intros bound p base H; generalize (PdivBound_correct bound p base); intuition.
Qed.

(* Specifications: *)
Theorem PdivBound_correct2 :
forall bound p base,
1 < nat_of_P base ->
oZ (fst (fst (PdivBound bound p base))) < nat_of_P bound.
Theorem PdivBound_correct3 :
forall bound p base,
nat_of_P p < nat_of_P bound ->
PdivBound bound p base = (Some _ p, None _, 0).