intros bound p base H; (unfold PdivBound in |- *; apply Pdivless1; auto).
apply nat_of_P_gt_Gt_compare_complement_morphism; auto with arith.
Qed.

Theorem PdivBound_correct4 :
forall bound p base bound',
1 < nat_of_P base ->
nat_of_P bound = nat_of_P base * bound' ->
nat_of_P bound <= nat_of_P p ->
nat_of_P bound <=
nat_of_P base * oZ (fst (fst (PdivBound bound p base))).