intros; cut (multZ (neg n) (negOZ q) = multZ (pos n) (posOZ q)); intros.
rewrite H0; intros; exact (tech_div1 n0 n q r H).
cut (negOZ q = oppZ (posOZ q)); intros. rewrite H0.
elim (tech_opp_pos_negZ n); intros; elim H1.
apply (mult_opp_opp Z IdZ addZ multZ OZ oppZ Z_ring (pos n) (posOZ q) I I).
elim q; reflexivity.
Qed.

(**************)
Lemma tech_div5 :
forall n0 n q : nat, S n0 = q * S n -> neg n0 = multZ (neg n) (posOZ q).