Section congruence_1.
Variable (b1 b2 : nat) (Hb1 : 2 <= b1) (Hb2 : 2 <= b2)
(q : nat) (Hq : q <> 0) (Hb : nat2Zp Hq b1 = nat2Zp Hq b2).
Hint Resolve Zle_0_nat : core.
End congruence_1.

Corollary alpha_nat_congruence_1 b n : b-2 <> 0 -> rem (alpha_nat b n) (b-2) = rem n (b-2).