intros a; try assumption.
elim angle_cons with (a := a) (u := u); intros v H0; try exact H0.
exists (cons v u).
apply transitive with (plus (cons u v) (cons v u)).
apply compatible; auto.
auto.
Qed.
Parameter pisurdeux : AV.

(* Specifications: *)
Axiom double_pisurdeux : R (double pisurdeux) pi.
Hint Resolve double_pisurdeux.
Lemma construction_orthogonal : forall u : V, exists v : V, orthogonal v u.
intros u; try assumption.
Axiom double_pisurdeux : R (double pisurdeux) pi.
Hint Resolve double_pisurdeux.
Lemma construction_orthogonal : forall u : V, exists v : V, orthogonal v u.
intros u; try assumption.