(** Divides with bounded ex quantifier. *)

Definition bDivides (d n : nat) :=
  n = 0 \/ (exists q : nat, q < S n /\ n = d * q).

Theorem notdiv_rem : forall d n : nat, 0 < d -> ~ Divides d n -> exists q : nat, (exists r : nat, 0 < r /\ r < d /\ n = q * d + r).