intros A B C H; try assumption.
unfold double in |- *.
unfold isocele in H.
apply
transitive
with
(plus (cons (vec A B) (vec A C))
(plus (cons (vec B C) (vec B A)) (cons (vec C A) (vec C B)))).
apply compatible.
apply reflexive.
apply compatible.
apply reflexive.
try exact H.
apply somme_triangle.
Qed.
Axiom
calcul3 :
forall a b c d e f : AV,
R (plus (plus a (plus b c)) (plus d (plus e f)))
(plus (plus a d) (plus (plus b e) (plus c f))).

(* Specifications: *)
Lemma somme_permute :
forall u v w : V,
R (plus (cons v u) (plus (cons (opp u) w) (cons (opp w) (opp v)))) pi.