elim divdn.
intros.
elim (even_or_odd d); auto with arith.
intros evend.
absurd (even n).
apply odd_even; auto with arith.
rewrite H.
apply mult_even; auto with arith.
Qed.

Lemma div_plus : forall n m d : nat, div d n -> div d m -> div d (n + m).
intros n m d divdn divdm.