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