(** Divides with bounded ex quantifier. *)

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

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