Ltac zero_or_not a :=
  destruct (Z.eq_dec a 0);
  [subst; rewrite ?Zmod_0_l, ?Zdiv_0_l, ?Zmod_0_r, ?Zdiv_0_r;
   auto with zarith|].

Lemma Zdiv_mult_cancel_r : forall a b c:Z, c <> 0 -> (a*c)/(b*c) = a/b.