elim non_vide_P; intros A H; clear H.
elim v_vec with (u := u) (A := A); intros B H; try exact H.
apply v_trans with (opp (opp (vec A B))).
apply opp_compatible; apply opp_compatible.
try exact H.
apply v_trans with (opp (vec B A)).
apply opp_compatible.
apply v_trans with (vec B A).
apply opp_vect.
apply v_refl.
apply v_trans with (vec A B).
apply opp_vect.
apply v_sym; auto.
Qed.
Hint Resolve opp_opp opp_compatible v_refl v_sym.

Lemma oppu_u : forall u : V, R (cons (opp u) u) pi.
intros u; try assumption.