elim divdm; intros; elim divdn; intros.
rewrite H0; rewrite H.
elim mult_plus_distr_left.
unfold div in |- *.
exists (x0 + x); auto with arith.
Qed.
Hint Resolve div_plus.

(* Specifications: *)
Lemma div_minus : forall n m d : nat, div d n -> div d m -> div d (n - m).
intros n m d divdn divdm.