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|].

Theorem Zdiv_sgn: forall a b, 0 <= Z.sgn (a/b) * Z.sgn a * Z.sgn b.