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))).

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