intros; unfold PdivBound in |- *; apply Pdivless_correct; auto.
Qed.

Theorem PdivBound_correct1 :
forall bound p base,
1 < nat_of_P base ->
nat_of_P p =
oZ (fst (fst (PdivBound bound p base))) *
exp (nat_of_P base) (snd (PdivBound bound p base)) +
oZ (snd (fst (PdivBound bound p base))).