (2+k) 〛.
End in_Z.